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# THT's Fantasy Archives

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## Fantasy values by parallax

parallax n. : The apparent displacement of an object caused by a change in the position from which it is viewed.

Generating dollar values for fantasy players can be tedious. A common approach is to sum the stats above replacement level in a category and then divvy up those stats among a portion of the total budget and add up the contributions for each player. That’s doable, but there are challenges. For one thing, there are wrinkles to handling rate stats like BA and ERA and “clumpy” stats like saves and steals. Also, there is something unrealistic about treating categories as freely floating when there are obvious dependencies, such as between home runs and RBIs, or ERA and wins.

There is another approach. This one has its own challenges, including a longer time to derive the values, but it sidesteps the bumps with the usual method, and it’s easily tailored to many formats.

The key is to look at fantasy value from a different angle. Suppose that Roy Halladay is valued at \$30 in your league. It’s true this says that Halladay’s stats are “worth” \$30. But you could re-state this to say that paying \$30 for Halladay neither helps nor hurts your odds of winning. If you get Halladay for less than \$30, then your odds of winning go up, and if you pay more than \$30, then they fall. But paying \$30 neither raises nor reduces your odds; if it did, then \$30 would be the wrong price.

So we have turned a statement of value (“Halladay is worth \$X”) into a statement of probability (“Drafting Halladay at \$X neither raises nor lowers your odds of winning your league”). Why is this good? Because now, to find the value of a player, we need only to find the price at which ownership of the player doesn’t alter your odds of winning. There are no other calculations—no defining of the spread of player stats, no breakdowns of categorical value.

Note that this method works in fantasy because we have a fixed budget. In the real world, things are looser—there is no price at which owning C.C. Sabathia “hurts” your odds of winning. However, real businesses are in the business of maximizing profits, and C.C.’s salary can surely hurt those.

So we have the bare bones of an approach. Let’s create a two-team league. (In this exercise, we’ll stick with pitchers, so that we don’t have to worry about accommodating multiple positions.) On one roster, we’ll put our player of interest—in this case, Roy Halladay. Halladay always appears on this roster. The other eight slots on Roy’s roster, and all nine slots on the other one, are open:

```Roster #1              Roster #2
============           =========
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher```
The open slots will be randomly filled with 17 distinct pitchers (no duplication within or across rosters.) After populating the rosters, we will determine the side that “won,” based on whatever categories we have in our league, and behaving as if these were the only two teams in our league. For example, in standard 5x5 roto league, there would be five categories—wins, saves, ERA, WHIP, and strikeouts. Finishing first in a category in our two-team league is worth two points, and finishing last is worth one. We’ll repeat this exercise 1,000 times for various roster configurations and track the winners.

(Why do we need to track only two rosters, even if our real league has more teams? Because each Halladay-less roster is identical. Suppose that there are 10 other rosters like Roster No. 2. Each is indistinguishable from Roster No. 2, because all rosters draw from the same pool. If we can balance Halladay’s roster with Roster No. 2, then we’ll also have balanced Halladay’s roster with the other rosters. A one-in-two chance of beating Roster No. 2 equates to a 1-in-12 chance of beating the league.)

Our ultimate aim is to make Halladay expensive enough that his team wins exactly half the time. “That’s swell, but you have no dollar figures. So you can’t turn your probabilities into prices.” And that’s true. We need points of reference.

How many points? Perhaps as few as two. If we have two points of reference, we might be able to adapt the method of parallax, which is used by astronomers to determine the distance to stars. But that’s getting ahead of ourselves, because we don’t have two points of reference.

But we do. For any fantasy league, there are two statements that we can say with certainty (both statements require us to identify the draft-worthy pool of pitchers—we’ll tackle that later):

1. The last drafted player is worth \$1.

2. The worth of a slot that freely floats among all draft-worthy players is the average price spent on that slot. If owners in a 12-team league historically spend \$99 on nine pitchers, then a pitching slot that freely floats among all 108 draft-worthy pitchers is worth \$11.

