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May 29, 2006

Schrodinger's Bat

Quantifying High Impact Performances

by Dan Fox

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"Eddie (Murray) just didn't like to talk about what he did. He didn't care to give up his little secrets. He was the best clutch-hitter that I saw during the decade that we played together. Not only on our team, but in all of baseball."
--Teammate Mike Flanagan

One of the aspects of baseball that most interests me is the interplay of skill and chance that the game affords. In no other professional sport is that relationship so intertwined. The structure, speed, and sheer number of trials over the course of a season--compared to basketball, football, and even hockey--conspire to blur the line between ability and chance. This provides endless areas for speculation among performance analysts and fans of the game.

Recently I wrote about that blurring and what it means in the area of platoon splits, but nowhere has that speculation been more rampant over the years than in the realm of clutch performers. To get an overview of the debate that has raged for more than 30 years, take a look at the excellent list of links put together by fellow SABR member Cyril Morong. He recently added perhaps the seminal paper on the topic titled "Do Clutch Hitters Exist?" By Richard D. Cramer, published in the 1977 issue of SABR's Baseball Research Journal.

While weighing in on the controversy here is tempting, this week we'll simply take a look at quantifying performances that can be termed "clutch" by examining the approximately 192,000 plays of the 2005 season.

Clutch and Win Expectancy
In a previous column we discussed the Win Expectancy Framework (WX) which was created by Keith Woolner and explained in articles in both the 2005 and 2006 editions of Baseball Prospectus. Simply put, the framework allows one to calculate the probability of either team winning a game given a whole host of variables--including current inning, score, base/out state, run environment (both home and visiting teams), and run differential. The strength of the framework lies in its ability to provide these probabilities without relying solely on past observations of what actually took place.

Obviously, a framework like this allows all sorts of analysis. Woolner used it to analyze stolen bases in his BP2K6 article, both he and James Click used it in Baseball Between the Numbers, and it's also been incorporated in statistics here on our site such as WXRL.

But WX can also be used to quantify clutch performances as well as clutch performers. By assigning responsibility for each change in WX over the course of a game and then summing those changes for each player over the course of a season, we can derive an estimate of the impact of each player in terms of winning and losing. Woolner did this in his 2006 article for all position players from 1960 through 2005. Of course, players who get hits in situations that raise their team's WX by the greatest amount (rightly termed clutch hits) will tend to do well, while those who fail in those situations will be dinged accordingly. As you might imagine, the results of such an analysis (over the long haul anyway) are driven primarily by the overall performance of the player. That is, good players like Albert Pujols tend to come out on top and poor ones like Neifi Perez collect at the bottom. Since players are largely thrust into game situations over which they have little control because of chance--combined with the constraints of the batting order--the opportunity to perform when it means the most tends to even out over time. This is not the case for players who specialize, such as LOOGYs, closers (hence the utility of WXRL), or elite pinch hitters and setup men who get used strategically.

And to bring the discussion full circle, good players also tend to do better when measured by WX because the general consensus in the performance analysis community has been that clutch hitting ability is at the least a relatively minor phenomena (an exception discussed in the previous column on this topic may be that of Willie McCovey) when compared with the normal variation you find between hitters.

Anatomy of the Big Play
But even if things tend to even out for most players most of the time, we fans love the drama associated with games where the outcome hinges on single plays and fortunes are reversed with one swing of the bat.

Over the last couple weeks, two performances again reminded us of this. And in thinking about those performances it occurred to me that most folks probably don't have a good feel for the change in WX associated with clutch plays, nor how changes in WX are distributed over the course of a season. So for the remainder of this article we'll take a look at quantifying these high impact performances and discuss a few related issues. But before we do, I'll bet you're curious about the two plays in question.

First, on Thursday May 11th, Phillies center fielder Aaron Rowand made a remarkable grab on a drive to right center by the Mets' Xavier Nady. Although the catch in and of itself was extraordinary, it took on even greater weight since it came with the bases loaded and two outs in the top of the first. Had Rowand not made the catch (and broken his nose in the process), the Mets almost certainly would have scored three runs. As it was, Phillies starter Gavin Floyd went on to pitch his first career shutout in a rain-shortened five inning affair.

The question is, how do we quantify such a clutch play? Well, from a win expectancy standpoint, once Rowand made the catch the Phillies' chances of winning the game were around 55% (there would have been zero outs in the bottom of the first of a 0-0 game in a park with a run environment of 5.2 runs per game based on 2005 numbers). Had he not made the catch--and the Mets scored three runs--the Phils' chances would have plummeted to around 26% (based on a 3-0 lead with two outs in the top of the first and a runner on third) for a net change of 29%. So we can say that Rowand's catch was worth a little less than a third of win.

The second play that came to mind was the walk-off home run that Jorge Posada hit on May 17th to cap the Yankees' 14-13 victory over the Rangers (after they came back from an early 10-1 deficit).

Because the Yankees were down 10-1 entering the bottom of the third, their WX at that point hovered around 2%. After battling back to 13-12 with two outs in the bottom of the ninth with Johnny Damon on second, their WX stood at 46%. The Posada homer therefore catapulted the Yankees to 100% for a change of 54%.

These plays illustrate three aspects of WX that should be taken into account.

