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June 13, 2011 Resident Fantasy GeniusWhen Hitters' Stats StabilizeFour years ago, former BPer Russell Carleton (then monikered “Pizza Cutter”) ran a study at the nowdefunct MVN’s StatSpeak blog that examined how long it takes for different stats to “stabilize.” Since then, it has become perhaps the mostreferenced study in our little corner of the internet. It has been a while since the initial study was run, and since there are a few little pieces of the methodology that I believe could be improved, I decided to run a similar study myself.
Methodology Like Russell and Harry, I ran a splithalf correlation on a number of stats, which means that I would take, say, 100 plate appearances from every hitter, split them into two 50 PA groups for each hitter, and run a correlation between the two groups. Unlike Russell and Harry’s initial studies (and per Tango’s suggestion), I randomized selected PAs to put into each group instead of going odds and evens, which eliminates accidentally catching parks, opponents, etc. in the correlation. Taking a step back for a second, the purpose of the study is to find the point at which each stat produces an R of 0.50. It's at this point that we can predict 50 percent of the future variation in a stat. Put another way, if a stat stabilizes at 100 PA and we have 100 PA of data for a player, we'd use a 50/50 split of the player's actual data and the league average (or whatever mean we choose) to estimate his true talent for that stat. The more data we observe for a player, the less league average we use. Russell ran the correlations at several different intervals and stopped once he reached his stabilization point. But per Tango’s suggestion, I ran the correlation at about 15 different intervals because even if the R isn’t 0.50 at a particular interval, based on what the R is, we can estimate at what interval the R would be 0.50. I took all of these implied intervals and weighted them by the sample size at each interval to arrive at a final result. Another change to the initial methodology is the denominators I use for each stat. Russell used plate appearances as his denominator for every stat, but I think we'd be better off using an individualized denominator for each stat. As an example, Adam Dunn has put the ball into play 48 percent of the time this year, while A.J. Pierzynski has put the ball into play 88 percent of the time. If we’re trying to figure out how long it will take their BABIPs to stabilize, how can we expect them to stabilize after the same number of plate appearances? Pierzynski is putting far more balls into play and will therefore see his stabilize sooner. Finally, Russell’s study was done four years ago, so he had much less data to work with than I do now. In my study, I’ve used 11 years (20002010) of data for most stats and as much as possible for battedball types (20042010 for Retrosheet, 20052010 for MLBAM). I had considered adjusting for various contextual factors (ballparks, opponents, umpires, weather, etc.) but decided that it would be most useful not to. When you, the readers, are looking at stats online trying to make decisions for your fantasy team, you’re not going to be making these adjustments, so I didn’t want these figures to be reflective of them. But if we were using these for a projection system, we would want to account for context.
The Results for Hitters To read the “Stabilizes” column—the one we most care about—we would say, “Strikeout rate, defined as K/(PAIBBHBP), stabilizes after 100 PAIBBHBP.” The “Years” column is for a leagueaverage player (assuming 650 PA is one full season) and will sometimes vary significantly from player to player. It’s there as a quickanddirty way to make comparisons between stats since they’re all using different denominators. This allows us to say, “OK, strikeout rate takes about onefifth of a year to stabilize, but singles rate takes over two years.” Hitters
*Stolenbase success rate came back inconclusive. It’s a stat that we know has a lot of random variation in it, but this method proved unsuccessful in putting a number on it. At every interval, the correlation was between 0.10 and 0.15, so each interval implied a wildly different stabilization figure, ranging from 30 attempts to 450 attempts. The weighted average was 94 attempts, but with such a wide range of outcomes, I don’t trust that number. Most of these findings are similar to Russell’s. Things like strikeout rate and walk rate stabilize pretty quickly, while things like hits take a while. Home runs stabilize quicker than some might believe, and hitbypitches actually stabilize in under a year, which I found moderately surprising. When looking at this table, you likely noticed two sets of batted balls. Since battedball types are subjective and classified at the discretion of the scorer, data providers will classify balls differently. I ran these tests on the classifications used by Retrosheet (RS) and by MLBAM. It’s interesting to note that all of the MLBAM battedball types stabilize a bit sooner than the Retrosheet types, which might indicate that MLBAM scores them more accurately than Retrosheet does (or at least has done so over the past six years or so—it’s possible things have systematically changed over that time; also, I used slightly different time frames, so it’s not a perfect applestoapples comparison). I’d love to run these tests using Baseball Info Solutions classifications—another major battedball provider—but unfortunately I don’t have access to the necessary data. If someone from BIS is reading this and would be curious to know, feel free to get in touch with me and I’d be happy to run the data. It’s also interesting to note the difference between what I found for linedrive rate and what Russell found. Russell found linedrive rate to stabilize the quickest of all battedball rates, but here it’s the slowest for both Retrosheet and MLBAM (which jives with common wisdom and with numerous lessrigorous tests that have been conducted over the past couple years). Ground balls stabilize very quickly, and both categories of fly balls come shortly after. Infield flies are often an afterthought when analyzing a player, but they stabilize quickly and should be acknowledged.