Now, in a real auction, you can’t draft a “freely floating” slot. However, in our simulation, we can—in fact, in our diagram, each slot labeled “Pitcher” is exactly that. In a particular run of the simulation, the slot could be worth \$1, or it could be worth \$50. But the expected value of the slot is \$11. (Actually, it is slightly less, since one pitcher—Halladay—is not available. But \$11 works for our purposes.)

Armed with our two points of reference, we can employ parallax. Here’s the approach: Roster No. 2 will never change—it will always contain nine freely floating pitching slots. For our first 1,000 runs, Roster No. 1 will also be the same. Over time, though, we’ll swap free-floating slots (worth \$11) for the last drafted player (worth \$1). Each switch means a drop in value of \$10 for Halladay’s team.

Eventually, we’ll reach a point at which Halladay’s roster wins only half the time. Since the odds are the same, the total value of each team must also be the same. We know the value of Roster No. 2 (\$99), and of the non-Halladay slots on Roster No. 1 (either \$1 or \$11), so it’s easy enough to solve for Roy’s value.

If we replace all eight floating pitchers, we could end up with a graph like this (not real numbers):

Here, when Halladay is paired with eight freely floating pitchers, his team wins more than 75 percent of the time. However, when he’s stuck with eight \$1 pitchers, he wins only about 15 percent of the time.

To find Halladay’s value, just read off the point at which the trend line crosses 50 percent. In this case, that’s around 3.5. So Roster No. 1 would be balanced with Roster No. 2 if 3-1/2 slots worth \$11 were replaced with the same number of slots worth \$1. Ergo, Halladay is worth \$35.

That’s the idea, anyway. Will it work?

NEXT WEEK: Will it work?

Posted by John Burnson at 4:00am

## Waiver Wire: NL

Yorvit Torrealba | Colorado | C
YTD: .277/.339/.358
True Talent: .257/.315/.385
Next Week Forecast: 0.4 HR, 2 Runs, 2 RBI, .254 BA, 0.1 SB
It's kind of surprising to see any starting catcher still out there on so many waiver wires, particularly one who's getting so much PT of late. Torrealba has supplanted Ianetta as Colorado's regular backstop of late, even though he's not been hitting any better (.276/.339/.356 in September). Tracy clearly must like the way Yorvit's handling the rotation—but whatever the reason, you can pick up a few more counting stats if you need a catcher, since he's so readily available. True Talent shows you he's about where he should be in his ratios, making him best suited for 15-teams NL leagues. Just remember that Tracy could also change his mind back at any time, and put Ianetta back in, but he's unlikely to do so while the team's pushing toward the playoffs.

Rafael Betancourt | Colorado | RP/CL
YTD: 9.5 K/9, 2.8 K/BB, 2.70 ERA
True Talent: 8.4 K/9, 2.9 K/BB, 3.49 ERA
Next Week Forecast: 0.0 Saves, 3.20 ERA
Huston Street's not much closer to returning, and Franklin Morales has started to falter with more exposure, as I expected he might, surrendering three ER in his last two outings. Betancourt swooped in to snatch the save the second time Morales got into trouble, and could get another look, particularly if Morales struggles again. Betancourt has done far better with Colorado than he did with Cleveland, mostly by controlling his walks, dropping from 4.4 to 1.9 BB/9, and has been a very good reliever in every situation but the closer's role in his career. Street should still be back at some point, so Betancourt's a longshot no matter how you slice it, but saves are saves, and he might pick up one or two more. He's still going to collect some strikeouts, too, and if True Talent sees a bit of a correction, it shouldn't be much. As save gambles go, he's better than most.

