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September 22, 2005

Crooked Numbers

Popping the Clutch

by James Click

Win probability is not a new concept. Events in a baseball game have long been analyzed by not only the number of runs they produce, but by their impact on a team’s probability of winning the game. The Mills brothers were some of the earlier analysts to discuss the concept in depth with their metric Player Win Average (PWA), but it has been refined many times and various frameworks are employed both here at Baseball Prospectus and elsewhere. Currently, our version--discussed in depth by Keith Woolner in Baseball Prospectus 2005--is employed in our pitching metrics, particularly the reliever evaluation tools like WXRL.

The framework is not applied to batters in any of our regular reports, but it can be revealing when applied to hitters. Much like the reliever reports, each plate appearance can be analyzed by the difference in the team’s probability of winning the game before and after. Looking at the ninth inning of Tuesday’s Giants/Nationals game makes for a good walk-through. Randy Winn led off the inning with the Giants down 2-1. Given the Giants’ and Nats’ levels of offense, the Giants at that point had a 15.3% chance to win the game. After Winn grounded out to third, that dropped to 8.4%. A few batters later, Moises Alou’s three-run home run catapulted the Giants from 14.3% to 92.9%. Looking at the full list can highlight some basic issues and assumptions:

Batter          Inn  Outs  Lead  Result  WEx_In  WEx_Out  WEx_Change
--------------- ---  ----  ----  ------  ------  -------  ----------
Randy Winn       9    0     -1    5-3    15.3%     8.4%     -6.8%
Omar Vizquel     9    1     -1    BB      8.4%    16.9%      8.5%
Edgardo Alfonzo  9    1     -1     8     16.9%     7.4%     -9.6%
Barry Bonds      9    2     -1    BB      7.4%    14.3%      7.0%
Moises Alou      9    2     -1    HR     14.3%    92.9%     78.6%
Ray Durham       9    2      2     8     92.9%    92.6%     -0.3%
Preston Wilson   9    0     -2    1-3     7.4%     3.9%     -3.6%
Vinny Castilla   9    1     -2    2B      3.9%    11.2%      7.3%
Brian Schneider  9    1     -2    BB     11.2%    19.0%      7.8%
Ryan Church      9    1     -2    BB     19.0%    31.6%     12.6%
Ryan Zimmerman   9    1     -2    SF7    31.6%    16.5%    -15.0%
Brad Wilkerson   9    2     -1     7     16.5%     0.0%    -16.5%

First, because this is only the ninth inning of the game and the lead was never more than two runs, the change in Win Expectancy (WEx) is significantly larger than it is in other parts of a game or when the lead is larger. A simple groundout by Winn cost the Giants a 6.8% chance to win the game in the top of the ninth while the same maneuver by Preston Wilson cost the Nats 3.6% in the bottom of the inning. Those values are significantly higher than the same outs earlier in the game. But this is what WE tells us that simple run metrics do not: they add context to performance, crediting clutch hits more than stat-padding home runs in blowouts.

And now, the requisite clutch hitting versus context independence blurb: Clutch hits exist, clutch hitters do not. There is no statistical evidence to support the idea that some hitters consistently perform better in situations defined as “clutch” as compared to normal situations. Good hitters are good clutch hitters; bad hitters are bad clutch hitters. Using WEx isn’t conceding the idea that some hitters are better in clutch situations than they are in normal situations going forward, but rather we’re looking to identify which hitters have contributed the most to their team’s chances of winning games given the situations in which they came to the plate. Not unlike teams that are outperforming their third-order winning percentage or a person who’s up at a blackjack table, those gains are banked and there is no correction going forward, but the best predictor of future performance is their third-order winning percentage, basic odds at blackjack, or overall hitting performance in all situations.

Let’s take a look at the league leaders in total WEx added (WINS) to provide a few examples. In this case, WINS is defined as the total change in WEx over the season in each batter’s PAs. Fielding and defense are not considered.

Batter          Team   WINS   VORP
--------------- ----   ----   ----
David Ortiz      BOS   7.12   80.3
Carlos Delgado   FLO   5.80   67.8
Chipper Jones    ATL   5.50   43.6
Tony Clark       ARI   4.98   43.3
Derrek Lee       CHN   4.98   99.9
Jason Bay        PIT   4.85   81.5
Bobby Abreu      PHI   4.62   61.2
Alex Rodriguez   NYA   4.59   93.1
Travis Hafner    CLE   4.57   67.0
Andruw Jones     ATL   4.55   62.9