In the first situation we calculated the change in WX based on what might have happened and not what actually did happen. It is of course difficult if not impossible to consider all possible outcomes given a particular scenario--so when WX is calculated for games and seasons it is done based only on the events that transpired and not what might have been. So in the case of Rowand's great catch, the most he could have been credited with is a change in WX of around 6% assuming that all the credit were assigned to him, which, in practice, is not typically what happens. This approach tends to penalize defensive players.

That brings us to the second aspect of WX. While it's simple to assign credit to hitters and to pitchers since they are the principle actors in most events on the field, partitioning a change in WX among multiple fielders, pitchers, and base runners is more art than science. When you couple that with the reality that raw play by play data rarely includes any grading of fielding plays, you begin to get a feel for how difficult assigning WX credit for fielders can be.

Finally, as hinted at above, the fundamental reason Posada's homer was worth almost twice as much as Rowand's catch is simply because of its timing. In Rowand's case, had the play come later in the game the stakes would have risen accordingly. For example, if the same events had transpired in a scoreless game in the top of the 9th inning the catch would have had a change of around 61%.

But even given the limitations of WX--and with some help from Dave Studeman who has done some excellent work in applying the WX framework to different run environments--let's take a look at the five highest impact plays of 2005 as tracked by WX:

  • September 20, Giants at Washington. With two outs in the top of the ninth and the Giants down 2-1, Moises Alou steps in against the Nationals' Livan Hernandez with runners on first and second. At that point the Nats have an 87% chance of winning. Alou smacks the first pitch he sees for a line drive homer to left for a 4-2 lead and a change in WX of 80%.

    Changes in WX over the course of a game are often charted as follows:

    chart 1

    As you can see, Alou's homer resulted in a nearly straight vertical drop for the Nats. However, the Nats loaded the bases in the 9th with one out, raising their WX to 32% before Ryan Zimmerman and Brad Wilkerson flew out to left to end the game.

  • September 7, Houston at Philadelphia. With two outs in the top of the ninth and the Phillies clinging to a 6-5 lead, the Astros send Craig Biggio to the plate with runners on first and second to face his old teammate Billy Wagner. On a 1-1 pitch Biggio sends one over the left field fence for an 8-6 lead which raises the Astros' WX from 13% to 90% for a net gain of 77%. The sad thing for the Phillies is that all three runs were unearned. With two outs and nobody on in the top of the 9th David Bell committed an error on a grounder by Jose Vizcaino that opened the door.

    chart 2

  • September 11, Atlanta at Washington. In a taste of what was to come nine days later, the Nats held a 7-6 lead with two outs in the top of the 9th with Chad Cordero on the mound. Their 93% WX, however, was shattered by a two-run blast to right-center off the bat of Chipper Jones dropping their WX 76%, all the way to 17%.

    chart 3

    The chart for this game is more interesting in that it captures the Nats' comeback from being down 6-0 with two outs in the bottom of the 6th all the way back to take the lead with two outs in the bottom of the eighth on an RBI single by Ryan Zimmerman. So close, yet so far.

  • May 13, Atlanta at Los Angeles. In the bottom of the eighth inning the Braves were leading 4-2 with two outs. However, the bases were loaded courtesy of three singles (two of them of the infield variety) when Milton Bradley came to the plate. Bradley hit a 3-1 pitch over the right field wall for a home run off of Braves reliever Chris Reitsma. Prior to the home run, the Dodgers had a 21% chance of winning--afterward, they had a 94% probability, which was a difference of 73%. You'll note this is the only game of the top five where the big play occurred in the 8th inning.

    chart 4

  • April 9, Texas at Seattle. In our lone American League game, the Mariners held a 6-5 lead with two down in the top of the ninth. The Mariners started the inning up 6-3 but thanks to a one-out error by Bret Boone and a two run homer by Hank Blalock, the Rangers were in business. After Michael Young singled to left and Mark Teixeira struck out, Richard Hidalgo hit a three-run home run off of Eddie Guardado to give the Rangers a 7-6 lead which they would not relinquish. Before the home run the Mariners were at 92%--after, they were at 20%, for a 72% drop.

    chart 5

What Are the Odds?
As illustrated by these five games, and as you would have guessed, the late home run is almost always the play that turns fortunes quickly. In fact, of the top 100 changes in WX in 2005 74 of them are home runs and the earliest of those occurred in the fifth inning. In case you're wondering, the most costly error (15th overall) occurred on April 21st when Cristian Guzman made a throwing error that resulted in two runs scoring and dropped the Nats' chance of winning 64%. However, that error is the only non-hit in the top 100.

And because good defense doesn't really get a fair shake when calculating WX as described above, the top two defensive plays occur 210th and 211th on the list and both are double plays that increased their team's chances of winning by 39%.

Finally, to give you a feel for how changes in WX are distributed, the following table shows the percentages of plays in various ranges.

Change in WX  Pct of Plays
--------------------------
0 - 2%           44.4%
2% - 4%          30.3%
4% - 8%          16.4%
8% - 15%          6.7%
15% - 25          1.7%
> 25%             0.5%
As you can see, the vast majority of plays (some 90%) change the WX less than 8%. Those high impact plays are special indeed.
Related Content:  The Who,  Good Plays,  Science Of Hitting,  Nats

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