Correcting Misconceptions about the Use of these Numbers First, note that these numbers are not magic. Once a hitter reaches 100 TPAIBBHBP, his strikeout rate doesn’t suddenly become a perfect representation of his talent. 99 TPAIBBHBP tells us almost exactly as much. One writer described the concept of stats stabilizing as “pretty simple—at a certain threshold of either plate appearances (for hitters) or batters faced (for pitchers) a number will stabilize such that it can be taken at close to face value.” That’s not true, though. Once a hitter reaches a threshold, his rate still can’t be taken at face value. At any particular threshold, we still need to include 50 percent of mean performance to get the most accurate representation of the player. Another way writers often use these numbers is to say that once a hitter reaches a threshold in a particular year, it becomes safe to assume that he has reached a new level of production. But that’s also not true. Just because a hitter reaches, say, a 100 PA threshold doesn’t mean that every plate appearance before the most recent 100 are meaningless. Recent performance is more important than older performance, but older performance still matters. What we should do is weight the older performance less, include it with the recent performance, and then use our threshold to determine how much mean performance we need. So while a player may have just reached the 100 PA threshold, he may have 300 effective plate appearances once we account for past data, in which case we’d use 75 percent of the player and 25 percent of the mean.  Next week, I’ll take a look at how fast stats stabilize for pitchers. If anyone has any questions, as always, feel free to get in touch with me via18 comments have been left for this article. (Click to hide comments) BP Comment Quick Links SirVLCIV (43229) Is there any way a similar analysis could be undertaken to find the point at which stats stabilize to produce an rsquared of .75, .90, .95, etc.? Would that even be interesting? Jun 13, 2011 09:47 AM I could do this, but it wouldn't tell us anything new, really. What's important is where the rsquared is 0.50, because that's where it's easiest to run our regression equation (see my response to the first comment). But once we've run the study, we can find out where the rsquared would be at any number other than 0.50. Jun 13, 2011 10:47 AM Sky Kalkman (3454) Derek, why did you use .5 R^2 and not .5 R? I was under the impression that .5 R would show the point where you would regress halfway to leagueaverage going forward...? Jun 13, 2011 10:14 AM One minor edit. In my original piece, I looked for where the R passed .70, which is (roughly) an R^2 of 50%. At that point, a projection of talent incorporating regression to the mean would be 70% performance and 30% league average (or whatever mean you want to use). Jun 13, 2011 11:55 AM NumberPower (16703) As a reader, I would like to see articles like this one end with a couple of short examples of how this analysis can help us think about a particular player. I don't always read the methodology closely, but I would like to know what it means for how to understand players. Applying the study's insight to analyze a case or two would make me much more likely to click on methodological articles in the future. Jun 13, 2011 13:38 PM Thanks for the feedback. Maybe for my Thursday article I'll do that. Jun 13, 2011 13:43 PM edwardarthur (4967) Let me second NumberPower's idea. As I was reading this, I kept thinking, so what does this allow me to conclude about Jorge Posada's true current hitting ability.... Jun 13, 2011 15:00 PM Nick J (23779) So hopefully at some point these sorts of things will be included in the inseason PECOTAs? Jun 13, 2011 19:33 PM The analysis behind the inseason PECOTA forecasts is a bit more rigorous, although it's along the same lines. We don't actually need to regress the inseason PECOTAs to the mean, exactly. Jun 13, 2011 20:05 PM Brian Cartwright (4519) How about Jun 13, 2011 21:40 PM Eric M. Van (31218) I'll second the nomination for (2B + 3B) / (1B + 2B + 3B), and add 1B / (1B + AB  H  SO + SF), which is to say 1B / (1B + Outs in Play). Jun 14, 2011 00:13 AM Brian Cartwright (4519) Eric, here's my logic. Jun 14, 2011 21:09 PM Not a subscriber? Sign up today!

Interesting analysis. I haven't fully absorbed all of it yet but it is food for thought. One small question  what is the rationale behind the "....we’d use 75 percent of the player and 25 percent of the mean." or more specifically, how was the 75/25 split derived?
I used the regression to the mean equation n/(n + x) where n is the sample size and x is a constant. So if a player has 300 PA (n) and it stabilizes after 100 PA (x), it would be 300/(300+100) = 75%. So we'd use 75% player and 25% mean.