There’s been a lot of gnashing of teeth lately by the Red Sox Nation—I should know, as I’m currently driving across the country with a card-carrying member. On some level, it’s not surprising; I’ve never seen any other fan base so strongly embrace a “cursed” persona, and the Red Sox held a 10.5 game lead over the Yankees as recently as July 7. Still, it’s clear that Red Sox fans’ growing apprehension has a lot more to do with the shape of the race through the season than the actual lead.

As of games played last night, Boston holds a 5.5 game lead over New York with 42 and 41 games left to play, respectively. The Red Sox have won 60% of their games so far this season, and even since July 7, a period in which the Yankees have made up five games in the standings, they won almost 56% of their games. If they win 60% of their remaining games, they’d end up with 97 wins and the Yankees would have to go 30-11 (winning 73% of their remaining games) just to tie the Red Sox.

Even if you subscribe to the theory that the more recent Sox are the “real” Sox (even though there’s no reason to ignore the first three months of the season), the Red Sox could be expected to win 95 games and the Yankees would have to go 28-13 (winning 68% of their remaining games) to keep pace.

Granted, the Yankees have won 74% of their games in the past five weeks, so if you’re a pessimistic Red Sox fan, you might be worried. But look at who they played in that stretch: the Angels (two games), Devil Rays (eight games), Blue Jays (seven games), Royals (seven games), Orioles (seven games), White Sox (three games), Cleveland (three games) and Tigers (one game). All in all, that’s only 13 games out of 38 against teams above .500.

So while it’s not outside the realm of possibility for the Yankees to catch the Red Sox, a two unlikely pieces would **both** have to fall into place:

1) The Yankees would have to play as well as they have the past five weeks against the rest of their significantly harder schedule (just 15 of 41 remaining games against teams currently under .500)

2) The Red Sox would have to play worse than they have for the past five weeks.

Neither of these is likely, and both happening are extremely unlikely. A quick glance at Baseball Prospectus’ PECOTA-adjusted postseason odds corroborates this admittedly crude analysis, giving the Red Sox a 91% chance of winning the division. This passes the sniff test: that number would be roughly correct if you assigned 30% chances to both the Yankees maintaining their recent form and the Red Sox slumping even worse than they have (0.3 * 0.3 = 0.09).

Of course, I haven’t even mentioned the words “wild card,” yet, though the shame of giving up the division to the Yankees would last at least until the first pitch of ALDS. So calm down, Red Sox fans, and stop worrying about the Yankees. You’re better off worrying about Eric Gagne giving up a big home run in the postseason.

###### Clutch?

**I have been pondering a question recently concerning Pythagorean won-loss records and I thought I would ask you if you could clarify it a little (I’m far from a statistics guru). Essentially I wanted to find a relationship between the performance of relief pitchers and teams that outperform their expected won-loss record as determined by Pythag. To do this I looked at the total WPA of relief pitchers on each team, isolated those teams with significantly high or low bullpen WPA totals (I took this as +/- 2) and looked at whether the teams with high bullpen WPA had a large positive deviation from their expected win-loss record and vice versa. **

For 2007 this gave me a sampling of teams with high bullpen WPA as follows: Angels, Cardinals, Diamondbacks, Dodgers, Indians, Mariners, Mets, Nationals, Padres, Rangers, Red Sox, Twins. These teams were a combined 29 games above their expected record.

The corresponding sample for teams with a low bullpen WPA was smaller: Reds, Orioles, Devil Rays, who are a combined seven games below their expected record.

This is a fairly crude analysis, however there clearly seems to be a correlation between a high WPA of relief pitchers and positive deviations from Pythag. The implications of this would be that the construction of a team can give it an inherent advantage over other teams with the same run differential. In other words, two teams may have exactly the same run differential, but the fact that one team has a comparatively better bullpen should raise that team’s expected won-loss record.

To compare the two teams and conclude that the reason this team outperformed its rival was entirely down to luck, would clearly be incorrect. Is this a fair conclusion? Would this analysis hold up in a larger sample?

- Stuart B.

**John Beamer:** I don’t think your finding is particularly surprising. Dave Studeman often looks at bullpen WPA as a reason for deviation from Pythagorean runs, and if you think about it it makes perfect sense.

By definition the biggest swings in win expectancy occur in close games at the end of the game. At this point your best relievers will be in the game. If you win a lot of close game then you’ll outperform your Pythagorean record and your relievers will get rewarded with a lot of positive WPA.

As to your final point, which is whether you can compare two teams with same run differential but different won-loss records and chalk the difference down to luck, then that depends. It is important to separate talent from luck. For instance, is the bullpen that is currently lights out able to maintain that for the rest of the year or are they playing above station? More often than not is the latter—remember that teams with better records tend to outperform their Pythagorean record!

