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August 12, 2014 Baseball TherapyI Believe In Clutch HittingI know, I’m not supposed to, but I believe in clutch hitting. By clutch hitting, I mean that certain players have some sort of ability to perform better in higher leverage situations. Leverage, for the uninitiated, is a concept formalized by sabermetrician Tom Tango. We know that some situations in a game are more important than others. When it’s 151, no one cares what happens in a plate appearance. When it’s the bottom of the ninth with runners on second and third, two outs, and the home team is down by one, pretty much the entire game rides on this atbat. Leverage index is a mathematical model of how much more important that late game situation is. Leverage is based on the idea of win probability. We can look at each game situation (let’s say, bottom of the third, one out, runner on first, and the home team down by two) and figure out over some past time frame how often the home and visiting team won. More to the point, we can figure out how much that win probability can change based on whatever is about to happen next. In the 151 situation, whatever the batter does is going to move the needle very little. In the bottom of the ninth, the win probability could go from roughly 50–50 to 100–0 in a hurry. When a batter does something positive that increases his team’s chances of winning, we give him credit for adding win probability (even if giving him all the credit is silly). In a highleverage situation, a batter can accumulate a lot of win probability in a single atbat. The standard test for whether there is such a thing as clutch hitting has been to look at the win probability that a player records over the course of a season and compare it to what his win probability would have been in situations where the leverage index was 1. (This is the basis of how our friends at FanGraphs calculate clutch.) From season to season, players show very little correlation on this measure of clutch. In general, the interpretation has been “clutch doesn’t exist” rather than “we had a poor measure of clutch to begin with.” Indeed, I have found that this measure of clutch eventually does become reliable. It just takes a while. Maybe there is signal in all that noise; maybe we need a better antenna. Warning! Gory Mathematical Details Ahead! I then took each equation and calculated the chances that each player would swing at a first pitch when the leverage index was 1 (average) and 2 (a situation twice as important as the average situation). Then, I subtracted the two and got a rough indicator of how high leverage began to affect a player (at least on this one behavior). I used a minimum of 250 plate appearances in a season and looked at players from 2009 to 2013. In the past, I’d found that clutch, as described above, had a yeartoyear correlation of .074. (I used a method known as autoregressive intraclass correlation.) For this group, across the five years, the ICC was .30. That’s not huge, but we call home runs a true outcome for pitchers with yeartoyear correlations in the same neighborhood. I termed this difference between predicted firstpitch swing rate “swing difference.” Some players swing a lot more when the leverage goes up. Some barely notice. A few start to freeze. Next, I wanted to see if swing difference predicted changes in outcomes. For the years 2009 to 2013, I used the logodds ratio method (which I have used multiple times before) to create a predicted percentage that each plate appearance would end in a strikeout based on the batter and pitcher’s usual rates in that area. I did the same for walks and singles and home runs and the rest of it. Next, I looked at all plate appearances in which a batter with 250 PA in that season faced a pitcher with 250 batters faced in that season. I created a binary logit regression in which I had my predicted percentage of a strikeout (for the initiated, expressed in a log of the odds ratio), and then entered in the leverage index for each plate appearance, the swing difference stat for the batter and the multiplicative interaction of swing difference and leverage. This type of analysis, called a moderator analysis, is wellsuited to answering the “clutch question.” If certain players have some sort of clutch factor (and here, we’re using swing difference as a rough measure of clutch) then as leverage increases, we would expect to see those who are higher on this clutch factor to show greater increases (or sharper decreases). That’s what the interaction term between swing difference and leverage does. If it’s significant, it means that as leverage goes up (or down), the effect it has will depend, at least in part, on that clutch factor. What I found is that for hitters who show more of an effect on swing difference (leverage makes them swing at the first pitch more), they were less likely than expected to walk and less likely to strike out as leverage went up. Instead, they showed higher rates of both extra base hits and outs in play. To show some sense of how much of an effect this could have, here are the numbers for strikeout rate. Let’s say that our pitcherbatter matchup stats alone would suggest that the chances of a strikeout are 20 percent. Now, let’s take a look at what would happen in a situation that has a leverage value of 1, and compare a batter who has a swing difference of .10 (he swings at first pitches ten percent more often in higher leverage situations than he does in mediumleverage situations) and a batter who has a swing difference of 0 (he swings equally in both situations). The values are the likelihood of a strikeout happening.
In an averageleverage situation, the two hitters are about the same (they differ at the fourth decimal place), but once the leverage is turned up a bit, they get different results. Not by a lot, but it’s there. You get the same basic effect sizes for the other outcomes. Before we go further, the careful observer will note that there’s a certain tautology that goes along with these analyses. I think it doubles as both a feature and a bug. A batter who is more likely to swing at the first pitch in highleverage situations is probably just more likely to swing in highleverage situations. It’s no wonder he sees a drop in his expected walk rate (and in some sense his expected strikeout rate). And if we’re saying that his swing rate drops because of leverage (or at least in accordance with leverage), then it’s not surprising that the effect appears. We’ll talk about this more in a bit. Clutch. Heart. Grit. Myocardial Infarction. These analyses may not completely prove that clutch ability exists, but they do lay what I hope is a foundation for how we might continue the search. “Clutch” is a way of saying that the situation matters because players are human. What we have here is an indicator that has reasonable (if not great) consistency across years, and it explains differences between players in how leverage affects them. More searching might find something with more consistency. Even then, yeartoyear consistency is not the only way to establish that a measure is reflective of a player’s true talent level. Using a more trackingbased approach might help. Players can and do change, even within a season. There’s no reason clutch needs to be an enduring trait, rather than a state we can detect with some reliability. The rest is simply showing that the factor, whatever it is, can explain some of the differences between players’ performances in different leverage situations. As to these specific analyses, it might very well be that what’s driving things is that some players are looking at the sorts of relievers they face in highleverage situations and saying “Well, he usually comes right at me, so no point in messing around. I might as well swing when I see something interesting.” It might not be a mystical force at work, but a very reasonable reaction to the circumstances. In that case, clutch isn’t even something psychological, but a mental skill. Still, there could be problems with multicolinearity. What this might be showing is that some players swing more in highleverage situations, and so we would expect them to take fewer walks, somewhat by definition. Then again, even knowing that information could have strategic value. Maybe when we have other data sets to work with, we might be able to look at measures of how leverage affects a player that aren’t based on game results. The other piece of this, and it’s one that I tried to drive home in the piece in the Annual that started everything, is that knowing that a player swings more (or less) often in highleverage situations might be good within the context of one skill set and bad within another. These analyses fall into the largeN trap that assumes that more swinging is better (or seems to be) for everyone. But if nothing else, I’d present these analyses as a way of reopening what had been assumed to be a closed debate. Clutch hitting might just exist.
Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
28 comments have been left for this article.

Question to the community from a relative neophyte: have the studies that indicate little indication of clutch performance taken into account that, in the highestleverage at bats, the batter is generally facing the freshest, most skilled pitcher the other team has to offer? If a batter has an OPS of .850 over the course of the season (against leagueaverage pitchers), and an .850 OPS in highleverage situations when the game is on the line, he will usually be performing against far more skilled pitchers. I would interpret that as clutch performance.