The Hardball Times -- John Beamer http://www.hardballtimes.com/main Baseball. Insight. Daily. en studes@hardballtimes.com Copyright 2012 2012-02-10T11:32:15+00:00 Five questions: Atlanta Braves http://www.hardballtimes.com/main/article/five-questions-atlanta-braves6/ http://www.hardballtimes.com/main/article/five-questions-atlanta-braves6/#When:09:02:15
How things change. The Phillies have won the NL East four times on the spin and, with the acquisition of Cliff Lee, appear ready to cement their position as the new perennial champions. Can the Braves possibly challenge them? Read on and find out.


Will Bobby's departure have an impact?


Of course it will.

The man led Braves for over 20 years, so when an individual of his standing steps down, the team will be affected in some manner. The question is, how much?

First, let's examine the evidence. The accepted wisdom is that managers are generally responsible for two to three wins/losses per year, max. The general sabermetric view is that the majority of managers rely too much on tradition (rather than game theory or understanding optimal probabilities) when managing (read: tinkering with lineup, platoon plays, or reliever use) and, as a result, actually cost their teams games.

There is little doubt that Bobby Cox fits into this latter category. He used to make some ridiculous player decisions—wasn't it obvious Brooks Conrad should have been pulled before making his third error in the last fall's NLDS that cost the Braves Game Three?

However, playing the percentages effectively is only one attribute of a successful manager. The other is leadership and man management. And that was Cox's long suit. At every juncture, through every low point, the players respected him deeply. That engendered loyalty and, thus, he was often able to get more out of certain players that others would have.

With Cox moving upstairs, former Braves third base coach Fredi Gonzalez steps into the hot seat. Despite being fired by the Marlins last year, Gonzalez had a good record with the Fish. He steered them to winning seasons in the 2008 and 2009 campaigns despite having to work with the lowest budget in baseball.

That bodes well in a sense—the Braves aren't the big spenders they used to be, and Gonzalez isn't a doofus. However, the reasons for his firing still remain a mystery, with some suggestions that he lost the clubhouse following Hanley Ramirez's famous lollygagging incident last year.

Winning the players over is key to his success. Gonzalez starts in a good position, as he knows the senior players and has an affinity to the Braves. Cox won't be more of a phone call away either, so the new guy will be okay.


Will Jason Heyward suffer from a sophomore slump?


The famed sophomore slump is very real and is more commonly known as regression to the mean. The theory is straightforward: player A (a rookie) plays way above average in his first season so is more likely to get playing time the next. However, as he was lucky in the first season, he reverts to type and appears to have a sophomore slump.

Heyward's line is 2010 was .277/.393/.456, which was a little way off what many projections thought. In other words, he didn't overperform (if you believe the forecasts for a minute). His 2011 projections also show a stark improvement. Marcel the monkey has him at .286/.391/.476, mostly because of age adjustment—the kid is only 21.

Another factor that affected his 2010 season was injury. By the end of May, Heyward was averaging over .300 but hurt his thumb and suffered at the plate for most of June before taking a little time off to recuperate. He came back strongly, but his hand never fully healed, and that had an effect in the last third of the season. He should be fully healed know and, after a year in the bigs, better attuned to the demands of a long season.

Let me stick my neck out for a minute and hope it doesn't get chopped off: Heyward underperformed in 2010; that has hurt his 2011 projections, and regression to the mean works both ways, you know...when you underperform one year, the expectation is you bounce back the next. If Heyward were a traded security, I'd be taking a long position.


Dan Uggla...is he worth $62 million?


In the great scheme of things, trading for Uggla and re-upping his contract is a tidy piece of business by the Braves. Sure, stretching to a fifth year may end up costly, but he wouldn't likely have signed without it. Let's take a closer look.

Over the last three years, Uggla has averaged an fWAR of around 4.0 (indeed fangraphs pegs his 2011 fWAR at 3.8, as projected by the fans. Assuming that the going rate for a free agent is $4 million a year, then 4.0 fWAR is worth $16 million a year (versus an average annual contract value of $12M).

The problem is that Uggla is no spring chicken. In fact, he's a 31 years old, which means by all aging models he's expected to get worse over time. Not only that, but Uggla isn't the world's finest gloveman, and by the end of his contract he could well be shunted to a different position.

So if we factor in aging and assume Uggla will peak at 3.8 WAR in 2011 and lose, say, 0.5 WAR in each subsequent year, then over five years he projects to contribute 14 WAR, which (by no coincidence) when multiplied by $4.5 million per win gives you $63 million over the duration of his five-year contract. So say what you like about the deal, but unless you're predicting a serious injury, it doesn't look as though the Braves overpaid.

Perhaps the more important factor is that Uggla is likely to mash 30 long balls a year. His home run numbers are amazingly consistent, and last year the one thing the Braves lacked was consistency in the power department. Uggla will be a good foil to Heyward and Chipper, if Jones returns successfully. So, yes, he's worth $62 million. Just!


Can Derek Lowe maintain his September 2010 form?


Last year the big story in Atlanta, other than Heyward's impending debut, was whether the Braves would be unable to unload Lowe instead of Javier Vazquez. In 2009, after Lowe signed a cushy 4-year, $60 million deal, he posted a woeful 4.67 ERA for a WAR of precisely zero. Contrast that to Vazquez, who logged an ERA of 2.87, and you can see why the Braves were chomping at the bit to let Lowe go.

Despite trying, there we no takers for Lowe, while Vazquez was snapped up by the Yankees. We all know what happened next. Vazquez had his worst season in 12 years, going 10-10 with Yankees with a 5.32 ERA. He was hurt and ineffective.

Lowe stayed with the Braves and pitched more or less as expected. Going into September his ERA was 4.53, which was pretty much bang on league average. He was also on course to throw 190 innings, which has some value (although not $15 million a year worth of value).

However, then something strange happened. In September he suddenly started to appear dominant. He won all five stats, conceding only four earned runs and dropping his season ERA all the way down to 4.00. His form continued in the postseason where, despite losing both games, he pitched well. So, has Lowe made an important adjustment to his mechanics or is this a classic case of small sample size at work?

Let's take a look at what we can see using Joe Lefkovitz's awesome PITCHf/x tool. Below is a plot of pitch movement by type (as classified by MLBAM) for the two spells in question:

image

Lowe claims to have rediscovered his slider in September. Can we see it in the data? In both charts sliders are red dots. In September he definitely threw more sliders (the left panel has six times the number of pitches than the right, and going through the numbers he was throwing about twice the number of sliders in September). Also, the sliders seem more tightly clustered, which could imply that he was locating the pitch better.

Whether fluke or mechanical adjustment, the question is, can he maintain the pitch's effectiveness? It depends on exactly what adjustment Lowe has made. If it is a mechanical adjustment that results in a more effective pitch (which is hard to tell from the charts above), he is likely to maintain a small advantage.

However, game theory suggests that if he keeps throwing the pitch, hitters will likely make adjustments. Pretty much all the projection systems expect an ERA in the low fours. And that is likely where he'll end up—unfortunately, his September 2010 form won't hold.


Do the Tomahawks have enough to topple the Phillies?


Yikes. The Phillies added Cliff Lee in the offseason and probably have the best rotation in baseball since the Braves in the late 90s. The good news for the rest of the NL East is that the uber rotation will probably only be together for a maximum of two years, as both Cole Hamels' and Roy Oswalt's contracts come up at the end of 2012.

However, the situation isn't terrible for the Braves. Lee will contribute only slightly more than the Phillies will lose from the departure of Jayson Werth. Although the Phillies won the NL East last year, until the Braves faded in September it was a reasonably close race. Expect the same this year.

The Braves have a good, young rotation. Tommy Hanson and Jair Jurrjens should bounce back from down years and, as discussed above, Lowe will hurl 180+ innings at fourth-starter level, which is all the Braves need from him. And with Kris Medlen likely to miss most of the 2011 recovering from Tommy John surgery, don't be too surprised to see Julio Teheran called up. Teheran is the top prospect in the Braves system and arguably the best pitching prospect in the game.

The loss of Billy Wagner in the bullpen is a blow but Craig Kimbrel has the stuff to close and, provided he has the mental game, will do well. Uggla adds runs to the lineup, and Heyward will likely improve on his 2010 numbers.

I don't think the Phillies will win 97 games again next season. The Braves had the sniff of a 90-92 win team given how they played last year. My guess is that won't be quite enough to take the divison—the Phillies will likely do that—but it should be enough to secure the wild card and another heartbreaking loss in the NLDS.

Click here to learn about THT's download subscriptions.]]> John Beamer 2011-03-17T09:02:15+00:00 Five questions: Atlanta Braves http://www.hardballtimes.com/main/article/five-questions-atlanta-braves5/ http://www.hardballtimes.com/main/article/five-questions-atlanta-braves5/#When:10:30:15 Jason Heyward mash 75 homers? Can Billy Wagner strike out every hitter he faces? These questions and more are answered below.

To mix things up a bit I've teamed up with Alex Remington, who writes about the Braves at Chop-n-Change and also blogs at Fangraphs and at Yahoo! Sports Big League Stew. Hang on—here we go.

1. What production can we expect from Jason Heyward in 2010?


Alex: As I wrote elsewhere, I think that Heyward's superior control of the strike zone will lead him to exceed the expectations of most of the offseason projection systems, nearly all of which expect him to hit fewer than 20 homers with an OPS right around .800. I'm expecting a tick better on all those counts. Most importantly, though, he stabilizes the Braves' right field situation, where he'll be far, far, far better than the .262/.305/.409 that Jeff Francoeur produced from 2007 to 2009, and isn't likely to be a downgrade defensively.

Of course, he isn't guaranteed for immediate success. Even Matt Wieters, who once stole second, third and the shortstop's hat on the same pitch, had an adjustment period last year before catching fire in the last month of the season. While Heyward's floor is probably higher than Francoeur's baseline, it may not necessarily be that much higher. So he'll be a welcome improvement for the Braves, and he'll likely post Nick Johnson-like P/PA numbers, but he won't be an offensive catalyst just yet.

John: There's no doubt Heyward is good—you've just got to look at his spring training stats. His line is a massive .347/.467/.490 and some of his home runs were true monsters. The most impressive thing is his ability to get on base. Make no mistake: This kid has a 20:20 batting eye, and unlike Francoeur, whose place Heyward will inherit as face of the franchise, he'll walk enough to get to Everest and back (aside: for goodness sake, Jason, don't do any Delta ads). That should mean at the very least he'll survive in the bigs.

He also tops most prospect lists, which is encouraging but by no means guarantees success. Remember who the last Brave was to be the No. 1 rated prospect in all of baseball? Yes ... Andy Marte. His career line of .216/.272/.352/ is anything but magical and is a stark reminder of how quickly baseball talent turns from boom to bust. However, let's not kid ourselves. Heyward's minor league career has already been on a different planet than Marte's.

Given the weakness that the Braves have in the outfield, it wouldn't be too surprising to see Heyward top the pile come the end of the year. One thing is certain: It is unlikely the Braves will challenge for the division without a productive Heyward.

2. Is Wagner going to dominate the ninth?


Alex: Mariano Rivera's contemporaneous career has obscured just how good he's been, but Wagner has been one of the most consistent and excellent relievers of the modern closer era—as Mac Thomason has written,
"There aren’t many relievers, ever, who have been better than Wagner."

Wagner has had exactly one bad year in the major leagues: 2000, when he posted a 6.18 ERA in 27.2 innings before going on the DL and eventually undergoing elbow surgery. That is the only time in his major league career that he had an ERA over 3.00 or a K/9 under 10.

It was also, prior to 2009, the only time he'd ever pitched fewer than 47 innings in a season. Then, of course, he blew out his elbow again, but came off Tommy John surgery just in time to throw upper-90s heat in September to secure a one-year payday. When he's been healthy, he's never been anything short of excellent. If he's healthy, there's little reason to doubt that he can be excellent again, especially considering the year that the 41-year-old Trevor Hoffman just had in Milwaukee.

If he's healthy. After all, he's a 38-year-old lefty coming off his second elbow surgery. He's a physical freak—an undersized righty who can somehow throw 100 mph with his left hand—but even physical freaks can't stretch their tendons forever. Tommy John surgery is viewed as a relatively safe procedure, but it's not foolproof. Wagner had a nice stretch run in 2009 and has pitched well in the spring of 2010, but his arm will be monitored closely. If he goes down, the Braves will rely on their setup duo, fellow Tommy John returnee Peter Moylan and the 40-year-old Takashi Saito. If the Braves can get 150 innings out of that trio, the late innings will be well in hand. If not, they could be in trouble.

John: Certainty. That is what a great closer gives you. When did the Braves last have certainty in the ninth? In 2004, when John Smoltz was at the back end of the rotation. Since then the Braves have wheeled out sub-standard closers: Dan Kolb, Kyle Farnsworth, Mike Gonzalez, Rafael Soriano ... there's no certainty there. At least Soriano and Gonzalez can pitch ... day to day you can't be sure if they'll be healthy.

Certainty is what the Braves hope to get from Wagner. Sure he has been far from healthy over the last couple of years. But last year, after Tommy John surgery, he did well at Fenway Park. His heat was in the mid- to high-90s and he looked like his old self. I'm optimistic that Wagner will work out well for the Braves.

Let's go through the facts. First, Wagner is a seriously good pitcher. His career ERA is 2.39; his K/BB is 3.9 and his K/9 is 12. Second, despite being on the DL he is STILL a seriously good hurler. As Alex mentioned, the only time that Wagner has had an ERA over 3.00 was in 2000, and that was when we was hurt. You want me to prognosticate? He'll keep off the DL, put in a sub-3 ERA and get at least 30 saves. You heard it here!

3. How good is the rotation?


Alex: The Braves' 2009 Opening Day starter, Derek Lowe, was so unimpressive last year after signing a four-year, $60 million contract that the Braves spent most of the offseason fruitlessly trying to offload him. When it became clear that no one wanted him any more than the Braves did, they turned around and traded their best pitcher of 2009, Javier Vazquez, for Melky Cabrera and a flame-throwing teenager.

After all that, Lowe's still a Brave, and he's not bad for the back of the rotation, where he and Kenshin Kawakami are still likely to deliver an ERA somewhere south of 4.50. Anything better than that will be gravy.

That's because, as usual, the Braves' top three starters are terrific. Tommy Hanson, Jair Jurrjens and Tim Hudson are all No. 1/No. 2 starters, and all look set to excel in 2010. Like Wagner, Hudson came back from Tommy John surgery last year, and like Wagner, he pitched quite well in the final months of the year. Jurrjens is likely to come back to earth a bit after 2010, when he had an ERA about a run less than the year before despite virtually identical components. But his 2008 was plenty good. And Hanson was simply dominant during the final months of the season, looking every bit like the ace he was predicted to be. He and Jurrjens might be the best under-24 one-two punch in baseball.

John: I like the Braves' rotation. Sure I'd rather have seen Lowe disappear rather than Vasquez, but that was never going to happen when Lowe still has three years left on his $60 million contract. Anyway, our old friend, regression to the mean, should help Braves fans get past their initial disappointment.

