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February 11, 2014 Baseball TherapyWhen Sabermetrics Gets Personal
Let’s try something. In the recently released 2014 edition of the Baseball Prospectus annual, I wrote an essay calling for a new kind of analysis. The field of sabermetrics, as a whole, has spent a lot of time trying to figure out larger truths about baseball players in general. There’s nothing wrong with that. We’ve found some good ones. But just about every study begins with finding every single player who fits some criteria and has a big enough sample size to produce reliable data. That allows us to say things about baseball players as a group. In the annual essay, I tried to make the case that it’s a little strange that there is no parallel track of research for the study of individual players. It’s time we got a little more personal. One topic that I’ve done some research on is the question of how big a sample size we need for a stat before we can stop saying “small sample size.” The answer varies from stat to stat, both for pitchers and hitters. But the idea is that there comes a point—for example, 60 plate appearances for strikeout rate—where you can believe that a hitter’s strikeout rate over those 60 PA really is an adequate reflection of what his talent was at the time. That’s the base rate for hitters in general, but does that hold for this particular hitter? People often misinterpret the thresholds for various metrics to stabilize, believing that 60 PA means, “Now that we’re past 60 PA, from this point forward, we can believe that Smith will maintain this new strikeout rate.” It’s not a bad assumption, but it doesn’t always work like that. Maybe he will, maybe he won’t. Smith might make some sort of adjustment midseason, maybe a radical one. Baseball players are human, and many of them make changes in their lives. Some maintain a fairly consistent approach all year. (Which one is better is an empirical question.) In some sense, when a player makes a change, he’s become different player. Maybe it’s just a slightly different player, but so far we have lacked the vocabulary, statistical or otherwise, to describe those differences within a season. Baseball statistics come in many flavors, but they are almost always denoted in wholeseason format. A .300 hitter may have been a true talent .300 hitter all year, or perhaps was a .290 hitter for half the year and a .310 for the rest of it. How can we tell who’s who? Today, we’re going to look at the decision over which a hitter has the most control, whether or not to swing the bat. We can certainly look at his swing percentage for the year and try to get some idea of whether he’s a free swinger or a guy who just prefers to keep it on his shoulder, thank you very much. But does that change over the course of the year? (If you’re playing along at home or the office, you can do this with any rate stat.) To test that, I used a methodology that I’ve used in a slightly different context before. I looked at every pitch that a batter faced from 20092013 and coded it simply as swing/no swing. I used only playerseasons that included at least 250 PA and 1200 pitches seen. I did take the batter’s overall swing percentage for the year, but I also took a series of prior moving averages. For example, I looked at what the batter’s swing percentage was on the 50 pitches immediately preceding this one. And the 100 pitches immediate preceding this one. And the last 150 pitches, all the way up to 1000, in increments of 50. All of those swing rates were converted to the natural log of the odds ratio. We now have 21 contenders for the title of “most predictive indicator.” If one of the moving averages is the best predictor, we can assume that the hitter might be given to swings in…well, how often he swings. I then split the data set into individual data sets for each player (there were 475 such players). I set up a binary logistic regression predicting whether the batter would swing at each pitch he saw (starting with pitch no. 1,001 of his season) and—using a stepwise regression—asked my computer to pick out which of the 21 variables best predicted whether or not the batter would swing at each pitch. If we’re going to test predictive power of a variable, let’s see how well it predicts this next pitch. If the last 100 pitches are the best predictor, then that tells us something interesting, especially given that we are allowing the player’s seasonal swing rate to compete for the honor of most predictive. A hundred pitches might be a week’s worth of games, and the player could have a completely new swing percentage from one week to the next. He might not, but if you wanted the best predictor of his tendency to swing, you’d look over the last 100 pitches, rather than his whole body of work. (Note, for the initiated: it’s important to note that the best predictor of his swinging tendency is an equation containing his swing rate over the last 100 pitches. But still, we can map that.) You could make the case that hitters who are best described by their seasonal averages (or by a moving average containing a lot of pitches) are those who maintain the same approach in most situations. Those who are