Ian Desmond | Washington | MIF/OF
YTD: .588/.611/1.000
True Talent: .225/.286/.348
Next Week Forecast: 0.1 HR, 0 Runs, 0 RBI, .216 BA, 0.1 SB
The Nats are taking a look at Ian Desmond, a mid-level prospect who's got more leather than wood in his repertoire, though you wouldn't know that from his YTD line. Obviously, that screams "small sample size," representing just 18 PAs, and he's going to slide closer to his True Talent levels the more he plays. In the minors, however, his power (.477 SLG across two levels) and improved plate approach (.51 BB/K, vs. .39 in six minor-league seasons) came together nicely this year. He also pushed his contact rate from .78 to .80, so he's seeing the ball better and getting good wood on it, making some improvement to be expected. He averaged a bit over 20 SBs in the minors, so he'll swipe a bag now and then, too, despite average speed. Unless he defies expectations and keeps mashing, he's good for only part-time work down the stretch, so only the deepest of NL leagues will find any value here; similarly deep NL keeper leagues might stash him away for 2010 if they need a MIF who might prove to be a skosh above replacement level.

Billy Buckner | Arizona | SP
YTD: 7.4 K/9, 2.4 K/BB, 6.79 ERA
True Talent: N/A
Next Week Forecast: N/A
Buckner's secondary stats should have led to a better ERA, but he's given up lots of longballs (1.7 HR/9) and hits (11.9 H/9) this year, which tells you how hittable he's been. Since returning to the bigs in September, he's shown a sharper curve ball, which he needs to use to succeed, and has put together two good back-to-back starts, with 12 Ks vs. four BBs, two ER and 14 Hs in 13 IP. He'll keep getting starts down the stretch, as will plenty of other Baby Snakes, so you can expect less-than-stellar defense and offense behind him. He should keep collecting Ks but could hurt your ratios, as he's been prone to meltdowns this year, and wins could be hard to come by, too. That makes him a moderate-risk-to-moderate-reward play, something to keep in mind if you want to roll the dice with him in your deep NL league.

Kazuo Matsui | Houston | 2B
YTD: .252/.302/.353
True Talent: .266/.320/.374
Next Week Forecast: 0.3 HR, 3 Runs, 2 RBI, .261 BA, 0.8 SB
Kaz picked up his 2,000th career hit on Aug. 15, earning him membership into an elite Japanese baseball honor society. As often happens when players are trying to reach a milestone, Matsui was pressing to reach the mark and hit poorly. A week later, he loosened up and started on a tear that's seen him hit .321/.360/.488 with nine extra-base hits and seven SBs in the three weeks since then. True Talent shows you he's still short of expectations, so that hot streak might last a little while longer, and it's important to note that five of those steals have come in the last week. Though he has occasional health issues, Matsui's been playing in nearly every game for the past several months, and should continue to do so, barring injury. Though his TT levels peg him as a worthy addition best suited for NL-only leagues deeper than 12 teams, shallower leagues can ride him for as long as those SBs and XBHs continue.

Blake Hawksworth | St. Louis | RP
YTD: 3.9 K/9, 1.5 K/BB, 2.36 ERA
True Talent: 5.2 K/9, 1.4 K/BB, 4.96 ERA
Next Week Forecast: 0.0 Saves, 4.90 ERA
Owners have given Hawksworth some love lately because of his four wins out of the 'pen, but vulture wins (or Hawk wins?) are hard to predict. What's easier to predict is a surge in his artificially low ERA, which has been helped by a ridiculous .236 BABIP—his FIP is 3.72, and his xFIP is 4.39. True Talent not only confirms that his ERA should rise, it shows that his shaky command is right on target, as is his lack of dominance. This is a guy who gets by on his control—he's most often compared to Jeff Suppan, whom I covered last week—so he walks a fine line between good and bad, and one day hopes to slide into the back of the Cards' rotation. There are relievers you can count on for strikeouts or ratio control (or both), where the occasional win or save is a bonus. Chasing vulture wins is foolish when that's the only expected return, and that's why Blake Hawksworth should stay on your waiver wire, no matter what league you're in.