Also, for the first time in many years, the Braves have a stable rotation that should hold together for a few years. Kawakami is only one year into his contract, Hudson re-upped in the offseason, and Jurrjens and Hanson, the young whippersnappers, are still pre-arb. This crew could hang together for three more years (although if Lowe has a good year he'll be offloaded). The last time the Braves had a stable rotation, with a solid top three ... yup, Smoltz, Glavine, Maddux.

Now I'm not suggesting that the current trio is a patch on what may have been the best 1-2-3 in baseball. Nowhere near. But a look at the projections shows Jurrjens on a 3.80 ERA, Hudson with a 3.90 ERA and Hanson at a 3.50 ERA. On paper it sounds great—but then again most rotations do. One of these guys is bound to hit the DL at some stage and that is when the Braves will struggle. Who's the reserve starter at Turner Field? Jo-Jo Reyes? .... Please, no.

4. Can Chipper Jones and Troy Glaus stay on the field?


Alex: The pitching probably won't be the problem for the Braves. It's the offense. No regular slugged over .500 or hit 25 homers for the Braves in 2009, and there's a very good chance no one will in 2010 either, considering that Heyward won't turn 21 until August. The team is severely underpowered, and the No. 3 and No. 4 hitters are aging sluggers with injury problems.

Glaus and Jones were two of the best third basemen of the last decade, but they're both past their prime, and Glaus is trying to learn how to wear a first baseman's mitt, too. Glaus has played 149 games in three of the last five years, a total that Jones hasn't reached since 2003, but the fact is: Over the past seven years, Glaus is averaging 104 games played, and Chipper's averaging 131. (Over that same period, Jones is slugging .535, and Glaus is slugging .498.) When they've played, they've hit. They've just been off the field a lot.

If the Braves can get 1,000 combined at-bats out of their corner infielders, they'll have a decent middle of the order. The rest of the lineup is filled with pesky hitters with double-digit home run power: center fielder Nate McLouth, shortstop Yunel Escobar, second baseman Martin Prado, catcher Brian McCann (the Braves' best hitter in 2009), right fielder Heyward, and the left field platoon of Matt Diaz and Cabrera. None of them are automatic outs, but none of them is all that frightening, either. Without production from Jones and Glaus, the Braves will be playing a lot of 4-3 ballgames.

John: Who the hell is asking these questions ... another health-related conundrum. Given Alex has done such a good job with his answer and I'm bored of talking about the DL I'll answer a different question, "Can Chipper Jones regain batting title form?".

Chipper's demise has been predicted for years. Remember in 2004 when he went .248/.362/.485? Pundits were ready to pen an obituary to what even was at that point a stellar career. Since then Jones has accelerated: 2005 was .296/.412/.556 and then his average didn't drop below .300 until 2009, when he hit a disappointing .264/.388/.430. Can he bounce back once again?

Unfortunately, the odds are more against him than last time. He's 38 years old and at this point in their careers many hitters see a sharp drop-off in performance. And it wasn't like he was especially unhealthy in 2009. Sure he had some knocks and niggles, but he started 143 games—the most since 2003.

However, his batting eye is as sharp as a fox's, as evidenced by his ability to get on base at a .388 clip. That has a lot of value even if his arms can't deliver the power they used to. My admiration for Jones as a player has grown this season as he has confounded the baseball community with his approach at the plate.

The many projections figure that Jones should hit for a .290/.400/.470 clip. I don't know about you, but I'll take that line right now. My head tells me he'll be closer to where he was last season, but that's still better than the rest of the Braves infield.

5. The biggie... can Bobby win again?


Alex: The 2010 Braves look a lot like the teams that Cox took to the playoffs like clockwork: a deep, dominating starting rotation and a pesky but underpowered offense. They certainly look like one of the best four teams in the league, but while Cox certainly can escort this team to October, these Braves don't immediately look dominant enough to win it all. The Phillies return a terrific team with Roy Halladay at the fore, and the Marlins, Rockies, Cardinals, Dodgers and Giants all finished with better records than the Braves in 2009. Some of those wins may have been fluky—I'm looking at you, Ryan Franklin—but the Braves will have a lot of teams to leapfrog.

The Braves don't necessarily have more question marks than any other team—after all, just about every team has to caveat its chances against the likelihood of injury. The Braves had the third-best run differential in the NL last year, and they've had the best run differential in the Grapefruit League this spring. They're virtually guaranteed to score a lot more runs than they give up. But they won't bludgeon anyone to death—they'll win with pitching and singles. That may well be enough in the regular season, but it likely won't once October rolls around.

John: I could write an essay on this, but I'll keep it short. The Braves were unlucky last year. They score a lot more runs than they gave up and should have ended up with a better record. The rotation should be an improvement despite the loss of Vasquez. Lowe will improve a bit, Hudson will replace Vasquez, and Hanson and Jurrjens are a year wiser. Although the bullpen is a weak spot, a healthy Wagner will covert a lot of close games if he is given the chance. And Heyward has the discipline and power to be a rock star in the outfield.

If that happens, that I fancy their chances. If one of those factors goes off, then no way. The problem is that the NL East is probably the strongest division on the Senior Circuit. The Phillies have reached the last two World Series and, if anything, have upgraded with Doc Halladay over the offseason. The Mets have the talent but underperform and the Marlins are starting to up their payroll and still have a very talented bunch of ballplayers.

It's Bobby Cox's last season in charge. You know he wants it—that is why Heyward is starting. Here is hoping that the Tomahawks can give one of the greatest managers in the game the send-off he deserves. Go Braves!

Click here to learn about THT's download subscriptions.]]> John Beamer 2010-04-02T10:30:15+00:00 One sport that has the greatest-ever debate sewn up ... http://www.hardballtimes.com/main/blog_article/one-sport-that-has-the-greatest-ever-debate-sewn-up-/ http://www.hardballtimes.com/main/blog_article/one-sport-that-has-the-greatest-ever-debate-sewn-up-/#When:01:30:15
Click here to learn about THT's download subscriptions.]]> John Beamer 2009-08-17T01:30:15+00:00 The Rangers win the Teixeira trade http://www.hardballtimes.com/main/blog_article/the-rangers-win-the-teixeira-trade/ http://www.hardballtimes.com/main/blog_article/the-rangers-win-the-teixeira-trade/#When:20:32:15
Click here to learn about THT's download subscriptions.]]> John Beamer 2009-08-16T20:32:15+00:00 Will the Red Sox win the AL East? http://www.hardballtimes.com/main/blog_article/will-the-red-sox-win-the-al-east/ http://www.hardballtimes.com/main/blog_article/will-the-red-sox-win-the-al-east/#When:03:06:15
Click here to learn about THT's download subscriptions.]]> John Beamer 2009-08-15T03:06:15+00:00 A-Rod in the clutch http://www.hardballtimes.com/main/article/a-rod-in-the-clutch/ http://www.hardballtimes.com/main/article/a-rod-in-the-clutch/#When:05:01:15 Fangraphs. Proprietor David Appelman has done a tremendous job over the last three years transforming the site from a cutesy WPA-based portal to a full-fledged statistical powershop.

Now he has live WPA for every game, play-by-play data for each player, MGL's UZR, plate discipline stats, minor league stats, projections (courtesy of CHONE, Bill James, Oliver, ZiPS and Marcel) and a bushel of bloggers led by USSMariner's inestimable Dave Cameron.

Enough bluster and brown-nosing—I want to use Fangraphs to analyze how Alex Rodriguez performed in the clutch last year. There is continuous noise that the Yankees slugger can hit for toffee when it counts. Fangraphs will tell us if that is true.

Measuring clutch


There are plenty of ways to measure clutch. The most oft-used definition is close and late—for instance, beyond the seventh inning in a one-run ballgame with a runner in scoring position. While that feels intuitively correct it is ultimately a subjective measure. In this day and age we deserve a more quantitative measure of clutch.

Fortunately it exists. It is called Leverage Index, or LI for short.

What is LI and how does it work?

In simple terms, it is the maximum change in win expectancy from a given at-bat divided by the average change in win expectancy over all situations (0.364). Take the highest LI possible which is 10.9—bottom of ninth, down by one, two outs, bases loaded. Before the event, win expectancy is 22 percent, and the maximum swing in LI is when the batter mashes one over the fences for a walk-off homer—a swing of 0.88. Divide that by the average swing in win expectancy (0.36) and we get 10.9.

For the inquisitive among you, Tom Tango wrote a great three-part series on LI for THT which you can find here, here and here.

My view is that Leverage Index IS the most accurate measure of clutchiness. It is also continuous. In other words, an LI of 1.8 is more clutch than an LI of 1.6 and so we can measure the difference in clutchiness between these two situations. Some people disagree with this view and set a boundary on high clutch situations by defining it as LI > 3. This accounts for 5 percent of PA, which feels about right—I can live with that but it's still subjective. I've got an article in the pipe on using LI as a continuous measure of clutch.