best described by 50 or 100 pitches in the past are more given to wild variations in their approach at the plate. What’s interesting is that of the 475 players I was able to study, 60 percent (288) were best described by that seasonal average. No one was best described by the last 50 pitches. However, there were 19 players who were best described by the last 100 pitches they saw, and it was a mix of the good (Carlos Beltran, Prince Fielder, Adrian Gonzalez, Evan Longoria) and the flawed (Ryan Howard, Drew Stubbs, Dan Uggla). At 150, we find eight players, including both Nick Franklin and Mike Trout. And Scott Podsednik. There doesn’t seem to be much of a pattern forming. There were 29 players who were best described by either the past 200 or 250 pitches (again, a couple weeks’ worth of PA), 21 in the 300 or 350 range, and 18 in the 400 or 450 bracket. It isn’t very common to have a player who is on the inconsistent side, but it happens. And some of them are doing rather well for themselves, so it isn’t necessarily toxic, either. Steady or Stubborn? Adaptive or Clueless? More importantly, we have a method for looking at when a statistic becomes meaningful for an individual hitter, rather than just relying on benchmarks derived from a whole bunch of other guys. There are things that we might say about Ian Kinsler that do not apply to Prince Fielder. If we wanted to do a deep dive into studying Ian Kinsler, we now have a method for doing that. Who would want to study Ian Kinsler? Maybe a pitcher who is facing the Tigers in his next start. Next week, we’ll see what we can do with this newfound tool in the belt.
Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
15 comments have been left for this article. (Click to hide comments) BP Comment Quick Links therealn0d (51857) If I'm reading this right, and I like to think I am, this is just the beginning, the ground floor. Models don't come forth fully formed; there is work to be done before you know where you're going. To lay out the whole thing in one article would make it the length of an academic research paper. Feb 11, 2014 07:57 AM therealn0d (51857) In thinking about this, the questions posed by Peter and Robert, to my thinking, are what make this article a successful exercise. The questions are as important as the answers. I seem to recall Russell espousing the sentiment that, at this point in sabermetrics, we should be as creative with our questions as with our answers. This is a great way to further exploration in the field. I think it would be helpful if more of the people with interesting questions had the tools to provide their own answers. Maybe there could be a tutorial series on this site showing how to reproduce some of the studies. Feb 11, 2014 09:04 AM Ogremace (45343) I agree with this idea a lot. Immediately upon finishing this article rather than considering whether I agree or disagree or coming to some other conclusion I found myself projecting this model into a bunch of applications. Patterns may not be immediately obvious from the breakdown here, but can we correlate these results with other measures of batter tendencies to find a pattern? Can we correlate them with historical knowledge about those batter seasons to answer the questions posed in the penultimate paragraph? Obviously this is a skeleton, but the figure that could be built on it could be very interesting indeed. Feb 11, 2014 18:15 PM newsense (5112) Russell, did you account for multiplicity? How often would a player's preceding 100 pitches be more predictive than the swing rate for the previous 1000 just by chance? Feb 11, 2014 11:07 AM JohnChoiniere (65074) Are the results consistent seasontoseason for a given player? E.g., has Beltran *always* been bestdescribed by the last 100 pitches? Feb 11, 2014 15:59 PM Nathan Aderhold (68572) Awesome start. Really looking forward to you diving headlong into this stuff. Feb 12, 2014 12:14 PM Not a subscriber? Sign up today!

I am not sure I understand how/whether swing rate can be separated from pitch type and game situation. A pitcher will pitch to Prince Fielder differently if there's a guy on base and he's facing a team pushing for a playoff game, while that same pitcher might approach Scott Podsednik identically to a bases empty situation.
Does that confound your metric? Is there any way to control for changes in pitch offerings, game situations, etc., that might be different on a per player basis, or have you already done so in some way that I'm missing?
Yes it does and yes there are ways to control for that. I made a conscious decision not to get too deep into those weeds yet. Right now, we've got a nascent model, and little idea of where it's going to end up. Best not to overcomplicate something if you don't need to.
I understand Russell's desire to keep it simple, but I too wonder whether and how context might be an important factor.
Maybe taking into account context would help to separate the adaptive hitters, who are presumably better because they adjust to the pitcher and/or the game state (say, Mike Trout, Evan Longoria), from the nodiscipline hitters, who are just wildly varying their tendencies in an effort to fix whatever ails them (Ryan Howard, Dan Uggla).