March 8, 2010
Flash forward to July, 2010, as Prince Fielder is being interviewed after a Brewers win. Fielder has just gone 4-for-5 with two home runs, and the announcers tell Fielder that he’s gone 9-for-his-last-12 over the past few days. Fielder says, "Yeah, I’ve been feeling great and seeing the ball really clearly the past few days. Some days, you just see the ball better than others."
The next day, Fielder is up in the first inning, and the announcers once again point out his recent hot streak and recap Fielder’s comments with a little bit of hope in their voices. As they do so, Fielder takes strike two, and then looks a little foolish chasing after strike three on a high fastball out of the zone. In the third, he hits a weak grounder to short, and in the sixth he hits a nondescript fly ball to center field. In the eighth inning, he caps off a frustrating day by watching a called third strike slip past him. What happened to Fielder’s streak? He said that he was seeing the ball better… how did it all just disappear like that?
Ever have one of those days? The sort of day where no matter what happens, you feel awful. No matter what, nothing goes your way. Ever have a couple of days like that? If you say you haven’t, you’re either lying or you’re Eric Seidman. It’s one of those universal human experiences to have a bad day or two. Thankfully, there are some days where you feel great for no particular reason, and everything seems to be going your way.
There’s actually a biological basis behind the phenomenon. The body is filled with hormones and other chemicals that regulate all sorts of things, including mood and energy level. These hormones, in general, run in cycles. The easiest cycle to see is the 24-hour cycle that your body keeps. You generally wake up at a certain time each day, have a small post-lunch crash, and get tired each night around the same time. If, for some reason, you have to wake up early one day, your body feels a little off. Well, there are dozens of cycles that work like that. Some of them are daily cycles. Some cycles happen several times a day (your hunger cycle), while others take several days (or weeks or months!) to complete. At some point, all of the good parts of the cycles might coincide over a day or two, and you get a day where you feel just fantastic. And when you’re in a better mood, you feel like you’re working so much better.
And yes, these cycles happen to baseball players too. They’re human beings. But does it make a difference in their performance?
The idea of the streaking player is a common one in mainstream baseball analysis. A player has a small run of time in which he hits exceptionally well or exceptionally poorly. While it’s a matter of fact that a player might have gone 6-for-8 over the last two games, streaks are usually cited by announcers as having some larger significance. In general, it’s understood that the player probably won’t keep this up forever. But like Mario after he catches one of those invincibility stars, he’s got a finite period of time in which everything he does will be amazing. Managers even move players around in the lineup based on their past few games, going with the "hot hand," or intentionally walk a player because "he’s been hot lately." Should they?
Several analyses prior to this one have found little evidence to support the claim that a player’s performance in the recent past is much of a predictor of his performance in the present. There have been well-founded mathematical arguments that streaks are simply random variation over a small sample size. There have been studies looking comparing the performance of groups of players who were recently on hot streaks vs. those on cold streaks. But what if we put the supposition to a very rigorous methodological test, one with a good amount of statistical power to detect even a small effect of streakiness?
As always, if you want to avert your eyes at this point, skip to "The Results."
Warning! Gory Methodological Details Ahead!
I took everything that happened in the last 10 years (2000-2009) and coded all plate appearances (except for intentional walks, which don’t really count), for whether they were on-base events or not. I then lined up each player’s plate appearances chronologically, within each year. I calculated what the player’s OBP was in the 10, 25, and 100 plate appearances immediately preceding this one. I also calculated the batter’s overall OBP for the season, as well as the OBP allowed by the pitcher he faced. Only plate appearances in which a batter who logged 250 or more PA in the season in question faced off against a pitcher who had logged more than 250 batters faced were considered.
I calculated the probability, given the batter/pitcher matchup, that this plate appearance would end up in an on-base event (a technique that I have used in earlier work). I converted all probabilities into odds ratio form, and then took the natural log of the odds ratio. I then constructed a binary logit regression, in which I predicted whether the plate appearance would end in an on-base event (1 = yes, 0 = no), with two predictors: the predicted probability based on batter/pitcher matchup, and the batter’s OBP over the last 10/25/100 PA. (I ran three different regressions.)
If performance is more affected by a batter’s "hotness" or "coldness," then that coefficient should jump out and be very significant. If it’s more due to a batter’s overall talent level (and the talent level of the pitcher whom he’s facing), then that coefficient should predominate.