A-Rod play-by-play


Below is a long list of every batting play for A-Rod in 2008 (from Fangraphs). Along with the date and pitcher faced we have Leverage Index, Run Expectancy, Win Expectancy, Win Probability Average and RE24 (run expectancy above average). I've omitted the play-by-play description of each event but you can work out whether A-Rod made an out by the direction of WPA or RE24 in the table. The table is ordered by descending LI. (Press page down about six times to get to the end.)
Date       Pitcher       LI         RE         WE         WPA        RE24
Aug-15     J  Soria      6.76       0.46       17.80%     0.102      0.34
Aug-30     B  Ryan       6.01       1.55       53.20%     -0.383     -1.21
03-Sep     S  Shields    4.46       1.62       77.50%     0.141      1
Aug-16     J  Peralta    4.28       0.95       71.40%     -0.072     -0.43
12-Sep     J  Papelbon   4.03       0.47       24.70%     -0.107     -0.47
04-Sep     M  Delcarmen  3.88       0.8        17.70%     -0.102     -0.8
Aug-15     L  Nunez      3.81       1.23       51.10%     0.032      0.02
May-27     G  Sherrill   3.71       0.36       45.50%     0.013      0.13
09-Sep     J  Soria      3.56       0.54       21.30%     0.135      0.39
Jun-30     C  Wilson     3.56       0.54       21.30%     -0.093     -0.25
01-Sep     F  Rodriguez  3.56       0.54       21.30%     -0.093     -0.25
02-Sep     J  Accardo    3.55       1.55       19.20%     -0.083     -0.6
Apr-28     A  Laffey     3.47       2.39       47.20%     0.13       1
07-Sep     Y  Yabuta     3.46       0.46       59.10%     -0.091     -0.46
Jul-29     G  Sherrill   3.46       2.04       22.60%     -0.086     -0.59
06-Sep     R  Mahay      3.35       0.56       32.30%     -0.082     -0.31
Aug-22     J  Walker     3.32       1          35.90%     0.23       1.1
12-Sep     J  Blanton    3.32       1.4        48.00%     0.126      0.85
12-Sep     J  Litsch     3.32       0.73       41.70%     0.193      1.68
May-31     D  Reyes      3.27       0.69       55.80%     -0.163     -0.58
Apr-26     J  Lewis      3.19       0.95       55.90%     -0.074     -0.5
Sep-20     J  Miller     3.18       1.55       82.10%     0.006      -0.33
Jul-19     J  Blevins    3.16       0.71       70.40%     0.01       0.24
Jul-19     L  DiNardo    3.16       0.71       70.40%     0.01       0.24
May-22     J  Johnson    3.16       0.93       71.80%     -0.078     -0.38
Aug-26     J  Masterson  3.08       1.62       18.00%     -0.142     -1.62
01-Sep     N  Blackburn  3.06       1.59       40.10%     -0.084     -0.81
May-31     D  Reyes      3.05       0.53       50.00%     0.058      0.16
10-Sep     P  Maholm     2.92       0.45       48.70%     -0.076     -0.45
02-Sep     J  Nathan     2.88       0.51       16.50%     0.115      0.39
02-Sep     D  Reyes      2.83       1.51       64.50%     0.064      0.35
May-27     M  Albers     2.83       2.45       82.70%     -0.36      -1.96
Aug-28     J  Lester     2.83       1.23       36.70%     -0.099     -0.7
Aug-13     J  Crain      2.79       0.51       13.80%     -0.078     -0.51
Aug-19     B  Ryan       2.78       0.44       14.90%     -0.068     -0.21
May-25     J  Putz       2.73       1.17       28.30%     0.092      0.38
Jun-29     B  Wagner     2.66       1.12       16.20%     -0.067     -0.44
05-Sep     S  Downs      2.64       0.71       41.20%     -0.066     -0.33
Aug-16     Z  Greinke    2.63       2.39       64.40%     -0.084     -0.77
10-Sep     J  Arredondo  2.58       0.69       54.30%     -0.126     -0.58
Jun-28     J  Santana    2.47       1.49       49.40%     0.095      0.85
02-Sep     W  Madrigal   2.47       1.17       50.20%     0.055      0.38
05-Sep     E  Guardado   2.4        0.68       10.80%     -0.108     -0.68
Aug-26     T  Wakefield  2.39       0.95       24.80%     -0.056     -0.5
Aug-16     R  Ramirez    2.38       0.56       61.10%     0.062      0.4
08-Sep     J  Garland    2.38       0.9        39.90%     -0.122     -0.79
12-Sep     J  Nathan     2.34       0.23       42.60%     -0.066     -0.23
09-Sep     L  Hochevar   2.32       1.17       32.90%     0.262      1.37
Aug-20     D  Purcey     2.31       2.26       67.10%     -0.068     -0.76
May-31     B  Bonser     2.31       0.61       40.00%     0.187      1.62
08-Sep     J  Weaver     2.31       0.61       40.00%     0.017      0.17
06-Sep     H  Okajima    2.3        0.54       64.50%     -0.06      -0.25
Sep-16     G  Floyd      2.29       0.46       28.80%     0.045      0.34
03-Sep     D  McGowan    2.28       2.04       64.00%     -0.087     -0.59
04-Sep     F  Francisco  2.18       0.69       29.50%     -0.061     -0.31
Jun-19     J  Banks      2.14       0.97       65.40%     0.084      0.59
Jun-21     D  Thompson   2.1        0.95       59.70%     -0.049     -0.5
05-Sep     J  Putz       2.09       0.68       9.40%      -0.057     -0.32
Sep-13     J  Howell     2.09       0.71       62.50%     -0.06      -0.37
03-Sep     J  Lackey     2.07       1.89       22.20%     0.064      0.5
Jul-27     J  Lester     2.03       2.41       18.90%     -0.053     -0.77
02-Sep     L  Mendoza    2.03       0.52       33.40%     0.03       0.28
Jul-30     D  Sarfate    2          0.95       49.10%     0.192      2.02
03-Sep     J  Arredondo  2          0.56       59.20%     0.055      0.4
10-Sep     D  Eveland    1.97       1.12       57.00%     0.025      0.17
Jul-20     J  Duchscherer1.97       1.23       62.80%     0.023      0.11
Jul-29     D  Cabrera    1.97       0.46       43.30%     0.036      0.34
Sep-14     E  Jackson    1.92       2.39       70.30%     0.155      2.15
May-30     G  Perkins    1.92       0.9        54.70%     0.157      1.24
10-Sep     D  Moseley    1.91       0.92       53.70%     -0.044     -0.48
Jun-25     Z  Duke       1.91       0.93       53.70%     0.058      0.66
03-Sep     D  McGowan    1.91       0.93       48.10%     -0.045     -0.38
May-22     B  Burres     1.91       0.93       48.10%     -0.045     -0.38
Apr-15     E  Jackson    1.89       0.88       42.10%     0.135      1.1
02-Sep     L  Hernandez  1.89       0.95       56.50%     -0.08      -0.58
Aug-17     B  Bannister  1.89       0.95       31.20%     0.215      2.33
Apr-14     G  Glover     1.87       0.5        74.90%     -0.052     -0.5
Aug-16     R  Tejeda     1.86       0.29       58.50%     -0.047     -0.17
04-Sep     J  Beckett    1.86       0.95       58.50%     0.177      2.02
09-Sep     E  Jackson    1.86       0.95       58.50%     -0.037     -0.43
01-Sep     E  Santana    1.86       0.95       58.50%     -0.043     -0.5
Aug-28     J  Lester     1.86       0.95       58.50%     -0.043     -0.5
Sep-16     G  Floyd      1.86       0.95       58.50%     -0.043     -0.5
Jul-25     J  Beckett    1.86       0.97       53.60%     -0.044     -0.5
Apr-13     D  Matsuzaka  1.86       0.97       53.60%     -0.086     -0.97
10-Sep     J  Saunders   1.86       0.37       48.40%     -0.051     -0.37
Apr-15     J  Howell     1.85       0.77       83.20%     -0.047     -0.77
01-Sep     E  Santana    1.85       0.34       55.30%     0.012      0.12
01-Sep     J  Verlander  1.83       2.46       64.80%     0.111      1.5
Sep-19     R  Liz        1.83       0.46       54.80%     -0.048     -0.46
Jul-19     B  Ziegler    1.82       0.25       55.20%     -0.052     -0.25
12-Sep     M  Guerrier   1.82       0.27       44.00%     0.378      1
May-31     D  Reyes      1.82       0.27       44.00%     0.06       0.26
03-Sep     J  Lester     1.8        1.23       42.30%     -0.066     -0.7
12-Sep     B  Bonser     1.79       0.44       63.10%     -0.046     -0.44
03-Sep     R  Halladay   1.78       0.56       42.50%     -0.044     -0.31
08-Sep     J  Garland    1.78       1.2        56.40%     0.066      0.73
Apr-18     D  Cabrera    1.75       0.6        50.10%     0.023      0.15
May-26     G  Olson      1.75       0.6        50.10%     0.023      0.15
11-Sep     J  Duchscherer1.74       0.46       62.60%     -0.046     -0.46
02-Sep     M  Garza      1.74       0.94       43.10%     0.028      0.24
05-Sep     J  Masterson  1.73       0.95       70.00%     0.051      0.67
Apr-28     A  Laffey     1.72       1.23       56.20%     -0.063     -0.7
Apr-15     E  Jackson    1.72       0.94       55.80%     0.045      0.32
06-Sep     K  Davies     1.72       1.23       61.20%     -0.112     -1.23
May-28     J  Johnson    1.7        0.4        71.10%     -0.049     -0.4
Jun-27     M  Pelfrey    1.7        1.23       74.50%     -0.054     -0.6
Jun-22     J  Cueto      1.69       0.93       60.30%     -0.04      -0.38
01-Sep     E  Santana    1.69       0.93       60.30%     -0.04      -0.38
01-Sep     R  Halladay   1.69       0.93       60.30%     -0.09      -0.82
06-Sep     R  Corcoran   1.66       0.94       75.70%     0.014      0.24
05-Sep     B  Ryan       1.64       0.25       4.90%      0.002      0.09
08-Sep     B  Bannister  1.64       0.87       54.00%     -0.038     -0.36
Aug-13     K  Slowey     1.64       0.53       22.40%     -0.04      -0.3
11-Sep     G  Perkins    1.64       0.53       22.40%     -0.07      -0.53
07-Sep     J  Hammel     1.64       0.52       66.60%     -0.047     -0.52
07-Sep     R  Feierabend 1.64       0.32       33.50%     0.015      0.11
05-Sep     D  McGowan    1.63       1.45       20.50%     -0.025     -0.07
06-Sep     R  Rowland-Smi1.62       0.43       60.90%     0.028      0.33
08-Sep     R  Mahay      1.61       1.23       84.30%     0.085      0.89
Jun-20     E  Volquez    1.6        0.93       48.70%     0.025      0.24
Apr-27     C  Sabathia   1.59       0.97       71.00%     -0.069     -0.59
May-31     B  Bonser     1.59       0.33       47.80%     -0.045     -0.33
Aug-16     Z  Greinke    1.58       0.54       22.90%     0.099      0.63
06-Sep     T  Wakefield  1.58       0.54       22.90%     0.068      0.39
Apr-25     R  Betancourt 1.57       0.54       8.00%      -0.041     -0.25
01-Sep     J  Rupe       1.56       0.54       40.40%     -0.041     -0.25
May-27     D  Sarfate    1.56       0.59       50.00%     -0.042     -0.27
Jul-25     J  Beckett    1.55       0.95       68.90%     0.029      0.24
02-Sep     L  Hernandez  1.54       0.51       50.00%     0.108      0.63
Aug-22     R  Liz        1.54       1.62       66.60%     -0.091     -1.22
01-Sep     R  Halladay   1.52       0.54       59.10%     0.056      0.39
Sep-20     B  Burres     1.52       0.54       59.10%     0.056      0.39
01-Sep     B  Bass       1.51       0.53       25.10%     -0.036     -0.3
03-Sep     J  Lackey     1.51       1.89       18.70%     -0.047     -0.66
12-Sep     N  Blackburn  1.51       0.53       37.90%     -0.036     -0.3
Sep-16     G  Floyd      1.51       0.38       54.20%     -0.042     -0.38
Apr-26     J  Sowers     1.5        0.93       23.10%     0.061      0.62
01-Sep     J  Rupe       1.49       0.25       54.30%     -0.043     -0.25
Jun-27     P  Martinez   1.49       1.12       57.40%     0.035      0.37
May-25     J  Washburn   1.48       0.25       35.60%     0.017      0.09
Sep-19     L  Cormier    1.48       0.46       77.70%     -0.039     -0.46
Jun-27     M  Pelfrey    1.47       0.97       38.10%     0.063      0.59
Jun-30     S  Feldman    1.47       0.93       58.90%     0.025      0.24
10-Sep     J  Bale       1.46       1.18       81.00%     0.019      0.05
Sep-28     D  Matsuzaka  1.46       0.73       52.00%     0.023      0.24
Aug-15     G  Meche      1.46       0.71       46.20%     -0.042     -0.37
05-Sep     M  Harrison   1.45       1.11       26.30%     -0.082     -0.96
Jun-29     O  Perez      1.45       0.68       28.70%     -0.04      -0.36
Sep-17     C  Richard    1.43       0.29       32.30%     0.054      0.27
Apr-20     S  Trachsel   1.43       0.76       51.90%     0.11       1
Aug-24     D  Cabrera    1.43       1.27       76.40%     0.022      0.4
09-Sep     J  Howell     1.43       0.29       56.40%     -0.036     -0.17
09-Sep     E  Santana    1.42       1.86       79.30%     0.125      1.65
Sep-13     M  Garza      1.42       1.45       63.10%     -0.002     -0.11
Jun-19     J  Banks      1.42       1.45       63.10%     -0.074     -0.82
Sep-20     B  Burres     1.42       0.56       56.40%     0.041      0.4
Aug-26     T  Wakefield  1.42       0.56       44.40%     -0.063     -0.56
Apr-18     D  Cabrera    1.41       0.6        50.10%     -0.025     -0.24
Jul-19     S  Gallagher  1.4        0.63       74.90%     -0.042     -0.63
10-Sep     J  Arredondo  1.4        0.27       45.30%     0.09       0.42
07-Sep     S  Feldman    1.4        1.11       63.70%     -0.083     -0.96
Jul-29     D  Cabrera    1.4        0.54       26.80%     0.135      1
04-Sep     A  Sonnanstine1.4        0.54       26.80%     -0.036     -0.25
09-Sep     E  Jackson    1.4        0.38       69.40%     -0.039     -0.38
12-Sep     J  Beckett    1.38       0.56       19.60%     0.059      0.4
Aug-24     R  Cherry     1.36       0.76       74.60%     0.016      0.25
10-Sep     J  Saunders   1.36       1.86       70.70%     0.082      1.14
May-31     J  Rincon     1.35       0.92       86.00%     -0.025     -0.42
Sep-13     M  Garza      1.35       0.54       42.20%     -0.035     -0.25
Sep-17     C  Richard    1.35       0.54       42.20%     -0.035     -0.25
03-Sep     R  Halladay   1.34       0.38       43.70%     0.013      0.14
Jul-20     J  Duchscherer1.32       0.54       57.80%     -0.034     -0.25
10-Sep     C  Gaudin     1.32       0.81       79.60%     -0.03      -0.34
Aug-29     A  Burnett    1.3        0.93       76.90%     -0.071     -0.82
Aug-22     R  Liz        1.3        0.6        50.10%     -0.033     -0.34
Jul-19     S  Gallagher  1.3        0.95       80.60%     -0.025     -0.43
Jun-14     W  Rodriguez  1.29       0.33       36.90%     0.013      0.12
01-Sep     K  Millwood   1.29       0.38       53.60%     -0.036     -0.38
Sep-20     B  Burres     1.29       0.38       53.60%     -0.036     -0.38
10-Sep     P  Maholm     1.29       0.33       48.10%     -0.037     -0.33
Jun-13     S  Chacon     1.28       0.37       48.70%     0.085      0.87
Jun-15     R  Oswalt     1.28       0.33       48.10%     0.011      0.12
Jun-28     J  Santana    1.28       0.52       66.40%     0.02       0.16
10-Sep     D  Eveland    1.28       0.3        64.00%     -0.035     -0.3
05-Sep     D  McGowan    1.28       1.23       80.70%     -0.047     -0.7
Jun-20     F  Cordero    1.27       0.29       4.90%      -0.033     -0.17
09-Sep     J  Lackey     1.27       0.51       81.60%     -0.036     -0.51
07-Sep     B  Bannister  1.27       0.38       34.30%     0.014      0.14
Jul-26     T  Wakefield  1.26       0.39       48.60%     -0.036     -0.39
Apr-16     J  Tavarez    1.26       0.54       29.70%     -0.033     -0.25
Apr-19     B  Burres     1.24       0.36       37.50%     -0.037     -0.36
Jun-20     E  Volquez    1.24       0.34       42.70%     0.004      0.04
Aug-19     A  Burnett    1.24       1.05       69.90%     -0.042     -0.42
10-Sep     P  Maholm     1.24       0.52       22.10%     -0.032     -0.24
Apr-19     B  Burres     1.23       0.4        48.50%     0.013      0.15
Aug-19     A  Burnett    1.23       0.48       67.90%     -0.028     -0.27
Jul-18     G  Smith      1.22       0.56       45.40%     0.037      0.4
08-Sep     R  Ramirez    1.21       0.51       10.40%     -0.029     -0.29
May-30     G  Perkins    1.2        0.69       51.80%     -0.034     -0.36
03-Sep     E  Jackson    1.2        0.68       63.30%     0.098      1
Sep-19     R  Liz        1.2        0.34       68.90%     0.008      0.12
05-Sep     J  Masterson  1.2        0.34       68.90%     0.005      0.04