Luke Gregerson | San Diego | RP
YTD: 11.0 K/9, 3.4 K/BB, 2.81 ERA
True Talent: 8.5 K/9, 2.1 K/BB, 3.82 ERA
Next Week Forecast: 0.0 Saves, 3.84 ERA
As a nice contrast to a reliever like Hawksworth, consider someone like Gregerson. Though the Punch-and-Judy Pads only managed to deliver Gregerson one relief win this season, he's delivered them plenty of Ks and very few BBs. He's done that throughout his short minor league career, with 10.2 K/9 in three seasons, mixing in a decent fastball with a much better slider. He'll give back a bit of that ERA, according to True Talent (his xFIP is just 2.84), but those strikeouts should continue. And he's much less likely to pick up many vulture wins with the Padres hitting behind him, but he's picked up 25 holds, if your league counts that. Even if yours doesn't, Gregerson makes a good roster addition for teams that are approaching their start/IP cap, or have already done so, NL-only league or not.

Josh Thole | New York | C
YTD: .423/.429/.462
True Talent: .245/.317/.335
Next Week Forecast: 0.1 HR, 1 Runs, 1 RBI, .242 BA, 0.0 SB
Jerry Manuel likes Thole's patient approach at the plate, and wants to hit him second, in front of David Wright, a good place to be. And Thole could be a good fit, as he's shown an outstanding eye in the minors (1.06 BB/K in five seasons) and an excellent 88% contact rate. He hasn't advanced higher than Double-A because his catching skills are still developing, but the Mets aren't too concerned with that right now, having lost eight of their last nine games fielding their Quadruple-A squad. Expect him to play at least 60% of the time in these last few weeks, and more than that if he keeps hitting—just don't expect him to hit for much power (.375 SLG in the minors, peaking at .427 last season). That makes him an NL-only option for deeper leagues, or for disappointed Mets fans (are there any other kind this year?) whose fantasy teams have also given up for the season.

True Talent and Next Week Forecasts courtesy of Heater Magazine.

Posted by Michael Street at 2:00am

## Waiver Wire: AL

Daric Barton | Oakland | 1B
YTD: .245/.357/.415
True Talent: .250/.347/.395
Next Week Forecast: 0.4 HR, 3 R, 2 RBI, .251 BA, 0.1 SB
Hitting .292/.381/.458 since his return, Barton is playing (almost) every day and showing exactly the sort of hitting skills that were long expected of him. True Talent thinks it's mostly illusion, but his seasonal BABIP is just .271, and can be expected to show some rise, though he's slow and hasn't hit the ball particularly hard. Especially in an OBP league, he could make a nice addition for the last few games.

Kyle Davies | Royals | SP
YTD: 6.3 K/9, 4.8 K/BB, 5.27 ERA
True Talent: 5.9 K/9, 1.4 K/BB, 5.18 ERA
Next Week Forecast: 0.3 W, 3 K, 5.91 ERA
When your YTD ERA is 5.27, and your BABIP is .285, it's very likely you're not a good pitcher ... and Davies isn't good. After this weekend, the Royals face Boston, Minnesota (twice), and the Yankees, so anyone not named Greinke is a questionable play to begin with. He'll be just 26 years old in 2010, and has proven to be very durable, so maybe there's hope for him in the future, but definitely someone to avoid in 2009.

Mark Ellis | Oakland | 2B
YTD: .270/.311/.411
True Talent: .259/.323/.404
Next Week Forecast: 0.7 HR, 3 R, 3 RBI, .257 BA, 0.5 SB
For his career, Mark Ellis has hit about .285/.350/.450 combined in August-October, and he was at it again this year until a rough series against Texas. Bad news for him is that the team faces LA, Texas, Seattle, and LA again. Seattle and Texas are both top three in run prevention, while LA is below-average on the season, but has a 4.27 ERA since the break, and a 2.56 ERA in September. The final series of the season may be Triple-A-quality pitching, as the Angels organize their rotation for the playoffs, but all-in-all, we'd avoid Ellis, historical trend notwithstanding.