It was an over-whelming victory for "overall performance." And it was the type of overwhelming that would come from the question: Whom do you want pitching Game Seven for you, Roy Halladay or Will Carroll? Statistically, there was no contest in any of the three regressions.
Still, something interesting did happen. While "overall performance" was the far superior predictor of events, OBP in the recent past was still a statistically significant predictor (in all three denominations of PA.) So while overall performance might be the better predictor, there’s still some effect for streakiness. How much?
I assumed that the batter and pitcher were both league average (OBP and OBP allowed of .333). I looked at what the model would predict for a batter who had a recent run of 10 PA where he had a .100 OBP and a .700 OBP. The difference… was measurable at the fifth decimal place. We would expect our hot hitter to get an extra hit every few thousand plate appearances over our cold hitter. So, strictly speaking, the effect for streakiness on a hitter’s performance is not zero, but it’s not important either. (The results were similar for the 25 and 100 PA samples.)
Why Does the "Hot Hand" Theory Persist?
There are several reasons wny the "hot hand" theory persists despite such evidence. The usual caveats that people infer far too much from a small sample size apply. Another is that believing in the predictive power of streaks means that you can give yourself the illusion of knowing the future with only a small amount of data, and that’s a very comforting thought. But there’s something more. Why are people so certain that a hot hand will continue to be hot, and why does the hot player himself say things that suggest that his ability to see and hit the ball has actually gotten better over the last few days?
For one, a hitter usually says these things in the post-game interview, after the fact. People often report that they "knew it was gonna happen" after an event, which makes them look smart… because the event that they were sure about just happened. When people are asked how sure they are of something happening beforehand, they rate themselves as less sure. It isn’t rocket science as to why.
Another factor is that people are very bad at what’s called introspection, which is the ability to monitor what’s going on inside themselves and are easily influenced in their perceptions by outside forces. In general, humans over-estimate their ability to understand their behaviors. As an example, there was an experiment in which people were given word pairs to learn. For some of the people, one of the word-pairs was moon-ocean. Another group had that one replaced with some other non-descript word pair. When asked what their favorite detergent was, 90 percent of the group that had moon-ocean picked (you guessed it!) Tide. It’s fairly clear why it happened, but when asked to explain it, the people in the group reported that they didn’t know why they picked it.
Finally, things that happen recently, particularly things that are emotionally charged, like a great performance which wins a game, are very much in people’s minds when reckoning the probabilities in a situation. Going back over the totality of a player’s career (or at least the past year or so) isn’t going to be as relevant because that sort of thing is boring. But it’s the better predictor.
There is psychology at work here, but it’s not powering actual meaningful changes in performance. Instead, it’s powering the brain wanting to believe in the hot hand and then going back and reconstructing events so that they fit with the desired theory. It’s backward logic, and backward logic is dangerous.
Let’s go to a real game situation. Bottom of the ninth, tie game, runner at third with no outs. A manager will sometimes call for an intentional walk here because the walk means very little in the grand scheme of things. Indeed, the only runner that matters is on third. (Some managers will issue two free passes to set up the force at any base. Let’s discount that for the moment.)
The decision of whether or not to issue the walk comes down to a choice between which of two hitters he’d rather face: the guy at the plate, or the guy on deck. Suppose that the choice is between a hitter who is clearly inferior overall, but has been hot lately, or a better hitter who has been cold. I’d argue that every time, the manager should pitch to the inferior hitter. There’s no evidence that Mr. Hot Hand is any more dangerous than he’s ever been, and if he’s the inferior hitter, that’s who you want at bat. But managers will sometimes betray how much they believe in the hot hand theory by walking the streaky hitter. This is a behavior that has to stop. Not that I’m holding my breath. It’s OK to walk Alex Rodriguez when he’s on a hot streak, but only because he’s A-Rod, not because of the streak.
Why won’t this type of behavior stop? The hot hand theory is more than just bad statistical literacy. It’s emotionally seductive to believe in the hot hand. Managers are human beings and are overly swayed by emotions. I look forward to the manager who can recognize those emotional responses and overcome them. Maybe he’s already out there. But I’m also looking forward to the time when commentators, announcers, and other folks who make their living talking about baseball will stop engaging in the folk psychology of "Well, this happens to me, this must be what’s happening to the players." There’s a lot of psychology that is present in the game. Just please use the real stuff.