Jun-28     D  Sanchez    1.19       0.52       74.90%     0.02       0.16
05-Sep     M  Harrison   1.19       0.68       33.20%     0.012      0.15
Aug-27     P  Byrd       1.18       0.54       43.40%     0.078      0.63
May-30     G  Perkins    1.17       1.44       28.30%     0.045      0.46
12-Sep     J  Blanton    1.16       0.3        48.60%     0.01       0.11
05-Sep     D  McGowan    1.16       0.97       68.30%     0.018      0.14
11-Sep     R  Halladay   1.16       0.3        48.60%     -0.032     -0.3
Aug-21     R  Halladay   1.16       0.3        48.60%     -0.032     -0.3
Aug-29     A  Burnett    1.16       0.71       70.10%     0.044      0.51
May-25     J  Washburn   1.16       0.29       36.30%     0.044      0.27
Jun-30     S  Feldman    1.16       0.29       36.30%     -0.029     -0.17
Jul-30     D  Sarfate    1.16       0.38       63.30%     0.068      0.73
04-Sep     A  Sonnanstine1.15       0.34       43.30%     -0.033     -0.34
Aug-31     R  Halladay   1.15       0.34       17.70%     -0.034     -0.34
Apr-13     D  Matsuzaka  1.15       0.35       27.60%     -0.034     -0.35
10-Sep     P  Maholm     1.15       0.54       50.20%     -0.028     -0.3
Jul-19     S  Gallagher  1.15       0.56       55.10%     -0.028     -0.31
Sep-26     D  Pauley     1.14       1.19       66.40%     -0.041     -0.46
10-Sep     J  Saunders   1.14       0.51       37.70%     0.046      0.39
May-25     J  Washburn   1.14       0.54       31.80%     -0.03      -0.25
01-Sep     K  Millwood   1.14       0.54       31.80%     -0.03      -0.25
03-Sep     S  Downs      1.13       0.95       88.30%     -0.026     -0.5
Jun-19     J  Hampson    1.13       0.56       73.80%     0.017      0.15
Jul-22     D  Reyes      1.13       0.56       73.80%     0.017      0.15
Jul-19     A  Embree     1.13       0.56       73.80%     -0.017     -0.22
Jun-22     G  Majewski   1.13       0.56       73.80%     -0.028     -0.31
May-28     J  Guthrie    1.12       0.59       38.80%     -0.03      -0.27
06-Sep     J  Shields    1.12       0.46       80.20%     0.018      0.34
03-Sep     E  Jackson    1.12       0.32       48.40%     -0.032     -0.32
Jun-25     Z  Duke       1.12       0.96       75.00%     -0.048     -0.59
Apr-20     S  Trachsel   1.12       1          78.80%     -0.027     -0.39
06-Sep     T  Hunter     1.12       0.4        57.00%     -0.035     -0.4
02-Sep     L  Hernandez  1.11       0.33       48.40%     0.174      1.78
Aug-30     J  Parrish    1.11       0.34       53.20%     0.089      0.91
Aug-15     G  Meche      1.11       0.34       53.20%     0.01       0.12
May-21     G  Olson      1.11       0.34       53.20%     -0.032     -0.34
09-Sep     L  Hochevar   1.11       0.34       53.20%     -0.032     -0.34
Sep-15     M  Buehrle    1.11       0.34       53.20%     -0.032     -0.34
Jun-24     T  Gorzelanny 1.11       0.33       48.30%     -0.032     -0.33
Aug-19     A  Burnett    1.11       0.63       62.40%     -0.03      -0.33
Jun-21     D  Thompson   1.11       0.25       53.20%     -0.032     -0.25
Aug-15     G  Meche      1.11       0.25       25.90%     -0.032     -0.25
Aug-27     P  Byrd       1.11       0.25       25.90%     -0.032     -0.25
Aug-22     D  Sarfate    1.1        0.27       46.20%     -0.033     -0.27
03-Sep     J  Lackey     1.1        0.34       33.90%     -0.032     -0.34
Sep-26     D  Pauley     1.09       0.35       48.20%     0.085      0.91
Jul-27     J  Lester     1.09       0.35       48.20%     -0.032     -0.35
Sep-13     M  Garza      1.08       0.56       66.80%     0.032      0.4
Apr-25     P  Byrd       1.08       0.54       50.00%     -0.028     -0.25
Apr-27     C  Sabathia   1.08       0.54       50.00%     -0.028     -0.25
06-Sep     W  Madrigal   1.07       1.35       83.50%     -0.08      -1.35
Apr-20     S  Trachsel   1.07       0.36       48.10%     -0.032     -0.36
May-26     G  Olson      1.07       0.36       48.10%     -0.032     -0.36
04-Sep     J  Beckett    1.07       0.54       56.20%     0.042      0.39
Aug-28     J  Lester     1.07       0.54       56.20%     -0.028     -0.25
Aug-30     B  Tallet     1.06       1.55       86.40%     -0.033     -0.6
Aug-28     J  Masterson  1.06       0.11       52.80%     -0.028     -0.11
12-Sep     N  Blackburn  1.05       0.53       59.90%     -0.025     -0.3
11-Sep     G  Perkins    1.04       0.51       27.00%     0.044      0.39
Jul-13     A  Burnett    1.04       1.05       14.60%     -0.03      -0.42
May-28     J  Guthrie    1.04       0.59       64.50%     -0.028     -0.27
Aug-23     J  Guthrie    1.04       0.59       64.50%     -0.028     -0.27
Jun-18     J  Peavy      1.04       0.71       65.90%     -0.03      -0.37
05-Sep     B  Morrow     1.03       0.23       34.10%     -0.029     -0.23
Jun-17     R  Wolf       1.01       0.38       75.20%     -0.028     -0.38
Apr-18     D  Cabrera    1.01       0.32       46.40%     0.037      0.28
May-26     G  Olson      1.01       0.32       46.40%     0.037      0.28
Aug-24     D  Sarfate    1.01       0.32       46.40%     0.037      0.28
07-Sep     J  Wright     1.01       1.08       86.10%     -0.048     -0.64
Jul-25     J  Beckett    1.01       0.56       65.10%     0.039      0.4
May-30     B  Bass       1.01       1.44       80.10%     0.025      0.43
01-Sep     F  Dolsi      1          0.84       90.60%     -0.027     -0.84
01-Sep     S  Downs      1          0.38       85.70%     0.005      0.14
Sep-15     M  Buehrle    0.99       0.29       54.30%     -0.025     -0.17
Jun-20     E  Volquez    0.99       0.54       44.70%     0.04       0.39
Sep-21     C  Waters     0.99       0.54       44.70%     0.04       0.39
May-24     C  Silva      0.99       0.54       55.70%     -0.026     -0.25
02-Sep     A  Burnett    0.99       0.54       44.70%     -0.026     -0.25
Apr-17     J  Beckett    0.99       0.54       44.70%     -0.026     -0.25
Aug-16     Z  Greinke    0.99       0.54       44.70%     -0.026     -0.25
May-27     B  Burres     0.99       0.59       50.00%     -0.027     -0.27
09-Sep     J  Lackey     0.98       0.27       46.60%     0.169      1
Apr-13     D  Aardsma    0.98       0.56       11.60%     -0.026     -0.26
Jul-21     N  Blackburn  0.98       0.52       81.60%     0.054      0.93
08-Sep     B  Bannister  0.97       0.49       39.30%     -0.024     -0.23
02-Sep     J  Weaver     0.97       0.54       34.80%     -0.025     -0.25
Sep-19     R  Liz        0.97       0.54       34.80%     -0.025     -0.25
10-Sep     F  Rodriguez  0.97       0.27       3.60%      -0.025     -0.17
May-31     B  Bonser     0.97       0.51       39.60%     -0.025     -0.24
06-Sep     R  Rowland-Smi0.96       0.49       66.40%     -0.024     -0.23
07-Sep     B  Tomko      0.95       0.56       7.80%      0.11       1.73
Jul-23     G  Perkins    0.94       1.55       89.10%     0.078      1.92
09-Sep     E  Santana    0.93       0.51       50.00%     0.037      0.39
Sep-23     J  Litsch     0.93       0.44       50.00%     -0.023     -0.21
09-Sep     Z  Greinke    0.93       0.49       50.00%     -0.023     -0.23
05-Sep     B  Morrow     0.93       0.49       50.00%     -0.023     -0.23
Apr-15     E  Jackson    0.93       0.5        50.00%     -0.024     -0.23
02-Sep     M  Garza      0.93       0.5        50.00%     -0.024     -0.23
09-Sep     J  Lackey     0.93       0.51       50.00%     -0.024     -0.24
11-Sep     C  Buchholz   0.93       0.56       50.00%     -0.024     -0.26
12-Sep     J  Beckett    0.93       0.56       50.00%     -0.024     -0.26
Sep-28     D  Matsuzaka  0.93       0.56       50.00%     -0.024     -0.26
May-28     J  Guthrie    0.93       0.59       50.00%     -0.025     -0.27
06-Sep     T  Hunter     0.93       0.69       50.00%     -0.026     -0.31
Jun-29     O  Perez      0.92       0.5        10.40%     -0.024     -0.24
Jun-17     R  Wolf       0.92       0.54       55.30%     0.102      1
06-Sep     T  Wakefield  0.92       0.54       55.30%     0.102      1
08-Sep     J  Weaver     0.92       0.51       30.20%     0.095      1
Jun-21     D  Thompson   0.92       0.54       55.30%     0.061      0.63
Jul-22     K  Slowey     0.92       0.54       55.30%     0.061      0.63
May-24     C  Silva      0.92       0.54       55.30%     0.036      0.39
May-25     J  Washburn   0.92       0.54       55.30%     0.036      0.39
Jun-30     S  Feldman    0.92       0.54       55.30%     0.036      0.39
02-Sep     L  Mendoza    0.92       0.54       55.30%     0.036      0.39
05-Sep     M  Harrison   0.92       0.69       33.30%     0.035      0.42
03-Sep     D  McGowan    0.92       0.54       55.30%     -0.024     -0.25
06-Sep     J  Shields    0.92       0.54       55.30%     -0.024     -0.25
May-22     B  Burres     0.92       0.54       55.30%     -0.024     -0.25
05-Sep     J  Masterson  0.92       0.54       55.30%     -0.024     -0.25
08-Sep     S  Kazmir     0.92       0.54       55.30%     -0.024     -0.25
Jul-23     G  Perkins    0.92       0.54       55.30%     -0.024     -0.25
Jul-31     J  Garland    0.92       0.54       55.30%     -0.024     -0.25
Aug-29     A  Burnett    0.92       0.54       55.30%     -0.024     -0.25
Sep-17     C  Richard    0.92       0.54       55.30%     -0.024     -0.25
Jul-26     T  Wakefield  0.92       0.25       36.20%     0.042      0.39
Sep-21     C  Waters     0.92       0.93       83.10%     -0.022     -0.38
Jul-25     J  Beckett    0.91       0.25       46.90%     0.029      0.28
May-26     G  Olson      0.91       0.27       46.80%     0.021      0.22
08-Sep     B  Bannister  0.91       0.26       32.50%     -0.022     -0.16
09-Sep     E  Santana    0.9        0.51       62.30%     -0.023     -0.24
Aug-13     K  Slowey     0.9        0.51       62.40%     -0.023     -0.24
Jun-24     T  Gorzelanny 0.89       0.52       18.70%     -0.023     -0.24
07-Sep     J  Peralta    0.88       0.29       53.80%     -0.022     -0.17
Apr-25     P  Byrd       0.87       0.29       19.50%     -0.022     -0.17
Sep-23     J  Litsch     0.87       0.44       63.60%     -0.021     -0.21
04-Sep     J  Beckett    0.87       0.25       16.90%     -0.025     -0.25
10-Sep     D  Eveland    0.87       0.47       73.30%     0.026      0.37
02-Sep     A  Burnett    0.87       0.93       6.30%      0.072      1.61
Jun-19     J  Banks      0.86       0.29       40.30%     -0.022     -0.17
07-Sep     J  Hammel     0.86       1.47       82.90%     0.033      0.47
11-Sep     R  Halladay   0.85       0.44       9.00%      -0.021     -0.21
04-Sep     J  Litsch     0.84       0.54       68.30%     -0.022     -0.25
Aug-30     J  Parrish    0.84       0.56       76.20%     -0.021     -0.31
04-Sep     V  Padilla    0.83       0.3        56.10%     -0.026     -0.3
08-Sep     Z  Greinke    0.83       0.56       73.00%     0.012      0.15
Apr-17     J  Beckett    0.83       0.34       11.10%     -0.024     -0.34
07-Sep     S  Feldman    0.82       0.69       74.00%     -0.023     -0.31
Jun-27     M  Pelfrey    0.82       0.25       42.40%     0.027      0.28
Jul-29     D  Cabrera    0.82       0.25       42.40%     0.027      0.28
05-Sep     J  Masterson  0.82       0.25       67.80%     0.011      0.09
Jun-14     W  Rodriguez  0.81       0.52       22.40%     0.08       1
Jun-30     S  Feldman    0.81       0.29       28.90%     0.114      1
12-Sep     J  Crain      0.81       0.53       81.70%     -0.036     -0.53
Aug-27     P  Byrd       0.8        0.25       33.10%     0.102      1.09
10-Sep     D  Moseley    0.8        0.23       58.60%     -0.023     -0.23
May-31     B  Bonser     0.8        0.23       58.70%     0.01       0.09
11-Sep     J  Duchscherer0.8        0.21       47.60%     -0.022     -0.21
12-Sep     J  Blanton    0.8        0.23       33.50%     0.032      0.24
Aug-31     R  Halladay   0.8        0.54       15.20%     0.072      1
07-Sep     B  Bannister  0.8        0.54       15.20%     0.034      0.39
Jun-24     T  Yates      0.8        0.69       6.70%      -0.022     -0.36
04-Sep     S  Kazmir     0.79       0.23       47.50%     0.01       0.09
Jul-21     N  Blackburn  0.79       0.25       52.30%     0.178      1.87
01-Sep     R  Halladay   0.79       0.25       52.30%     0.106      1.09
05-Sep     E  Jackson    0.79       0.25       52.30%     0.106      1.09
Aug-23     J  Guthrie    0.79       0.27       47.20%     0.103      1.14
11-Sep     G  Perkins    0.79       0.23       47.40%     0.026      0.27
01-Sep     N  Blackburn  0.79       0.23       47.40%     0.019      0.21
Apr-27     C  Sabathia   0.79       0.25       47.30%     0.019      0.21
Aug-24     D  Cabrera    0.79       0.27       47.20%     0.019      0.22
Jun-27     P  Martinez   0.79       0.23       47.40%     -0.022     -0.23
Jun-28     J  Santana    0.79       0.23       47.40%     -0.022     -0.23
Jun-15     R  Oswalt     0.79       0.24       47.40%     -0.023     -0.24
Apr-25     P  Byrd       0.79       0.25       47.30%     -0.023     -0.25
Apr-26     J  Sowers     0.79       0.25       47.30%     -0.023     -0.25
04-Sep     J  Litsch     0.79       0.25       52.30%     -0.023     -0.25
Jun-22     J  Cueto      0.79       0.25       52.30%     -0.023     -0.25
Apr-18     D  Cabrera    0.79       0.27       47.20%     -0.023     -0.27
May-27     B  Burres     0.79       0.27       47.20%     -0.023     -0.27
Apr-28     A  Laffey     0.79       0.29       47.20%     -0.02      -0.17
06-Sep     J  Shields    0.79       0.29       53.40%     0.049      0.43
06-Sep     K  Davies     0.79       0.29       53.40%     0.03       0.27
Jun-20     E  Volquez    0.79       0.29       53.40%     -0.02      -0.17
04-Sep     V  Padilla    0.79       0.3        46.90%     0.018      0.23
Jun-18     B  Corey      0.79       0.56       80.90%     0.012      0.15
Aug-30     B  League     0.79       0.54       78.50%     -0.02      -0.25
05-Sep     E  Jackson    0.78       0.29       41.40%     -0.02      -0.17
Aug-22     F  Cabrera    0.77       0.27       79.20%     0.029      0.4
Apr-17     J  Beckett    0.77       0.56       10.10%     0.027      0.4
Jul-28     J  Guthrie    0.76       0.54       18.90%     -0.02      -0.25
Jul-13     A  Burnett    0.76       0.48       7.00%      0.029      0.37
Jul-25     M  Delcarmen  0.75       0.3        70.80%     -0.019     -0.18
Jun-20     E  Volquez    0.75       0.29       10.50%     0.033      0.27
06-Sep     W  Madrigal   0.73       1.34       86.90%     -0.008     -0.25
May-31     C  Breslow    0.73       0.27       66.80%     -0.018     -0.17
Jul-26     T  Wakefield  0.73       0.3        60.50%     0.027      0.28
03-Sep     C  Bradford   0.73       1.19       90.70%     0.026      0.73
03-Sep     R  Halladay   0.73       0.29       53.10%     0.028      0.27
Jul-18     G  Smith      0.73       0.29       53.10%     0.028      0.27
Aug-31     R  Halladay   0.73       0.25       24.90%     -0.021     -0.25
Apr-19     B  Burres     0.72       0.59       9.70%      -0.019     -0.27
08-Sep     J  Garland    0.72       0.27       47.50%     -0.018     -0.17
Sep-28     J  Lopez      0.72       0.35       81.50%     0.009      0.19
Jun-28     J  Santana    0.72       0.26       63.70%     0.027      0.26
Aug-30     J  Parrish    0.71       0.25       62.10%     0.008      0.09
05-Sep     T  Miller     0.71       0.93       4.00%      0.032      0.62
Aug-17     B  Bannister  0.7        1.89       88.10%     0.016      0.5
01-Sep     J  Verlander  0.7        1.52       86.20%     0.022      0.5
11-Sep     R  Halladay   0.69       0.23       22.60%     0.03       0.24
May-22     B  Burres     0.69       0.11       51.80%     -0.018     -0.11