Freddy Garcia | Chicago | SP
YTD: 6.2 K/9, 2.4 K/BB, 4.41 ERA
True Talent: 6.4 K/9, 2.4 K/BB, 4.57 ERA
Next Week Forecast: 0.4 W, 4 K, 4.57 ERA
Not really Freddy Garcia news, but Jake Peavy is starting tomorrow, finally, after recovering from a liner off his elbow in the minors. Garcia gets the Royals, Tigers, and Tigers again, if the rotation stays the same. Detroit has scored 4.61 runs/game this season, compared to a 4.81 league average, and they are marginally worse against RHP (.326 OBP vs .338—AVG and SLG almost identical). Freddy allows his share of fly balls, so the chance is there for an M-Cab-aided disaster, but for an AL-only league, this is a pretty good pitcher to be able to add this late. The Royals start should be good, and his 88 mph tomfoolery might even get him a couple quality starts against Detroit.

Esteban German | Texas | UTIL
YTD: .333/.400/.444
True Talent: .270/.347/.374
Next Week Forecast: 0.1 HR, 1 R, 1 RBI, .271 BA, 0.2 SB
German is a devastating leadoff hitter ... in Triple-A. Saving his career by posting a .419 OBP with 35 SB for the RedHawks after a dismal .245/.303/.338 performance in 2008, he's been useful for the Rangers with Michael Young being injured. Young is going to try to play, but if he's hurt worse than the team is letting on, look for some exposure for German, who can still steal a base per week given the PA.

Kevin Jepsen | Los Angeles | RP
YTD: 7.6 K/9, 2.7 K/BB, 4.56 ERA
True Talent: 7.1 K/9, 1.5 K/BB, 4.81 ERA
Next Week Forecast: 0.0 Saves, 5.32 ERA
You don't hear much about ROOGY's in bullpen roles, but Jepsen's split stats would qualify him, as they are the mirror image of typical LOOGY stats (.358/.413/.432 against LHB, .202/.250/.236 vsR). Kevin Jepsen looks like a closer and has the upper-90s velocity typical to that role. With Brian Fuentes having problems with RHB (.372 OBP, .463 SLG), Mike Scioscia has stated that Jepsen will be in line for some situational saves. Also, this is a guy to keep a close eye on for 2010 and beyond—his fastball/cutter combo already makes him playable, and when (if) his rebuilt arm re-learns the control of his nasty curve, he could be truly exceptional.

David Purcey | Toronto | SP
YTD: 8.6 K/9, 1.4 K/BB, 6.32 ERA
True Talent: 7.7 K/9, 1.9 K/BB, 4.99 ERA
Next Week Forecast: 0.4 W, 5 K, 4.34 ERA
Way back in 2001, the M's offered their 20th-round pick, David Purcey, a huge \$1 Million bonus to sign. He turned them down, and stayed healthy enough in college to become the 16th overall pick in 2004. Needless to say, much was expected of this pitching talent, but injuries derailed his train to Toronto. Finally, his 2008 showed just enough promise (8.0 K/9, 4.0 BB/9) that there was some optimism again. As can be seen from the True Talent line, there's still enough here to not give up hope, though a 47.3% career FB% suggests a pitcher ill-suited for pitching in the AL East.

Ryan Sweeney | Oakland | OF
YTD: .288/.342/.404
True Talent: .277/.338/.393
Next Week Forecast: 0.4 HR, 3 R, 3 RBI, .278 BA, 0.4 SB
In their irrelevance, few have noticed that the A's have been hitting well of late—.294/.364/.461 in September. Right Fielder Ryan Sweeney has been a big part of that, crushing the ball for a .360/.421/.500 September line. There's a lot of data supporting the modest TT projection, but—like Barton—he was more highly regarded as a prospect than his results have indicated. Also, like Barton, he is soft in the roto categories—homers and SB. But he should be one of the better batting average aids available at this point, if that's what a team needs.

True Talent and Next Week Forecasts courtesy of Heater Magazine.

Posted by Rob McQuown at 2:00am

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