Baseball Musings: WRAP Up

November 06, 2004

WRAP Up

The NY Times has an interesting article on applying game theory to measure the worth of a player.

The method's logic is actually very simple: every confrontation between pitcher and batter affects, however marginally, each team's chances of winning. With various numbers of outs and men on base, a double or a strikeout or even a runner-advancing grounder either adds or subtracts a specific amount from the inning's run-scoring potential. Depending on the game's inning and score, each of those amounts takes on varying significance to the final outcome.

"It's just our way of looking at the world from studying game theory," Lonergan said. "Each team starts the game with even probability, and ends at either 0 or 1. In between, you're looking at what the players are doing for their team."

An example: when Beltre stepped to the plate on Aug. 23 with the Dodgers down, 7-4, in the top of the seventh in Montreal, Los Angeles had a 12.17 percent chance of coming back to win. (This percentage, derived from extensive data from the entire season, would have been 1.29 percent if there were two out in the ninth.) Beltre delivered an R.B.I. single, making the score 7-5 and the Dodgers' chances of winning 19.11 percent.

So Beltre was awarded with the difference in percentages, or 0.0694, of what Lonergan and Polak call Wins Relative to Average Player (WRAP); and on the other side of baseball's double-entry bookkeeping, the pitcher who surrendered the hit, Luis Ayala, was credited with a minus 0.0694.

They then use this system to show that Sheffield and Bonds should be the MVPs. However, the system also shows that Nathan and Gagne should be the Cy Young award winners.

A.L. CY YOUNG Despite having a higher E.R.A., Schilling tops Santana, 5.15 to 5.01, because he often performed in hitter-friendly Fenway Park (yes, WRAP accounts for this) and because he thrived in particularly tight situations. But the two were bested by Twins closer Joe Nathan (5.47), whose 1.62 E.R.A. and 44 saves do not truly quantify how many games his late pitching helped decide. (WRAP leans toward relievers because, although they influence fewer at-bats, the at-bats are inherently more crucial.)

It strikes me that this system isn't good at picking Cy Young award winners. There really should be a stamina component to that award. My other problem with the system is that, like linear weights, it can only be accurately evaluated after the season is over, when all the probabilities are correctly known. Just as an example, in a low run environment, the probability of coming back from a 2-run deficit is lower than in a high-run environment.

Still, it's nice to have another tool in the in the drawer, and this does appear to be a good way to measure how clutch a player turned out to be in a season.

Posted by David Pinto at 09:09 PM | Statistics | TrackBack (0)

Comments

Business Week did the exact same article last year. Interestingly, the game theorists had Roy Halladay, Estaban Loiza, Pedro Martinez, Mike Mussina, and Tim Hudson as the top AL Cy Young contenders, using -- as far as I know -- the exact same methodology. So maybe the starters aren't as disadvantaged by their system, after all. On the other hand, the fact that it has such seemingly vast discrepancies from season to season may be a sign that its reliability needs serious tweaking.

Posted by: Robert Tagorda at November 7, 2004 01:18 AM

I have problems with this system as well, similar to the discussion you have in posts above about the problem with pitcher wins.

First off, the system is extremely team-dependent; it's not clear why hitters should be docked points for playing on teams with bad pitchers. Imagine a team that gives up 9 runs a game; a home run down 9-0 credits a hitter much less than he would get if it were even 5-0 and especially 1-0. Lots of people tend to gloss over the fact that it over-credits good players on teams that are in more close games for what would net them less credit on a dominant team or a poor one.

On the flip side the pitchers struggle with the same issue. Santana starts a game and goes 5 with no runs allowed: how much credit to give him? The probabalistic system has no answer outside whether Henry Blanco got a hit with a guy on second in the fourth inning (which he almost surely didn't).

The best use of this system (which I have always seen called Player Game Percentage before) was an analysis of whether Shoeless Joe throttled back his performance in key situations in the 1919 Series (Bennett, J. M. (1993), "Did Shoeless Joe Jackson Throw the 1919 World Series?", The American Statistician, 47, 241-250). I think that provides the best model for how this technique should be used.

Posted by: Carl Sanders at November 9, 2004 05:41 PM

Many others have done this in recent years. Ed Oswalt, the people at the Rhoids website and Doug Drinen (at least for relief pitchers).

This kind of stat is highly correlated with stats like OPS, so WRAP or whatever does not add alot to what we know about hitters. It also has little, if any predictive power. In fact, Dick Cramer showed in 1977 that the Mills brothers "Player Win Average" had little predictive power (I think Cramer published this in the Baseball Research Journal). I explain this at my site.

"The Problem With “Total Clutch” Hitting Statistics"

by Cyril Morong

http://www.geocities.com/cyrilmorong@sbcglobal.net/totalclutch1.htm

I also give links to the Rhoids site and Ed Owalt's site. Both provide lots of data. I don't know of any site that contains or presents WRAP data. The Rhoids site has been presenting this kind of stat for 4 or 5 years now and Ed Oswalt presented his data at the SABR convention in 2003. So both Rhoids and Oswalt were doing this Mills brothers approach before Polak and Lonergan

Posted by: Cyril Morong at November 23, 2004 07:27 PM