Jun-28     D  Sanchez    0.68       0.26       72.50%     0.024      0.26
Jun-13     S  Chacon     0.68       0.28       59.80%     0.025      0.27
Aug-24     D  Cabrera    0.67       0.27       65.90%     -0.02      -0.27
11-Sep     C  Buchholz   0.67       0.12       43.90%     0.019      0.13
Jun-27     P  Martinez   0.67       1.85       90.50%     -0.029     -0.66
Jul-29     D  Cabrera    0.67       1.17       4.50%      0.027      0.38
Jun-13     S  Chacon     0.66       0.11       44.10%     -0.017     -0.11
Sep-16     M  Thornton   0.66       0.54       4.80%      -0.017     -0.25
Aug-20     D  Purcey     0.65       0.44       73.10%     -0.016     -0.21
Jul-22     K  Slowey     0.65       0.29       71.50%     0.023      0.27
07-Sep     R  Feierabend 0.65       0.23       69.70%     -0.018     -0.23
Apr-13     D  Matsuzaka  0.64       0.3        15.00%     -0.017     -0.18
Apr-26     J  Sowers     0.64       0.29       11.90%     0.028      0.27
Jul-28     J  Guthrie    0.64       0.25       12.80%     -0.019     -0.25
Jul-22     K  Slowey     0.63       0.29       66.10%     -0.016     -0.17
02-Sep     L  Hernandez  0.63       0.27       59.00%     0.024      0.26
08-Sep     S  Kazmir     0.62       0.54       78.20%     -0.016     -0.25
05-Sep     B  Ryan       0.61       0.11       1.60%      0.032      0.13
Jun-14     W  Wright     0.61       0.24       79.40%     0.019      0.28
Jun-18     J  Peavy      0.6        0.29       64.50%     0.099      1
Apr-18     R  Bierd      0.6        1.01       3.30%      -0.014     -0.52
06-Sep     K  Davies     0.6        0.11       20.70%     0.032      0.23
Sep-15     M  Buehrle    0.6        0.25       74.10%     -0.017     -0.25
10-Sep     H  Nomo       0.6        0.36       89.60%     0.004      0.14
Aug-23     L  Cormier    0.59       0.59       84.60%     -0.016     -0.27
08-Sep     Z  Greinke    0.59       0.11       51.60%     0.017      0.13
05-Sep     B  Morrow     0.58       0.26       7.80%      -0.015     -0.16
02-Sep     L  Mendoza    0.58       0.25       78.90%     0.013      0.21
Jun-14     G  Geary      0.57       0.37       92.00%     0.003      0.14
Jun-19     H  Bell       0.57       0.54       86.30%     -0.015     -0.25
Apr-16     C  Buchholz   0.55       0.29       62.40%     0.088      1
Sep-18     J  Vazquez    0.55       0.29       62.40%     0.021      0.27
Apr-27     M  Kobayashi  0.55       0.29       81.00%     -0.014     -0.17
12-Sep     J  Litsch     0.54       0.23       58.70%     -0.013     -0.14
05-Sep     E  Jackson    0.54       0.29       10.80%     -0.014     -0.17
Jul-27     J  Lester     0.53       0.56       8.80%      0.033      0.63
09-Sep     L  Hochevar   0.53       0.11       51.40%     -0.014     -0.11
Jul-23     G  Perkins    0.53       0.11       51.40%     -0.014     -0.11
Jun-14     W  Rodriguez  0.53       0.28       73.10%     -0.013     -0.17
Jun-18     C  Meredith   0.52       1.17       91.40%     0.034      0.76
Sep-21     L  Cormier    0.52       1.17       91.40%     -0.003     -0.2
11-Sep     C  Buchholz   0.52       0.12       45.10%     -0.014     -0.12
12-Sep     J  Beckett    0.52       0.12       45.10%     -0.014     -0.12
May-30     M  Guerrier   0.51       0.27       81.80%     0.033      0.42
09-Sep     J  Lackey     0.51       0.11       45.30%     0.015      0.13
09-Sep     Z  Greinke    0.51       0.1        45.40%     0.028      0.22
Apr-15     G  Glover     0.51       1.49       95.30%     -0.016     -0.58
May-23     E  Bedard     0.51       1.89       93.20%     -0.015     -0.44
07-Sep     M  Batista    0.51       0.1        7.20%      -0.013     -0.1
Sep-13     C  Bradford   0.5        0.46       93.40%     -0.013     -0.46
10-Sep     K  Jepsen     0.5        0.11       16.70%     -0.013     -0.11
04-Sep     S  Kazmir     0.5        0.5        3.50%      -0.014     -0.5
08-Sep     Z  Greinke    0.5        0.11       39.40%     0.015      0.13
Jun-13     D  Brocail    0.49       0.11       70.00%     -0.013     -0.11
Apr-14     A  Sonnanstine0.49       0.23       78.40%     0.011      0.21
09-Sep     Z  Greinke    0.48       0.1        16.20%     -0.013     -0.1
Jul-26     J  Masterson  0.48       1.47       93.80%     0.022      0.77
Aug-23     J  Guthrie    0.48       0.13       35.10%     0.014      0.14
Jul-18     G  Smith      0.48       0.38       90.40%     0.033      0.87
07-Sep     S  Dohmann    0.48       0.95       94.70%     -0.011     -0.5
May-21     G  Olson      0.47       0.54       83.50%     0.055      1
Sep-18     J  Vazquez    0.47       0.29       74.40%     -0.012     -0.17
03-Sep     G  Balfour    0.47       0.52       89.80%     -0.016     -0.42
08-Sep     Z  Greinke    0.46       0.29       71.30%     0.017      0.27
07-Sep     J  Hammel     0.46       0.29       71.30%     -0.012     -0.17
10-Sep     J  Bale       0.46       0.1        45.70%     -0.012     -0.1
Apr-13     M  Delcarmen  0.45       0.3        1.60%      -0.012     -0.18
Jun-18     B  Corey      0.45       0.29       79.20%     0.016      0.27
05-Sep     J  Masterson  0.44       0.11       66.60%     0.012      0.13
05-Sep     M  Harrison   0.44       0.15       12.50%     -0.012     -0.15
04-Sep     V  Padilla    0.44       0.15       67.30%     -0.013     -0.15
Jul-20     A  Embree     0.44       0.29       84.80%     0.015      0.27
11-Sep     J  Lopez      0.43       0.3        83.80%     0.015      0.28
Sep-23     J  Litsch     0.43       0.23       78.50%     -0.01      -0.14
Apr-15     J  Howell     0.43       0.5        86.70%     -0.011     -0.23
May-24     C  Silva      0.42       0.11       64.50%     -0.011     -0.11
06-Sep     T  Wakefield  0.42       0.11       64.50%     -0.011     -0.11
07-Sep     S  Feldman    0.41       0.15       54.00%     -0.012     -0.15
Sep-23     B  Tallet     0.41       0.21       86.80%     -0.011     -0.21
05-Sep     C  Wilson     0.41       1.11       2.40%      0.018      0.63
Jul-20     J  Duchscherer0.41       0.11       51.10%     0.012      0.13
May-23     E  Bedard     0.41       0.11       51.10%     -0.011     -0.11
Apr-16     D  Aardsma    0.41       0.29       82.70%     0.015      0.27
08-Sep     G  Balfour    0.41       0.29       82.70%     -0.01      -0.17
09-Sep     E  Jackson    0.4        0.11       63.00%     0.012      0.13
Sep-21     C  Waters     0.4        0.11       63.00%     0.012      0.13
Apr-16     C  Buchholz   0.4        0.11       63.00%     -0.011     -0.11
May-23     E  Bedard     0.4        0.11       63.00%     -0.011     -0.11
Aug-13     K  Slowey     0.4        0.11       46.20%     0.022      0.22
Sep-26     D  Aardsma    0.4        0.95       92.20%     -0.01      -0.38
02-Sep     A  Burnett    0.4        0.11       18.10%     -0.011     -0.11
Jun-29     O  Perez      0.4        0.1        46.20%     -0.01      -0.1
04-Sep     S  Kazmir     0.4        0.1        46.20%     0.012      0.13
10-Sep     J  Bale       0.4        0.1        46.30%     -0.01      -0.1
Jul-31     J  Garland    0.4        0.29       8.40%      0.024      0.43
03-Sep     J  Lester     0.4        0.29       8.40%      -0.01      -0.17
04-Sep     A  Sonnanstine0.39       0.11       20.30%     0.013      0.13
Jul-30     B  Burres     0.39       1.17       93.00%     -0.015     -0.46
Jul-13     A  Burnett    0.39       0.09       46.40%     -0.01      -0.09
Aug-31     S  Downs      0.39       0.29       3.10%      0.019      0.27
Sep-18     H  Ramirez    0.38       0.52       94.30%     0.023      1
Apr-14     A  Sonnanstine0.37       0.1        56.40%     0.096      1
06-Sep     R  Rowland-Smi0.37       0.1        56.50%     -0.009     -0.1
07-Sep     R  Feierabend 0.37       0.1        56.50%     -0.009     -0.1
Aug-26     T  Wakefield  0.37       0.11       61.00%     -0.01      -0.11
Jun-15     R  Oswalt     0.37       0.28       82.10%     -0.009     -0.17
Sep-28     J  Papelbon   0.35       0.64       96.30%     0.02       0.89
04-Sep     S  Camp       0.35       0.93       94.70%     -0.003     -0.22
Apr-16     M  Timlin     0.35       0.56       93.70%     0.024      0.89
03-Sep     G  Balfour    0.35       0.5        89.70%     0.013      0.39
Jul-30     D  Sarfate    0.35       0.29       82.30%     -0.009     -0.17
08-Sep     J  Weaver     0.35       0.11       12.40%     -0.009     -0.11
05-Sep     J  Lopez      0.34       0.29       87.20%     0.012      0.27
Jul-26     C  Hansen     0.33       0.53       95.90%     0.003      0.28
02-Sep     J  Weaver     0.33       0.54       90.80%     0.041      1
02-Sep     J  Weaver     0.32       0.11       73.20%     0.009      0.13
Jun-25     Z  Duke       0.32       0.52       89.60%     -0.008     -0.24
01-Sep     A  Lopez      0.31       0.13       78.70%     0.008      0.14
Sep-15     M  MacDougal  0.3        1.17       95.50%     -0.013     -0.46
Sep-28     H  Okajima    0.3        0.56       92.10%     -0.008     -0.26
May-27     B  Burres     0.3        0.13       76.80%     0.071      1
Jul-13     A  Burnett    0.3        0.44       1.20%      -0.007     -0.21
12-Sep     B  Tallet     0.3        0.44       89.50%     0.041      1
01-Sep     J  Crain      0.29       0.27       2.30%      -0.007     -0.17
08-Sep     J  Arredondo  0.28       0.51       1.80%      -0.007     -0.24
03-Sep     J  Lester     0.28       0.54       2.20%      -0.007     -0.25
06-Sep     R  Messenger  0.27       0.5        96.60%     -0.008     -0.5
02-Sep     M  Garza      0.26       0.5        92.10%     0.01       0.39
06-Sep     J  Howell     0.26       0.54       93.60%     -0.007     -0.25
Jun-24     T  Gorzelanny 0.25       0.11       7.50%      -0.006     -0.11
Sep-14     E  Jackson    0.24       0.11       79.50%     -0.006     -0.11
01-Sep     A  Lopez      0.24       2.46       97.20%     0.009      1
12-Sep     A  Brown      0.21       0.44       94.10%     -0.005     -0.21
04-Sep     J  Litsch     0.2        0.11       86.20%     0.011      0.23
12-Sep     B  Wolfe      0.2        0.81       96.80%     -0.004     -0.34
03-Sep     T  Percival   0.2        0.32       96.50%     0.028      1.78
04-Sep     S  Kazmir     0.19       0.1        6.90%      0.007      0.13
Jun-21     J  Burton     0.19       0.54       1.10%      -0.005     -0.25
Jul-18     G  Smith      0.18       0.25       93.70%     0.002      0.09
Sep-14     D  Price      0.18       0.29       92.10%     -0.005     -0.17
Jun-15     W  Wright     0.18       0.45       97.20%     0.023      2.66
11-Sep     J  Nathan     0.17       0.27       0.60%      -0.004     -0.17
May-24     C  Silva      0.17       0.11       89.30%     -0.005     -0.11
Aug-26     J  Papelbon   0.17       0.25       0.60%      -0.006     -0.25
May-20     D  Cabrera    0.17       0.54       2.50%      0.008      0.39
Apr-17     J  Beckett    0.17       0.11       2.10%      -0.005     -0.11
11-Sep     K  Calero     0.17       1.9        0.60%      -0.004     -0.57
09-Sep     Y  Yabuta     0.16       0.26       0.50%      0.009      0.26
11-Sep     D  Aardsma    0.16       0.25       95.70%     -0.005     -0.25
03-Sep     B  Tallet     0.16       0.25       1.40%      -0.005     -0.25
Aug-20     B  Tallet     0.16       0.44       94.90%     -0.004     -0.21
Aug-17     J  Newman     0.14       0.38       97.10%     0.009      0.62
04-Sep     J  Hammel     0.14       0.1        0.40%      0.008      1
Apr-14     S  Dohmann    0.14       0.23       94.90%     0.003      0.21
02-Sep     J  Hammel     0.13       0.5        96.60%     0.018      1
02-Sep     J  Wright     0.12       0.52       98.50%     0.013      2.59
Sep-14     D  Price      0.12       0.54       97.10%     0.009      0.63
Jun-22     M  Lincoln    0.12       0.54       97.10%     0.004      0.39
Jun-27     S  Schoeneweis0.12       0.32       97.30%     0.001      0.12
Jun-27     P  Feliciano  0.12       0.29       1.40%      0.012      1
Aug-20     J  Carlson    0.12       0.23       94.80%     -0.003     -0.14
09-Sep     J  Bulger     0.11       0.23       96.50%     0.003      0.21
Aug-21     R  Halladay   0.11       0.23       1.80%      -0.003     -0.14
Apr-14     S  Dohmann    0.1        0.5        97.00%     0.004      0.39
Jun-17     R  Wolf       0.09       0.34       97.90%     -0.003     -0.34
01-Sep     C  Fossum     0.09       0.61       98.10%     -0.002     -0.28
May-21     D  Sarfate    0.08       0.29       96.30%     0.005      0.43
Jul-21     B  Bonser     0.08       0.29       96.30%     -0.002     -0.17
Jul-28     R  Bierd      0.08       0.25       0.70%      -0.003     -0.25
Jul-27     M  Delcarmen  0.08       0.56       0.50%      0.004      0.4
Jul-18     D  Braden     0.08       0.29       96.90%     0.015      1
May-21     L  Cormier    0.08       0.71       98.60%     0.007      1
May-20     D  Cabrera    0.07       0.54       0.80%      -0.002     -0.25
10-Sep     H  Nomo       0.07       0.1        96.20%     0.021      1
Sep-17     S  Linebrink  0.07       0.11       96.50%     0.019      1
Jul-21     C  Breslow    0.07       1.17       98.90%     0.001      0.38
Jul-22     B  Bass       0.07       1.17       98.90%     0          -0.2
Jul-31     J  Garland    0.07       0.29       0.80%      -0.002     -0.17
08-Sep     J  Hammel     0.07       1.17       99.10%     -0.003     -0.46
04-Sep     C  Bradford   0.06       0.26       0.40%      -0.002     -0.16
Jul-28     J  Guthrie    0.06       0.46       0.30%      0.002      0.34
May-21     L  Cormier    0.06       0.95       99.30%     0.001      0.27
03-Sep     J  Frasor     0.06       0.52       0.20%      -0.002     -0.52
Sep-18     L  Broadway   0.06       0.63       99.30%     -0.002     -0.63
12-Sep     J  Frasor     0.05       0.21       98.50%     -0.001     -0.21
Aug-17     J  Newman     0.04       0.46       99.30%     0.001      0.34
11-Sep     R  Halladay   0.04       0.3        0.10%      -0.001     -0.3
02-Sep     D  O'Day      0.04       0.56       99.30%     -0.001     -0.31
Apr-19     J  Johnson    0.04       0.13       0.40%      0.002      0.14
May-26     C  Bradford   0.04       0.13       0.40%      -0.001     -0.13
11-Sep     J  Duchscherer0.03       0.09       0.60%      -0.001     -0.09
May-20     D  Cabrera    0.03       0.25       0.20%      0.004      1.87
May-24     B  Morrow     0.03       0.63       99.70%     0          0.17
Jul-23     J  Nathan     0.03       0.54       99.50%     -0.001     -0.25
Jun-17     C  Guevara    0.02       0.71       99.70%     0.001      0.26
Jun-25     T  Beam       0.02       0.11       99.10%     0          0.13
May-23     R  Dickey     0.02       0.52       99.80%     0          0.93
Jul-31     J  Arredondo  0.02       0.25       0.10%      -0.001     -0.25
Jun-27     J  Smith      0.01       0.5        99.80%     0          -0.5
Jul-30     F  Cabrera    0.01       0.54       99.80%     0.001      1
Jun-17     C  Guevara    0.01       0.29       99.60%     0.001      0.43
Aug-21     R  Halladay   0.01       0.44       0.10%      0.001      0.37
Jul-31     D  Oliver     0.01       0.29       0.10%      0          -0.17
Jul-18     L  DiNardo    0.01       0.25       99.70%     0          -0.25
Aug-17     J  Fulchino   0          0.34       99.90%     0          0.91
Jun-15     O  Villarreal 0          0.28       100.00%    0          0.27
Jun-24     F  Osoria     0          0.11       0.00%      0          -0.11
Jun-17     C  Guevara    0          0.46       100.00%    0          -0.46
Aug-27     M  Timlin     0          0.11       0.00%      0          -0.11
03-Sep     J  Lester     0          0.11       0.00%      0          -0.11
08-Sep     K  Jepsen     0          0.11       0.00%      0          -0.11

