Win Probabilities and the MVP
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by user Davis21wylie
Several years ago, the inimitable Bill James unveiled a new statistic called Win Shares. It was to be the culmination of James' considerable sabermetric career -- a single all-in-one stat that could definitively quantify a player's contribution to his team... in terms of wins. This was ground-breaking, because up to that point baseball players had been evaluated on the basis of various stats (first batting average and RBI, all the way up to runs created and VORP) that explain how a player contributes to a certain aspect of winning (run-based stats show contributions to scoring, fielding stats try to tie into runs allowed, etc.), but not to winning in general. James' approach changed all that, because he discovered that you could tie what he calls "Marginal Runs" (that is, runs scored above half the league average, or prevented below 1.5 times the league average) to a team's record, eliminating the need for the messy pythagorean formula in player evaluation. All of a team's marginal runs (hitting, fielding, pitching) go in a communal pot, and the end result is wins. Using nothing but traditional stats, James' result is genius, to say the least. But that's also the problem: it uses traditional stats. Which is fine if you want to compare Ty Cobb to Andruw Jones, but with today's wealth of play-by-play information, we can do better.
Enter Win Probability. From historical play-by-play data over the past 10 years, analysts have determined the likelihood of winning that an average team has at any point in a game, given the current inning and base-out situation. For example, if you lead by two runs in the ninth inning, your odds of winning the game are far greater than if you lead by three runs in the first inning. And every time an event happens (whether it be an out, walk, double, etc.), the average team's probability of winning the game changes. Here's an example: Let's say Boston is playing Toronto at Fenway. David Ortiz comes up with Mark Loretta on first, 2 outs, and the Sox are down by 1 run in the bottom of the 9th. What is the likelihood of Boston winning? According to the Win Expectancy Finder, the probability of the Red Sox winning is .091. (That is, they have about a 9.1% chance of winning.)
How does that relate to Win Shares, you ask? Well, baseball happens to be a very tidy sport that isolates a series of one-on-one matchups for us, most of which are of the pitcher vs. batter variety. Since there's usually only one player involved per team in each event, we can actually track the change in Win Probability from event to event, and parcel out credit (or blame) to each player involved in the change. Going back to out fictional example above, now let's say that Papi draws a walk (this is how you know it's ficticious -- had it been real life, Papi would have hit a walk-off HR). What's the Win Probability for Boston now? .180, meaning that they now have an 18% chance of winning. What's more, Ortiz by himself raised Boston's chances by 8.9%, and Toronto's pitcher (let's say it's B.J. Ryan) lowered their chances by the same amount. So give Ortiz +.089, and Ryan -.089 for Ortiz's plate appearance. Now imagine that Manny Ramirez steps to the plate... and hits a home run, ending the game. Since the game is over, and Boston won, the Sox's Win Probability is now 1.000 (likewise, Toronto's is .000). And because Boston's probability was .180 when Manny stepped in, Manny receives a whopping .820 WPA (that stands for "Win Probability Added"), and Ryan is further assessed -.820 for the fat pitch that he grooved to Manny.
See how it works? A player's true contribution to his team's wins can be achieved by summing all of his WPA from the entire season. This is favorable to Win Shares because while Win Shares makes a nominal "clutch adjustment" by upping the Runs Created of players who perform well with runners in scoring position or late in games, WPA is what we sabermetricians call a "Total Clutch" stat. Meaning that the "leverage" (the amount of pressure) of each game situation is built into the WPA formula, by virtue of the fact that it uses actual probabilities to calculate "wins added". In other words, it's not just how you produce, it's when you produce, as "clutch" at-bats carry more weight than at-bats that come early in games or after games have been decided. So for those who complain that Alex Rodriguez only produces in non-critical situations, this stat would reflect that. For those that say that David Ortiz is the Greek God of Clutch Hitting, this stat would reflect that as well.
I must provide this caveat, however: while WPA does a better job than any other stat of telling what a player's actual, real-life contribution to winning has been, it is by no means predictive. Even if a player had the ability to hit in the clutch (a dubious claim at best), there's no guarantee that he will continue to come up to bat under the same high-leverage situations, since most of the leverage factor has to do with whether or not your team is still "in" the game when you come up. So remember that, with WPA, everything is situational, and it all depends on context.
With that said, here are the 2006 leaders so far in WPA: (WPA numbers thanks to FanGraphs)
Batter WPA -------------------------- Albert Pujols 6.57 David Ortiz 5.32 Derek Jeter 4.09 Jermaine Dye 3.97 Chase Utley 3.76 Manny Ramirez 3.10 Barry Bonds 3.07 Ryan Howard 3.00 David Wright 2.93 Lance Berkman 2.83 Carlos Beltran 2.77 Justin Morneau 2.73 Ryan Zimmerman 2.72 Vernon Wells 2.70 Jason Giambi 2.62 Nick Johnson 2.57 Adam Dunn 2.54 Bobby Abreu 2.53 Frank Catalanotto 2.45 Carlos Guillen 2.36 Curtis Granderson 2.32 Miguel Cabrera 2.27 Jim Thome 2.27 Melvin Mora 2.25 Todd Helton 2.19 Mark Teahen 2.15 Jorge Posada 2.01 Travis Hafner 2.00 --------------------------
In this article, The Shark argued that Ortiz should be MVP on the basis of his clutch hitting. At the time, I argued that Ortiz was not even the best hitter on his own team, citing Ramirez's superior production in semi-traditional stats like OPS. While that still may be true, the evidence above is clear: Papi has, by virtue of his clutch hitting, been the Most Valuable Player in the American League so far (though Jeter closes the gap if you consider defense). Ortiz is a repeat offender here as well: last year, he led all players in WPA with +7.31 -- the 11th-best WPA season since 1972. Barry Bonds is the all-time leader in both single-season (+11.17 in 2004) and career (+102.65) WPA, keeping in mind that the data only extends back to 1972. Looks like this is one situation in which the conventional wisdom (production in the clutch > production in any other situation) rings true.
Date
Wed 08/02/06, 11:02 am EST
