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Monday, November 15, 2004

Value by Win Expectancy

I blogged a couple weeks ago about WRAP as discussed in a NY Times piece by Alan Schwarz. There I noted that WRAP was based on the Mills Brothers Player Win Averages (PWA) methodology created in the late 1960s as well as Bennett and Flueck's Player Game Percentage (PGP) documented in chapter 10 of Curve Ball. However, I did not know that fellow SABR member Ed Oswalt introduced a similar measure the 2003 SABR convention called "The Baseball Player Value Analysis System", the results of which for 1972-2002 are documented on his site. In particular the site contains a nice Win Expectancy chart that runs from +5 to -5 for 2002 data.

I also see that Cyril Morong has published an analysis of statistics such as these. His conclusion is that they are very highly correlated with normalized OPS (NOPS) and so don't really tell us anything we didn't already know. By the way, the Rhoids web site listed in the links here uses the same basic methodology but injects salary into the discussion and also includes "inning state runs" using run expectancy tables.

Cyril also informs me that Palmer and Thorn in The Hidden Game of Baseball (pages 171-174) mention a study done by Dick Cramer back in 1977 on the Mills brother's method and note that Cramer's study shows a high correlation between BWA (Batter Win Average created by Cramer and used to measure the runs a player contributes beyond the league average) and PWA and OPS and BWA. Further, Cramer found that the distribution of the differences was normal indicating that it was random and that one year's PWA was not a good predictor of subsequent years.

In other words, while PWA, WRAP, Rhoids, and other similar statistics do tell you exactly who was the most valuable in terms of producing or preventing runs or increasing the probability of victory for their team, these stats don't capture any difference in ablity and therefore can be biased by the situations the player finds themselves in. Because they are essentially retrospective I do think they can profitably used for postseason awards.

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