So how did he do?

Not as badly as you may think. A-Rod's highest LI plate appearance was on Aug. 15 against the intrepid Royals. It was the bottom of the ninth, two out, two on (first and second) with the Yankees behind 4-3. Yup—that checks the "clutch" box! The boy came through with an infield grounder up the middle that got him to first and moved both runners over. Job done, although New York went on to lose the game.

The second highest LI appearance was less successful. In a similar situation against the Blue Jays but with no outs A-Rod grounded into a double play. The Yankees lost that one too.

The next highest, against the Angels, was slightly better. LI was 4.46 and A-Rod reached, albeit on error. If we continue to go through play by play we'll be here all day. We need a more systematic approach. Check the table below:
LI         Number   Success    WPA
>3         28       0.464      -0.547
1.5-3      110      0.427      -0.195
1-1.5      138      0.391      -0.642
<1         348      0.44       1.871

By segmenting A-Rod's plate appearances into strata we can try to isolate how well he did in high LI (i.e., clutch) situations. We use an LI of 3 as a cut-off—this represents the top 5 percent of clutch PAs. In the table above, number is the number of instances of that LI situation occurring. Success is the number of times WE went up as a result of A-Rod's endeavours. It proxies to OBP but doesn't equal OBP as the list contains instances of A-Rod stealing or being picked-off. WPA is the sum of WPA in the stratum in question. A positive number is good.

What does all this mean?

Let's look at the numbers. In the highest LI stratum, "success" is above average (0.427)—in fact it is the highest of any strata. However, cumulative WPA is a disappointing -0.547. Compare that to the lowest LI bracket where WPA is 1.871. A word of caution: Be careful comparing the WPA data. First, the WPA is driven by leverage. In other words, high LI situations result in the biggest swings in win probability. Similarly the higher number of "trials" for lower LI events will drive cumulative WPA. (Note: Li x WPA is sometimes used as a metric to adjust for this issue.)

Superficially A-Rod did better in the clutch than he did in non-clutch situations, although WPA does not reflect that. However, the margin is small&mash;one walk-off HR could account for the WPA swing in the ">3" bracket. How else can we judge A-Rod's 2008 performance?

One way we can determine how good he was in the clutch in 2008 is to compare his performance to other years. Fangraphs gives LI and WPA data back to 2002. If we produce the same table for the years 2002-2007 we get the following:
LI         Number   Success    WPA
>3         128      0.422      1.004
1.5-3      684      0.447      7.596
1.5-1      949      0.447      5.713
<1         2666     0.405      10.228

Although we are ignoring aging, park etc., we at least can compare the 2002-2007 data to the 2008 data. First, "success" for the 2002-2007 period is 0.420 vs. 0.427 for 2008. However, in highest LI situations A-Rod performed better in 2008 than he did in previous years when judged by 'success'.

Finally it is also worth noting that that the lowest "success" is for the lowest LI situations.

Is this evidence that A-Rod performs well in the clutch or had a good 2008 in clutch situations? Not really. The simple truth is that clutch ability is impossible to predict and even harder to measure. However, based on this cursory look, Mr. Rodriguez doesn't do too badly in high LI situations. Give the dude a break.

Click here to learn about THT's download subscriptions.]]> John Beamer 2009-04-17T05:01:15+00:00 Five questions: Atlanta Braves http://www.hardballtimes.com/main/article/five-questions-atlanta-braves4/ http://www.hardballtimes.com/main/article/five-questions-atlanta-braves4/#When:05:01:15

1. Will it?


In all honesty, probably not.

In my book (well, the THT Season Preview) the Braves project as an 84-win team this time around;a large dollop of luck is required if they are to challenge the Phillies and Mets for the division. That gives the team a 20 percent chance of winning the division and a further 10 percent shot of making it via the wild card.

However, a look around the interweb suggests that, if anything, those THT numbers are a little conservative. CHONE, which was probably the best performing projection system of all last year, rates the Braves as an 86-win team—even with the Phillies and a game behind the Mets. PECOTA, interestingly, has the Braves as an 87-win team, which is tied with the Phillies but lags the Mets at 92 wins.

Prognostication is a fraught science and must be taken with a pinch of salt. At the start of last year many thought the division was a three-horse race, but the Braves lagged, finishing with only 72 wins, 12 games behind the Marlins. However, with the Mets significantly upgrading by adding two of the best in baseball to their bullpen, closing games shouldn't be a problem.

The only question is whether they can get into position to close games, with Daniel Murphy, Fernando Tatis and Ryan Church patrolling the outfield corners and Luis Castillo taking charge of the middle infield. There is hope.

2. Will the rotation work as advertised?


If the Braves are to challenge, the rotation needs to come good. Wren ripped apart last year's excuse for a pitching staff and rebuilt from the ground up. Please welcome: Derek Lowe, Jair Jurrjens, Tom Glavine, Javier Vasquez and Kenshin Kawakami as your starting five.

Perhaps the most impressive aspect on paper is its depth—Atlanta hasn't had a staff this good for half a decade. Let's start with the old. Jurrjens, who was acquired from the Tigers, was one of the bright spots for the Braves last year. He notched 13 wins and a 3.68 ERA in 188 innings. He's the real deal, too, with at least four pitchers and a fastball that clocks 94 on the gun.

Glavine is the other returnee from last year, although his 2008 was truncated by injury—he hurled only 63 innings. At 43, Glavine must be close to retirement, so let's hope he can sign off in style. If healthy there is no reason why he can't register a league average ERA.

Look up Derek Lowe in Merriam-Webster:

Derek Lowe: noun, workhorse.

Lowe, the sinker ball specialist, has averaged 15 wins a year over the last seven seasons and the last time his ERA was over 3.90 was in 2004, when he was pitching at Fenway. At the very least he should give the Braves innings, which they desperately need from a front-line starter. The only question mark is that his strong recent years were recorded in Dodger Stadium—yes, a pitcher's park.

Vasquez is another workhorse, albeit one with a slight limp. While he has pitched more than 200 innings in each of the last four years, he has had a sub 4.00 ERA only once, in 2007. Throughout his career he has been spotted as a breakout candidate, but the man is 31, for goodness sake. Knowing the Braves' luck, what are the odds that neither Vasquez and Lowe hurls 200 innings? It doesn't bear thinking about.

Kenshin Kawakami is the biggest unknown. So .... um .... what do we know about him? Well, he's Japanese (ed: c'mon, you can do better than that) ... oh, okay, ... and in Japan he has a 112-72 record with a 3.30 career ERA. It is always difficult to translate Nippon success to the majors, but Kenshin figures for a league average starter in the bigs. The only issue I suspect is that it may take him a while to settle in—let's hope there are some decent translators in the dugout.

3. Will Frenchy look better than a Double-A hitter?


With each passing season, this question gets easier to answer. Jeff Francoeur was nothing short of horrific last year, recording .239/.294/.359—and he is a corner outfielder from where you'd expect some pretty decent production! We can discount small sample size. Despite being relegated to the minors, the kid (he's no longer a kid, really) played in an eye-popping 155 games.

Walks and strikes remain a big problem—he swings and misses too much and entering his fifth year of big-league baseball many feel this is his last chance to rescue his career. Here's a quote from Frenchy in late 2006:

"I learned I've got to give up something ... if I'm covering out over the plate and he throws it inside, I've got to spit on it (take the pitch). You can still be a free swinger, but you need to be more selective. You just learn as you go. You learn to realize that's not a good pitch to swing at … I want to keep learning and get to the point where the team can totally depend on me, like they do Chipper (Jones) and Andruw (Jones)."


And this is what Bobby Cox said shortly after:

"(Francoeur) can sit on pitches now. He's sharp kid. He is still working. He is not going to walk an awful lot, which is fine with me where he is hitting in the lineup. And I think if you took his aggression at the plate away from him, I don't think he'd be as good."


Oh, ****.

4. Can Chipper win the batting title again?


yes I said yes I will Yes (to quote perhaps the famous ending of any English language novel).

After missing out on the last day of the 2007 season to Colorado's Matt Holliday, Chipper Jones stormed to the batting title last year with a career best .364 average. That belies a season of two halves. For the first half, Chipper was going like a jet and batted over .400 until mid-June. In the second half, he tailed off but still managed to hit over .300. Let's not forget that all this was at the tender age of 36! Impressive.

Given the providence of luck, a repeat is unlikely. But based on recent form expect Chipper to hit over .300—he's rapidly building a Hall of Fame resume.

5. Will the bullpen finally come good?


Although the Mets have loaded their bullpen with arms, the best and most cost-effective strategy is usually to fill the pen with middling pitchers bookended by a couple of relief aces for those high-leverage innings. The Braves have tried this strategy for the last couple of years but failed miserably

How do the Braves of 2009 fit with this model?

On paper, not badly. However, on paper, the Braves' pen last year wasn't bad and then Rafael Soriano goes and gets hurt pitching only 14 innings. Atlanta's other putative relief ace, Mike Gonzalez, has pitched fewer than 50 innings in two years. Ouch. Peter Moylan, another potential bright light, tossed fewer than six innings in 2008. Two out of those three need to remain healthy for the Braves to lock down close games.

Behind these three Jorge Campillo, Blaine Boyer, Manny Acosta and Jeff Bennett are usable relievers. Once more it's not a bad relief corps ... on paper at least, anyway.

Click here to learn about THT's download subscriptions.]]> John Beamer 2009-03-20T05:01:15+00:00 Statistical Shenanigans (part 2) http://www.hardballtimes.com/main/article/more-statistical-shenanigans/ http://www.hardballtimes.com/main/article/more-statistical-shenanigans/#When:05:01:15
There was a surprisingly positive reaction to my column a few weeks ago about the perils of correlation and regression—it appears that at least some THT readers are closet statheads. In this installment I take a look at how one can think about and interpret baseball analysis, specifically regression studies. This statistical tool is commonly used in sports analysis. Some of the lessons we discuss today also apply to non-regression techniques.

There are five things we’ll look:

  • First, how to determine that regression is the right tool for the job
  • Second, how to detect bias in sample data
  • Third, how to think through the regression equation to work out whether the dependent variables make sense
  • Fourth, how to interpret the results, in particular the coefficients
  • And fifth, what some watch-outs are when drawing conclusions

To help ease the pain we'll use plenty of examples to illustrate the relevant points. Let’s get cracking.

1. The right tool


Irrespective of whether you are poring over a regression, an important question is whether the analyst chosen the best tool for the job.

Regression is a much overused tool that often favored by academics—especially economists—but not always the best approach. Regression analysis is easy and convenient: you have a bushel of data and are unsure of the interdependencies—a natural tendency is to chuck it into a regression and see what falls out. This approach usually causes odd results.

The first question to ponder is whether a regression analysis is required. A perfect illustration is the use of regression to calculate linear weights (LWTS). The LWTS equation we want looks something like this: 
LWTS = a + b*1B + c*2B + d*3B +e*HR

The a,b,c,d coefficients represent the value of the various hitting events. Running this equation for 2002 game data gives the following coefficients: 
a = -4.5 (this is average runs per game)
1b= 0.47
2b= 0.81
3b= 1.09
HR = 1.43

Number of game in regression = 2,426

Superficially, the events appear weighted correctly. But they are not—both doubles and triples (which are relatively less common) are overvalued—this is a foible of the regression. If you do this for different years you’ll see the less frequent events jump around in value quite a lot, which is nonsensical. The valuation for triples is especially nonsensical. In some years it is close to a home run in value while in others it is closer to a double. The triple's rarity creates statistical noise in the equation, resulting in an error.

How do we know whether to use regression or a different tool?

The answer lies in having a deep understanding in whatever it is you’re trying to model. For instance, scoring in baseball depends on how many men are on base, which base these men are on, and how many outs are left. We can represent each base/out combination as a different state. If you have some mathematical background you’ll realize this could be modelled as a Markov process. On the other hand, thinking about baseball as “getting on base” and “moving runners over” will lead you to BaseRuns.

One tip is to identify how linked the outcome is to the dependent variables. In our LWTS example it is clear that hitting events are closely tied to offensive contribution, which speaks to a more fundamental (non-regression) model. Were we trying to link two things with no obvious link—say, payroll to wins—regression is probably better suited.

When a causal link is less obvious, regression probably will be a better right too. For instance, some of the work that Colin Wyers has been doing on wins and MRP. Regression should always be a second or third answer, never the first.

2. Bias in the Data


Biased data is one factor that will invariably lead to wonky conclusions—this affects all types of analyses, not just regressions. Selection bias happens a lot more frequently than you might imagine. Every time a study imposes an at-bat cut-off (or any arbitrary cut-off), bias is an issue.

Consider Jim Albert’s age-curve analysis. Jim’s study tries to work out age curves for ball players and tease out how it changes by decade of birth. Jim concludes that overall average peak age is 28.4 but for some decades, for example hitters born in the 1960s, it crept up to 30. That is substantially different from the oft quoted and generally accepted age peak of 27. What’s going on?

A 4.0 GPA isn’t required to work out that we have selection bias!

If you look at the criteria that Jim uses to select hitters he has a 5,000 career PA cut-off. This means that only very good hitters qualify for the study. In fact, we’d expect that the best hitters, those with 5,000 PA, probably have longer careers because either they peak later or don’t have a particularly steep drop-off.

Tellingly, the number of players included in the study rarely rises above 100 per decade. Given that thousands of players register at-bats every season, players with at least 5,000 plate appearances are the elite of the elite. Jim’s study is not finding the age curve of your average hitter, but rather finding the age curve of a select group of uber-batters.

