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September 22, 2005

Crooked Numbers

Popping the Clutch

by James Click

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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

The name at the top of the list should surprise to no one. David Ortiz cemented his reputation as a player who delivers big hits in last year's playoffs and he's done nothing to dispel the notion this year. Of course, he also delivers small and medium hits as well, so there's good reason for him to find himself atop this list. The first interesting case is the battle for the fourth spot between Derrek Lee and Tony Clark. Yes, that Tony Clark. How can Clark be leading Lee (by percentage points) when Lee so vastly outstrips Clark in VORP, WARP, and nearly every other metric available? Quite simply, it's because Clark has found himself in more high-leverage situations than Lee and has performed well in them. What's particularly amazing is that Clark has done this in a higher-scoring environment than Lee. We would expect to find players in low-scoring environments moving up this list since games in lower-scoring environments are necessarily closer than those in Coors Field.

The other discrepancy that Clark's presence near the top of the list highlights is that while we assume that batters see a roughly equal number of high leverage situations over the course of the season, clearly that's not always the case. With players like Clark and Chipper Jones near the top of the list despite not topping 400 PA, it's clear that some players found themselves at the plate in a higher percentage of crucial situations. Some of this has to do with the run environment, some with the lineup order, and some with luck.

To get a rough gauge of which players produced a disproportionate number of WINS given their VORP, we can run a linear regression on WINS and VORP and determine how many WINS a player would be expected to produce given their VORP. (For the curious, the r-squared between VORP and WINS this year is .48.) This process is by no means exhaustive, but it highlights which players' performances don't match up between VORP and win expectation. For now, we'll call the difference between WINS and Expected WINS "Clutch" as I duck for cover.


Batter          Team  WINS  VORP  PrWINS   Clutch
--------------- ----  ----  ----  ------   ------
Chipper Jones    ATL  5.50  43.6   1.72     3.78
David Ortiz      BOS  7.12  80.3   3.45     3.67
Tony Clark       ARI  4.98  43.3   1.70     3.28
Carlos Delgado   FLO  5.80  67.8   2.86     2.94
Moises Alou      SFN  4.49  41.3   1.61     2.88
Lyle Overbay     MIL  4.05  33.4   1.23     2.82
Nick Johnson     WAS  4.09  35.0   1.31     2.78
Jose Guillen     WAS  3.98  34.9   1.30     2.68
Bobby Abreu      PHI  4.62  61.2   2.55     2.07
Andruw Jones     ATL  4.55  62.9   2.63     1.92
Travis Lee       TBA  2.17  14.3   0.33     1.85
Pat Burrell      PHI  3.65  46.1   1.83     1.81
Shannon Stewart  MIN  1.88   8.9   0.07     1.80
Travis Hafner    CLE  4.57  67.0   2.82     1.75
Garret Anderson  ANA  2.14  16.5   0.43     1.71
Todd Helton      COL  3.88  53.6   2.19     1.69
Adam Dunn        CIN  3.90  55.3   2.27     1.63
Ryan Langerhans  ATL  1.64   7.4   0.00     1.63
Matt Stairs      KCA  2.62  28.7   1.01     1.60
J.T. Snow        SFN  1.59   8.2   0.04     1.55

And the least clutch in 2005:


Batter          Team  WINS  VORP  PrWINS   Clutch
--------------- ----  ----  ----  ------   ------
Jimmy Rollins    PHI -1.95  37.4   1.42    -3.38
Alex Gonzalez    FLO -2.87  14.4   0.33    -3.21
David Bell       PHI -3.24  -0.2  -0.36    -2.89
Casey Blake      CLE -2.47  12.3   0.23    -2.71
Jorge Posada     NYA -1.54  30.8   1.11    -2.65
Nick Punto       MIN -3.05  -2.1  -0.45    -2.60
Ron Belliard     CLE -1.60  24.3   0.80    -2.40
Mike Lowell      FLO -2.79  -1.3  -0.41    -2.38
Miguel Tejada    BAL  0.44  66.9   2.82    -2.38
Felipe Lopez     CIN -0.45  47.6   1.91    -2.35
Tike Redman      PIT -2.69   0.1  -0.34    -2.35
John Buck        KCA -2.47   4.7  -0.12    -2.34
Jose Reyes       NYN -1.26  29.6   1.05    -2.31
Neifi Perez      CHN -2.03  13.1   0.27    -2.31
Rafael Furcal    ATL -0.56  43.7   1.72    -2.28
Derek Jeter      NYA  0.30  61.6   2.57    -2.27
Shawn Green      ARI -0.63  40.9   1.59    -2.21
Julio Lugo       TBA -0.32  45.5   1.81    -2.12
Kevin Mench      TEX -1.16  26.7   0.92    -2.07
Cristian Guzman  WAS -3.06 -13.5  -0.99    -2.07

There are interesting names on both lists. Jones and Clark have been mentioned, but note the presence of Nick Johnson and Jose Guillen on the top list and Cristian Guzman on the lower one, some of the best and worst hitters on the team most often involved in close games. Also, only four hitters from the top three highest run environments--Texas, Boston, and Tampa Bay--make the list. Anecdotally, there seems to be something to the idea that players in lower scoring environments would be moved to the margins, but then again, there are no Astros on either list, so the effect is probably very small. There are also a few notable names going against the public perception. Adam Dunn usually finds himself on the wrong end of discussions of doing what it takes to win--cutting down on strikeouts and the like--but he's among the league leaders on the clutch list. Perhaps even more surprising is the 16th-least clutch player in the major leagues, Derek Jeter. The Yankee captain and poster boy for defensive metrics debates has contributed significantly less than expected given his VORP total this year. It's certainly possible that Jeter simply isn't presented with the same number of clutch opportunities as other players in the league, but when looking at his track record this year, he's contributed less from a WINS standpoint than such notables as Clark and C.C. Sabathia who went 2-for-6 with a double and a home run for the Indians in interleague play.

So what can we learn from this updated version of the old Mills Brothers' Player Win Average and a rough estimate of "Clutch"? First, more advanced purely offensive metrics like VORP map very well to WINS, although it's possible for some players with a few big hits to accumulate more WINS than their VORP or other offensive numbers would portend. Second, there does appear to be a slight bias towards players in lower scoring environments, despite the presence of Ortiz atop the list. This makes intuitive sense: Ortiz' performance would be much more valuable to the Nationals than the Red Sox because the Nationals are involved in so many close, low-scoring games while Red Sox games have seen nearly 400 more runs scored than their Washington counterparts. Finally, players over- or under-performing the expected number of WINS they should contribute based on their overall performance and run-scoring environment should not be expected to continue to do so into the future.

Over the long haul, runs contributed--whether measured by VORP, EqR, RC, Linear Weights, or any respectably accurate metric--are going to match closely to measures of performance based on win expectation like WINS. Over the short term, there can be glaring discrepancies between the two as some players come up with a few key hits while others fall short in similar situations or are not presented with as many situations. Regardless, when looking back and evaluating performance, something like WINS can reveal a great deal about how much a player contributed to the only number that truly matters in the standings: wins.

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