###### Get the picture

**Okay, let’s all admit it: mainstream baseball doesn’t like sabermetrics. It’s too complex for the piddly noggins of most broadcasters to make sense out of. So why don’t we make things easy for them to see the benefit without having to worry about the details? I was specifically thinking of something like this:
**

While my categories are entirely arbitrary, and my numbers absolutely suck (I didn’t bother to polish them all off on a semi-equivalent scale), the benefit is that the sabermagicians can use whatever math they like to evaluate the player in X amount of categories, and create an easy visual reference in regards to what type of player they are.

Barry Bonds looks like a patient monster, Juan Pierre looks like a cracked out jumpy defensive specialist, and Hanley Ramirez looks well-rounded.

Ideally, we would also include durability (something involving games played, perhaps?) or somesuch, and consolidate OBP along with patience. Additionally, tossing in a “speed” metric wouldn’t be so bad.

Hell, toss in the THT clutch stat as well!

I really think that a method of reaching the public like this would be far less threatening, and would be something (like fangraphs or hittracker) that would really be accessible to the average fan. If you built-in a PHP type back-end to allow for comparison of players, it would be even **more**interesting.

Make the overlap obvious, so that you could see (visually) how Reyes and Ramirez stack up.

Obviously you’d also have to make the various categories expand equally. The ones I provided are exceedingly basic and I didn’t bother to go through all the legwork. I use IsoP for power, IsoD for patience, fielding win shares for defense, OBP for OBP, and BABIP for luck. I then take the median in each stat, and create a percentage of the median (since the middle line on the graph is ‘average’ and the outer limit is 200%, it means that the absurd win shares by good defenders fly off the graph, as does Bonds’ patience).

The best part about it is that it doesn’t matter how you decide to calculate the stats! No broadcaster will be getting confused over super-computer basement-nerd Robot “Moneyball”

Beanbot’s new “AwfgulARP6″ stat. They see a nice little graph, with nice little visual representations of ability, and they don’t even need any numbers! If it crosses the midway black line, they are above average at that position. If it crosses the high one, it mean they’re doing twice as well as average!

You can make the calculations complex to the point of being absurd, and it won’t make a difference to the audience.

I’d do this myself, but my math is marginal, and my ability to create new PHP back-ends to do statistical stuff is mediocre at best and currently being taxed to the limit on another project. But I beg you at THT to create an easily accessible segment of your site to appeal to the baseball world at large to the point where we see it on the backs of baseball cards, and next to the infoboxes during game broadcasts!

I beg you!

- Joshua M.

**Dave Studeman:** Great idea. I’ve basically dedicated my Internet career to using graphics to help people better understand baseball statistics. Hopefully, you can see that in my articles, on our team page, or my site http://www.baseballgraphs.com. It’s also why we give a lot of support to fangraphs.com, as well as John Burnson’s annual book, The Graphical Player. Heater magazine is also a great source of statistics and graphs.

Your spiderweb graphs are a very interesting idea. I often see these used on personality tests and the like. The key is that each one of the dimensions should be of equal importance, or the dimensions should vary to reflect each stat’s importance. Otherwise, the graph is misleading. I don’t know if that’s possible, but it’s certainly worth investigating.

Thanks for the idea.

**Bryan Tsao**: Another place I’ve seen something like this is in the team ratings section of Pro Evolution Soccer 2007. You’re absolutely right in that it’s a great visualization that allows for quick and easy parsing of a team or individual’s rating in a number of different categories.

**I was experimenting with the Pythagenport formula, and since I’m fairly new to the world of sabermetrics, I hit a bump in the road because I was wondering if, in the equation:**

X = .45 + 1.5 * log10 ((RS+RA)/G)

Is the log10 for the ((RS+RA)/G) part? Or is it stand-alone?

I haven’t taken statistics in college yet, so pardon my ignorance.

So I can see how it works, let’s use the Phillies’ information as it stands currently: 571 RS, 528 RA. What answer should I be getting?

- Bill B.

**David Gassko:** You’re reading that correctly. You take the logarithm of runs scored plus runs allowed per game. As the Phillies had played 104 games at the time of your e-mail, the exponent you should have gotten was 1.99.

However, the better formula for computing a Pythagoren exponent is Pythagenpat: ((RS + RA)/G)^.287. At this point, even Clay Davenport, the inventor of the formula you quoted, has said so. I won’t get into why because this answer is geeky enough as is! The answer Pythagenpat gives in this case is 1.97.

## Leave a Reply