Players who are less good may peak earlier, or may have a steeper decline phase that dramatically alters the shape of the age curve. To account for this effect, a different study needs to be run. In fact, a rigorous analysis would cut the data by position, handedness, and talent (based on regressed OPS) to work out age curves for different player types.

This example is typical of many analyses. Remember that any criteria used to choose a sample, either before or after the data have been captured, has potential to introduce bias. If this happens the insight and conclusions must be caveated appropriately.

3. Making sense of the variables


An analysis using the wrong variables is about as useful as a credit card, sans credit. There are no shortcuts except common sense and logic. Here’s a slightly facetious example that proves that team OPS and team ERA have nothing to do with wins. Don’t believe me? Run the following regression (go on, do it): 
Wins = a*winning% + b*teamOPS +c*teamERA

It will spit out:
Wins = 162*winning% + 0 *teamOPS + 0*teamERA

As promised teamOPS and teamERA are completely unrelated to wins!

The problem, as I’m sure you can see, is that winning% absorbs the effect of OPS and ERA—in other words, the model suffers from what statisticians pithily call multicorrlinearity. It is an obvious problem, but would still exist (more subtly) if we swapped winning% for runs scored and runs allowed. Someone who knew nothing about baseball would infer that OPS and ERA aren’t important.

This isn't the only problem—the equation is tautological (wins=game*win%). Sometimes it is almost impossible to get around this issue.

A couple of years ago David Gassko penned an article about why teams outperform Pythagorean records, which contained this subtle flaw (sorry David). He concludes that one of the main factors is performance of the bullpen in close games—he uses a regression to calculate the effect, which he terms leverage.

However, he uses saves as an independent variable. Of course, teams that rack up more saves will win close games and outperform their pythag—by definition a save equals a win in a close game. Using a variable dependent on winning in close games to determine win difference from Pythag isn't correct. A better approach would have been to use a metric like relative bullpen ERA, which isn't polluted by the save stat. David, Guy and I had a good discussion on Ballhype about this.

Unfortunately there is no recipe to wheedle out unsuitable variables, but rigor and thought go a long way. I find it useful to apply three tests.

  • First: Look at the independent variables and ask whether they are correlated with each other, or indeed if they are closely and obviously linked to the dependent variable. If they are, omit some, or run a correlation and see.
  • Second: Systematically go through each variable and work out what effect it is testing. Try to build a counter argument to see how robust the hypothetical effect is—identify the weak spots in the approach and address them in your commentary.
  • Third: Take a blank sheet of paper and ask what over variables you’d possibly include. Refer back to the model to see if anything is obviously missing. Apply 1) and 2) above to make sure they will add new information to the model. If so include them; if not don't.

Let’s try this approach by looking at a study that attempts to regress the independent variables below on attendance.
1) Games Behind (sum of GB for both teams)
2) Whether the game is a weekend game
3) Whether the game is a night game
4) Population of home city
5) Unemployment rate of home city
6) Per Capita Income of home city
7) Distance between the teams' two cities

Okay. Let’s apply the first test which is to work out whether any of the independent variables are correlated. Here are a few potential snares:

  • Sunday games tend to be day games, so there is a chance that variables 2) and 3) capture part of the same effect
  • The population of a city is likely to be related to per capita income (money attracts money), which means 4) and 6) could be ambiguous
  • Ditto for unemployment—a richer city will likely have lower unemployment, which throws 5) and 6) together

These points feel relatively minor so we’ll live with them for the time being—if I had to tinker I’d probably drop unemployment rate. Now let’s take apply the second test and look at the rationale for including each variable:

  • I’m not sure the sum of GB for both teams drives attendance. If a contending team is one game out of lead but their opponents are 30 then I’d bet that attendance would still be healthy. At the very least this needs to be separated into two variables.
  • Fans are more likely to flock to the yard when they aren’t working, i.e. at weekend or in the evening. Variables 2) and 3) make sense to me.
  • Cities that have more people or that are richer are likely to attract more fans—this accounts for 4), 5) and 6).
  • Distance between the two teams could be a bit of a red herring. Would Braves fans travel to Chicago but not San Francisco to watch their team play? Probably not—this doesn’t feel like a real effect for me

The final test is to think through whether there any are other variables missing (this is really is the realm of brainstorming). Here are a couple of ideas:

  • Ballpark age is likely to be a factor, especially in recent times
  • Ballpark amenities: Concessions, parking, proximity to public transport
  • Depth of fan base (there are Yankees fans everywhere)

Some of these are difficult to measure but the point is that by following a reasonably rigorous approach it is easy to pinpoint the strengths and weaknesses of a model. It’s amazing how far a little thought goes.

Arriving at the best regression takes time. The discerning analyst should try multiple combinations of different variables to see how coefficients and significance changes across different models. This will give a sense of what variables should be included and which omitted.

4. Results and interpretation


Exhaustion might be setting in, but our most important work is still ahead. Correctly interpreting the results is the trickiest part of any analysis, regression or otherwise. There are two steps: First, understand the structure of the regression equation to allow correct interpretation, and second, develop the insight from the results.

Understand the equation

If the regression equation is complicated (e.g. is a logarithm or a logit) then some mathematical gymnastics may be required to translate the coefficients into something meaningful.

Let’s take a look at a simple example. Suppose you saw the following correlation (more details here):
ln(player salary) = 3.681*OBP + 2.175*SLG + …..

The 3.681 coefficient is meaningless because the dependent variable is a logarithm. Say we want to find out the impact of a 0.100 OBP increase we have to take the exponent of 0.368, which gives 1.44. This means at extra .100 points of OBP increases salary by 44%. It is always helpful to read the notes to the equation so you know how the authors have presented their results.

Once you have a feel for what the coefficient means you can interpret the equation and start to test some of the underlying assumptions. For instance, take David Gassko's DIPS 3.0 equation:
DIPS ERA = (-0.041*IF+0.05*GB+0.251*OF+0.224*LD+0.316*BB-0.12*SO+0.43*HBP)/IP*9

The GB coefficient, for instance, says that for every extra GB a pitcher gives up DIPS ERA increases by 0.05/IP*9. Think about that for a second. The assumption is that all hurlers give up ground balls in a similar way. If hurler A only gave up hard ground balls that found the gap while hurler B gave up soft worm burners that always lollygagged to the shortstop then we expect a difference in the GB contribution to ERA. However, although some pitchers can induce softer grounders than others, the effect is probably small and can be ignored.

Develop the insight

The next step is to develop the insight. This is largely predicated on deep understanding of what you are analysing—there is no substitute for expertise. A skeptical eye is critical, so always look for alternative explanations.

A good example is the Jim Albert paper we discussed earlier. If you cast you mind back you’ll remember that Jim concludes that peak age has increased in recent decades. The obvious explanation is better health, fitness and nutrition.

A good analyst won’t be satisfied with that. Are there any other reasons? Yes—absolutely. Jim defines peak age using linear weights per plate appearance. We know that over the last 15-20 years run scoring has increased. Could this be responsible for part of the age effect we are seeing?

If run scoring has become easier then we’d expect LWTS/PA to drift upwards over time—this would shift the age curve. Given the spate of power hitting since the 1990s this is a likely explanation. This explanation is equally as plausible as better nutrition.

Another example is a ludicrous paper on home field advantage (HFA) in baseball by a couple of professors at Georgia Southern University.

They model the propensity to win at home by looking a bunch of variables, including runs, runs squared (why?), one-run games, two-run games, and roster size (25 vs 40 man). The main conclusion is that HFA is more prevalent in close games (one or two run games) than in games where three or more runs are scored.

I’m sure you’ll agree that this conclusion seems a bit suspicious. Why should HFA evaporate in blowouts? It doesn’t make sense. Do the authors proffer any explanations? No. When there is no rational explanation for the result then that is a signal that something with the data or the study isn’t right.

A deeper look at the study reveals that the authors forgot about the impact of the bottom of the 9th and extra innings. This means that home teams are more likely to win by one or two runs than they are by three or more as, Tom Tango discovers.

There are no hard and fast rules on interpreting studies, and it is not uncommon for people to interpret the same results differently. It is often helpful to think through under what conditions the model would throw up exceptions. For instance, PrOPS, which is a regression model, underrates speedsters (they are more likely to turn a ground ball into a base) and overrates sluggards.

Check whether the results pass the sniff test and proceed to think up a bunch of possible counter arguments. Then use your baseball intuition and knowledge to pass judgement. If the answer is ambiguous, then either the wrong question was asked or more work is required. Issues normally lie hidden in the methodology or data selection so revisit those parts of the analysis for ideas of what may be wrong. Most important of all remain deeply dissatisfied.

5. Other watchouts


There are a couple of other tips and tricks worth knowing that we haven’t covered, namely statistical significance and effect size, and standardized coefficients.

Statistical significance and effect size

People bandy around correlation and regression as statistically significant without really understanding what it means. Significance is the confidence that we have in the results—and is calculated from standard errors. The higher the sample size, the lower the standard error so if we have a lot of data points it isn’t too difficult to demonstrate significance.

However, significance is irrelevant if the effect is small. Consider, say, a hypothetical study trying to work out a link between HFA and team OPS. Such a study may yield an equation like this, which has all coefficients significant at the 1 percent level:
Team_OPS = 0.001*Home_Team + …

Great. But check out the Home_Team coefficient. The equation says that we expect that HFA accounts only for one additional point of OPS (remember this is all fabricated). It may be significant but the effect is negligible to the point that it is not worth worrying about.

Sometimes effect size and significance work in the opposite direction too. An analyst can detect a strong effect that, because of data inadequacy, doesn’t appear significant. This is not an excuse to blindly disregard the effects fail our significance test—with different data or sample the effect may become valid. The trick is to keep an open mind and try to understand what is possible.

J.C. Bradbury’s DIPS study analyses which pitching components have the biggest impact on ERA. He does regressions for each year and concludes that, in general, BABIP is rarely statistically significant True, but a glace at table 6 shows that although BABIP coefficient is always negative and in many cases would be significant at the 10-20 percent level. This indicates that BABIP does loosely influence ERA, and indeed further DIPS studies have borne that out.

Standardized coefficients

Also in some analyses it is difficult to compare the relative impact of two variables. Imagine if you wanted ran a regression to see the impact of height and weight on the amount of food someone eats. From the equation that is spat out it is difficult to assess the relative impact of the two dependent variables because they are calculated in completely different units. Standardized coefficients adjust for this. A standarized coefficient will tell you that how many standard deviations the independent variable will change with a one standard deviation change in the dependent variable. It normalizes for both units and variance.

For instance, consider an equation that appeared in the THT 2007 annual that attempts to work out whether hitters or pitchers have more say on whether a pitch outcome is a groundball or not:
Match-up GB% = 0.67*hitters GB% + 0.33 *pitchers GB%

The author goes on to conclude that this means that hitters have a bigger influence on outcomes than pitchers do. However, this isn't necessarily true. First, it isn't anchored to the mean, as match-up GB% is a scale from 0-100, where 0 is scaled to the pitcher's GB% and 100 to the hitter's GB%. This means that every single batter pitcher match-up is using a different scale (based on their relative GB%). The right way to do this would have been to anchor the result around the mean—imagine a match-up between a .300 hitter (above average) and a .300 pitcher (below average) ... our expected result is not .300. The correct representation is +0.03 for the hitter and -0.03 for the pitcher.

Also the higher coefficient for hitters could simply reflect (indeed, likely reflects) greater variance among hitters than pitchers. The hitter coefficient tells us that a 1 percent GB-rate increase for hitters adds 0.67 to match-up GB%—however, that does not imply that hitters have more "influence" on GB outcomes—just more variance. Imagine if we take a 100 such match-ups all on a scale between 0 and 100 (these marks are not anchored). If the hitter GB% has more variance, then we'd expect the results to be closer to 100 more often than not—this is what the regression found. The fact that we refer to groundball pitchers rather than groundball hitters is a big clue. Use of a beta coefficient, which adjusts for variance would correct this.

One final point is to be careful about what conclusions you draw. The old adage that correlation is not causality is very true. Doing this stuff it isn’t too difficult to look like a complete ass. That is something I try to avoid … and you should too!

In summary

Phew. That was tough work, right? Anyway, I hope you’ve learned a thing a two about regression and will cast an even more eagle eye over any baseball analysis you see in the future, regression or otherwise.

Click here to learn about THT's download subscriptions.]]> John Beamer 2009-03-19T05:01:15+00:00 Statistical shenanigans (part 1) http://www.hardballtimes.com/main/article/statistical-shenanigans/ http://www.hardballtimes.com/main/article/statistical-shenanigans/#When:05:05:15
Correlation and regression coefficients are perhaps the two most abused statistical measures by (baseball) analysts. How often do you see a baseball study quoting a correlation of 0.2, or an R squared of 0.49, and being told that the result is meaningful? Quite often I’d posit. Is it? Some studies say a correlation of 0.3 is strong, others dismiss it. Who is right?

As you probably imagine the answer isn’t simple. Regression and correlation are two very useful tools, no question. But one must be clear about their limitations before drawing meaningful insight from data. Today I want to share with you three lessons that I urge you to heed the next time you come across a study relying on correlation or regression. In part 2 we'll spend more time specifically on interpreting regression analyses—this article focuses mostly on R and R squared metrics.

(Note: Nothing I’m saying is this article is new. Others like MGL, Tango and Phil Birnbaum have written extensively and more lucidly than I ever could on this topic. What I want to do is to use real data to show some statistical watch-outs.)

Some Definitions

Before starting let’s be clear on definitions. Correlation is defined as the degree of relationship between two data sets (technically it is the amount of shared variance between two data sets). A correlation is a unitless number ranging from 1 to -1. It is denoted by the letter R. An R of 1 implies a perfect relationship—if you were to plot the two variables you'd be able to draw a straight line through all the points. If you take a ton of towns and cities and plot the distance between them in meters on the x-axis and yards on the y-axis the R is 1 (clear relationship). If you plot meters on the x-axis and, say, height above sea-level on the y-axis, R is close to zero (absolutely no relationship).

R squared is a frequently used statistic. This is simply R, well, squared. If R = 0.5, R squared = 0.25, and so on. R squared is a common output from a regression analysis and is a measure of variance in the data. We'll expand on these definitions later. At this point all you need to know is that correlation and regression are intimately related.

Lesson 1: Understand the context

That’s enough on definitions.

Let’s dive into data and have a look at some correlations. A common technique to determine whether a team/hitter/pitcher has any talent is to run a year-to-year correlation. This works on the premise that if the talent you are trying to measure is a skill then a player who shows more of that talent in, say, 2008 will repeat in 2009.

We can do this for batting average. To overcome sample size limitations I took all player seasons going back to 1980 and created paired samples by using even and odd years. For instance, Bonds 1990 and 1991 is one paired sample; his 1992 and 1993 is another; and so on. This gives us 7384 paired samples—which should be enough to get a reliable correlation.

Below is the graph we get if we plot odd against even years assuming a cut-off of 100 at-bats in both years. (We’ll return to this assumption later.) This leaves 3,602 paired samples.

image

We can see a relationship and our calculator reveals an R of 0.37. We can interpret this as follows: If a player’s batting average is one standard deviation above the mean in year one then in year two it’ll be 0.37 standard deviations above the mean. To put some numbers to that if in year one a player hits .300, mean batting average is .267 with a standard deviation of .033, then we expect that player to bat .280 in year two.

Would you be prepared to take that at face value? Is an R of 0.37 a lot? What does it really mean? Is batting average a repeatable skill?

To probe these questions we must understand the context of the study. The first concern is the at-bat cut-off. By having a lower limit of 100 at-bats we’ll have a bunch of bench players and pitchers in our sample that could bias the data. After all, our intuition tells us that some players have more batting talent than others.

What happens if we push up the at-bat cut-off to 300 at-bats? R rises to 0.46. 400 at-bats? R increases again, this time to 0.50. If we keep increasing the at-bat limit we find a startling relationship: the more at-bats players have the stronger the year-to-year relationship.

This actually isn’t too surprising. Correlation is dependent on two factors. One is the spread of talent as, obviously, the more diverse the talent base the greater the likelihood that a relationship will show—think about it, if everyone bats .280 R will be zero. Two is the number of trials in each sample (number of at-bats) as this reduces the uncertainty in our measurement.

So by upping the at-bat limit the correlation improves as the error around each player sample decreases. The implication is profound though—we can get a vastly different Rs just by manipulating data differently. At an extreme if we had infinite trials our R would be 1—a perfect relationship! When looking at a year-to-year correlation it is important to understand the context.

Let me show you something else surprising. Reduce the at-bat cut-off to 30. What R do we get? Unbelievably it shoots up to 0.53. In fact, here is the correlation across a whole range of different at-bat cut-offs.
Cut-off       # batters     R
1             6996          0.33
10            5890          0.5
20            5420          0.54
30            5072          0.54
50            4506          0.51
70            4034          0.4
100           3602          0.37
200           2550          0.43
300           1801          0.46
400           1141          0.5
500           556           0.46
550           321           0.41
600           90            0.34

That doesn’t fit with the theory above. The issue here is deeper than the limit we place on the at-bats. There is something odd going on with the other determinant of correlation: the spread in talent.

It turns out that we are at the mercy of selective sampling. Think about it: by definition players with fewer at-bats are likely to be worse performers. Between 30 and 300 at-bats we are adding a ton of low-quality hitters that shifts the shape of the talent curve and makes the regression appear stronger. In our original lingo, the spread in talent has increased dramatically.

image

This confuses our conclusions. There is a danger that by using a cut-off of 30 at-bats we’d conclude that the batting average is a stronger talent than it really is. To prove the point the R between batting average and at-bats is 0.55, suggesting, rightly, that better players get more playing time. The old aphorism that correlation doesn't imply causation is certainly true here.

Lesson 2: Interpret correctly

Another correlation debate doing the rounds in stat circles was the conclusion by the authors of a book called Wages of Wins that payroll in baseball isn’t strongly linked to wins. To prove this they run a regression between payroll and wins and report an R squared of 0.18.

Their argument is that the R squared is quite small. In statistical lingo the variance in payroll only explains 18 percent of the variance in wins. Other factors such as luck, strength of the farm, weather, and God only knows what else—we are not told—account for the remaining 82 percent.

The issue is that we have no idea whether an R squared of 0.18 is meaningful or not.

The first test is to look at the study and apply lesson one: understand the context. If we only take the first two weeks of the season what will the data show? Not a lot I’d guess. It doesn’t need a post doc to work out that two weeks is far too short a period in which to measure talent. As we learned from the batting average study, the greater the number of trials the higher the R squared. Over a couple of weeks an R squared of 0.18 is a lot more impressive that if it was for two seasons.

As it happens the data spans 162 games or a season—does that make the 0.18 impressive? Bear with me ... but we simply can’t tell. Let’s revisit the spread in talent argument to work out how best to interpret the results.

Imagine the quite ridiculous situation where each team has the same payroll. Now even if all teams were of equal talent they wouldn’t all win the same number of games. Some would be lucky, others less so. Either way the R would be 0. Suppose one team added $7m to its payroll and wins a few more games as a result. An R squared of 0.18 in this case is quite impressive—after all just one team has accounted for all this variance.

On the other hand, each team could have vastly different payrolls but with a much looser association to wins. An R squared of 0.18, the SAME as above, in this context would be much less impressive.

The point is that we have two effects counteracting each other. The 18 percent could be caused by a really strong link between payroll and wins but little spread in payroll among teams, or could be caused by a large spread in payroll but only a slight link. We can’t tell by looking at the R squared alone! Let me repeat that. An R squared of 0.18 tells you absolutely nothing except that there is some sort of relationship.

We can glean a bit more information if we dig a little further into the data. Behind every regression stands an equation that gives us more information and the regression coefficients tell us the size of the effect. Here it transpires that a win costs $5 million. Is this a lot? I’ll leave that for you to debate.

How does this change if we increase or reduce the number of trials? The short answer is it doesn’t. Even if only use a week’s worth of data this $5 million stays the same. However, the uncertainty in our answer greatly increases. If we do a series of weekly correlations we’ll see that one week could give us $15 million a win while the next may give us $2 million a win. A longer time period will give us tighter confidence intervals, which means we more certain of the result.

Surely 18 percent R squared tells us something?

Yes, it does. It allows us to answer the question: how important is payroll when trying to work out how many games a team will win in a year? The answer is that payroll variance accounts for 18 percent of the total variance. In math speak if the standard deviation of wins in a season is 11 then variance equals 121. Taking away 18 percent and the remaining variance is 99—put in English knowing a team's payroll allows us to reduce the error in our estimate by one win.

What accounts for the rest of the variance?

Luck is probably the main factor. If we strip this out the maximum R squared we can feasibly get is about 0.5 (see note at end). In this context an R squared of 0.18 suddenly doesn’t look too shabby after all!

Lesson 3: Apply the results appropriately

The foibles of regression and correlation we discuss above illustrate perfectly why it is essential to understand regression to the mean when analyzing baseball statistics.

We saw above that the higher the number of trials the stronger the correlation coefficient. This has implications when we try to evaluate talent. If player A has hit .300 is 30 at-bats and player B has hit .280 in 300 at-bats, who is better?

To answer we must use regression to the mean.

The concept is straightforward but critically important. Dave Studeman wrote a very readable article on this a couple of years ago—it is, however, worth repeating. It is most simply illustrated by reverting to the batting average data we used earlier. If we chop the year one batting averages into performance quartiles and compare the average from year one to year two we should see a convergence towards the mean. (Note: we’re using a minimum of 300 at-bats.)
Quartile Year 1 BA Year 2 BA
1          0.242          0.260
2          0.268          0.270
3          0.287          0.279
4         0.314           0.293

The regression to the mean equation is simply:

R = Ave AB
---------------
Ave AB + X

So, for a 300 at-bat cut off we have Ave AB = 490 and R = 0.46. This allows us to work out X, which is 575. That means in order to estimate a player’s batting average in year 2 we have to add 575 “average” at-bats.

If we add 575 average at-bats at 0.277 we get:
Quartile Year 1 BA Year 2 BA Year 2 BA (Theoretical)
1          0.242          0.260          0.260
2          0.268          0.270          0.273
3          0.287          0.279          0.282
4          0.314          0.293          0.295

Hey—it comes out pretty close! Another test is to see how our correlation adjusts based on the number of at-bats in the sample. Below are the correlations we’d expect to see with out batting average data adjusting for sample size.
Cut-off       Count         R             Expected R
1             6996          0.332         0.297
10            5890          0.499         0.33
20            5420          0.543         0.345
30            5072          0.536         0.357
50            4506          0.506         0.377
70            4034          0.404         0.395
100           3602          0.369         0.411
150           3008          0.404         0.433
200           2550          0.427         0.45
250           2164          0.438         0.464
300           1801          0.465         0.476
350           1489          0.476         0.486
400           1141          0.5           0.497
450           829           0.474         0.508
500           556           0.456         0.517
550           321           0.412         0.527
600           90            0.336         0.539

We can see that although it works well around between the 150-450 at-bat range, outside of this it breaks down. This is because above 500 at-bats the spread in talent becomes smaller (more elite hitters) and below 100 at-bats the spread in talent is wider (more quad-A players). We know that a hitter like Albert Pujols is going to be a lot lot better than Brad Ausmus. We’re not taking that into account as we’re just regressing to the overall mean.

This raises another important point, which is we must always regress to the most appropriate mean. There are a number of ways to approach this:

  • Rather than use single season plate appearance we can use career plate appearances. A player who has more career at-bats is a better player so should be regressed to a higher mean
  • Use any other available information when regressing, particularly if little at-bat information is available. Examples are: handedness, size, weight, line-up spot

I want to leave you with a two more profound insights that regression from the mean leads to but on the pitching side of the ledger:

  • After half a season bullpen performance regresses about 75 percent to the mean. In other words it is very hard to tell anything about bullpen talent based on half a year's worth of data
  • After a full season the amount to regress a starter's ERA is about 70 percent whereas for a stat like FIP it is closer to 40 percent. That doesn't mean that Johan Santana is suddenly going to register an ERA of 4.50 next year—he's got a decade of pitching seasons to regress to. But it does mean that Tim Lincecum might not be quite as good as we thought (although his 2008 FIP was especially impressive)

Rounding it All Up

Today we’ve covered some basic but critically important statistical concepts. Apologies for the heavy reading and especially to those who are fluent in these concepts—these concepts are pretty fundamental to any baseball analysis.

Happy data crunching, folks!

NOTE: CALCULATING MAXIMUM R SQUARED FOR PAYROLL AND WINS
R = var(expected)/var(observed) = 85/110 = 0.7 … and … R squared = 0.5.

There is also a more complicated method to regress to the mean outlined in The Book. This involves using mathematical gymnastics to compute the implied observed variance from each sample point (ie, each batter) and dividing the expected variance by the implied observed variance to get an R, from which you can work out the regression to the mean factor.

Click here to learn about THT's download subscriptions.]]> John Beamer 2009-03-02T05:05:15+00:00 A season full of surprises http://www.hardballtimes.com/main/article/a-season-full-of-surprises/ http://www.hardballtimes.com/main/article/a-season-full-of-surprises/#When:05:05:15
Let's take a look at two of the surprising stories that have emerged this year and whether they'll be sustained.

Tampa Bay Rays


For as long as anyone can remember, the AL East has been a two-horse race between the Yankees and Red Sox. In fact 2007 was the first year in 10 when Gotham's stranglehold on the division was finally broken. The one other certainty in the AL East has been that Tampa Bay would perennially pick up the wooden spoon.

Alas, no more. After a decade when the Floridians hoarded draft talent by virtue of being so poor, the assembled motley crew has started to perform. As we currently stand, the Rays have the best record in the junior circuit and hold a slender 0.5-game lead over the Sox in baseball's toughest division. Had this article been penned last week the results would have been wildly different—back then Tampa was the hottest team in baseball, but since then the Rays have been on a tough six-game losing streak.

Can they maintain their dwindling division lead?

The betting markets believe that the Red Sox are marginal favorites, with the Rays hanging on to their coat tails. Dial back to last week and the Rays were considered favorites, which shows just how quickly luck can change in baseball. Have a look at the Tradesports graph below:

image

There are a couple of reasons why the betting markets think like this. First is history. As mentioned above, no team outside the Sox and Yankees has won this division in over 10 years. Second, the Sox are defending World Champions and man for man have a higher talent level than the Rays. Turn back to any preseason forecast and there is a 10-game difference between the teams.

Based on latest data this gap may have closed some, but you won't find many who think that the Rays are the better team. A quick look at pythagorean records confirms as much. The Red Sox are one game off their projected records while the Rays are three games ahead. Boston is the better team.

Unlike their contemporaries in the East, the Rays have been getting it done through pitching rather than hitting. The most productive batter on the team is Evan Longoria batting .281/.383/.525—a good, but not great line. Taken as a whole though the batting isn't terrible. Only one player among the regulars and semi-regulars, shortstop Jason Bartlett, has an OPS+ lower than 90. There is something to be said for mediocrity!

Pitching, on the other hand, is a different story. A rotation of Scott Kazmir, Matt Garza and James Shields is strong. Andrew Sonnanstine, the worst of the starting five, has a very respectable ERA of 4.58 and has won 10 games to boot. All these guys are 26 and under and represent a fine foundation from which to build. The bullpen is also strong with Troy Percival and Dan Wheeler anchoring the starters. A glance down the roster reveals few weak links.

A combination of batting consistency and stingy pitching has held the Rays in good stead. Will it be enough to topple the Sox? Tricky question ... but probably not.

Cleveland Indians


The biggest surprise of the season has been the form of the Cleveland Indians. Last year the Tribe dominated the AL Central and many thought that the young Indians team would dominate the division for several years to come. Midway through the season, Mark Shapiro's team haven't even won 40 games and are some 14 games behind the division-leading White Sox. The team has even had to trade prized pitcher C.C. Sabathia. What's gone wrong?

It's easy to point fingers but the first culprit is the famed batting line. Travis Hafner, who has been MVP-esque in the past few years, has been severely below par for this campaign. He line is a paltry .217/.326/.350—although some will say that the decline started last year. A DH at 31 doesn't bode well for the future.

The rest of the offense has been a mixture of good and bad. Well, to be more accurate there has been one bright point in Grady Sizemore. The center fielder continues to reaffirm his considerable talent but outside of him it is a woeful tale. Production from first, second and right field has been dreadful—Ryan Garko, Jamey Carroll and Franklin Gutierrez all under performing. The problem is compounded with a lack of depth on the bench.

Andy Marte, who a couple of years ago was the most touted prospect in baseball tried his luck again in the bigs. After 75 at-bats his line is .160/.203/.200—another stark reminder to teams contemplating taking a prospect from the Braves.

What about pitching?

Actually not bad. Sabathia continued to be as effective as usual with a 3.83 ERA in 18 games before being traded to the Brewers. Faustino Carmona, who played a starring role in last year's run has also been surprisingly effective this time around (to the slight surprise of quite a few pundits).

And don't forget Cliff Lee. Who can't forget his stellar start to the year when he won his first six games and had as sub 1.00 ERA until mid-May. Since then he has continued to pitch well and currently sports a 12-2 record with a meager 2.31 ERA. Other members of the rotation like Jake Westbrook (3.12 ERA) and Aaron Laffey (3.45 ERA) have proved useful.

It is the bullpen where the team has struggled. Closer Joe Borowski is showing his age and sports a hefty 7.36 ERA. In fact only Rafael Perez and Masahide Kobayashi are showing any sort of form in the pen.

Does some medicore batting, a poor bullpen and a healthy rotation really cause a 14-game deficit? Nope. The story lies in our old friend Pythagoras. In 2008 the Indians have been unlucky. They are underplaying their pythagorean record by some seven games. That would put them at a .500 record and level with their preseason rivals the Detroit Tigers.

Don't expect to find the Tribe on the floor of the division come September; they won't be on the top either.

Up Next


We'll continue this series in a couple of weeks time when we'll look at the Minnesota Twins and New York Mets.

Click here to learn about THT's download subscriptions.]]> John Beamer 2008-07-14T05:05:15+00:00