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Last week in this space, I updated a study originally run four years ago by former BPer Russell Carleton (then monikered “Pizza Cutter”) at the now-defunct MVN’s StatSpeak blog. The study examined how long it takes for different stats to “stabilize.” Since I looked at hitting last week, I’ll be looking at pitching this week.

Before I get started, I wanted to make one quick announcement. After my first chat was such a success, I’ll be holding my second-ever live BP chat tomorrow afternoon at 1 p.m. EST to answer all of your fantasy questions.

Methodology
Note: This section is copied from last week’s article, here only for convenience, as the methodology for hitters and pitchers is identical.

The methodology I used was a combination of the one used by Russell, a similar methodology used by Harry Pavlidis at The Hardball Times, and some improvements suggested by Tom Tango.

Like Russell and Harry, I ran a split-half 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 (2000-2010) of data for most stats and as much as possible for batted-ball types (2005-2010).

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 Pitchers
Here are the results of running these tests for a number of stats. The following table has the stat in the first column, the denominator used in the second, how many units of that denominator before it stabilizes in the third, and approximately how many years that translates to in the fourth.

To read the “Stabilizes” column—the one we most care about—we would say, “Strikeout rate, defined as K/(PA-IBB-HBP), stabilizes after 100 PA-IBB-HBP.”

The “Years” column is for a league-average player (assuming 650 PA is one full season) and will sometimes vary significantly from player to player. It’s there as a quick-and-dirty way to make comparisons between stats since they’re all using different denominators. This allows us to say, “OK, strikeout rate takes about one-fifth of a year to stabilize, but hit-by-pitch rate takes over two years.”

 Stat Denominator Stabilizes Years K PA-IBB-HBP 126 0.2 UIBB PA-IBB-HBP 303 0.5 943 1.5 PA-IBB 1346 2.1 PA-HBP-K-BB-HR-ROE 3893 8.4 2B PA-HBP-K-BB-HR-ROE 2305 5.0 3B PA-HBP-K-BB-HR-ROE 4977 10.7 2B+3B PA-HBP-K-BB-HR-ROE 1882 4.0 2B 2B+3B 351 11.0 3B 2B+3B 351 11.0 1B+2B+3B (BABIP) PA-HBP-K-BB-HR-ROE 3729 8.0 PA-K-BB-HBP 1271 2.7 HR (HR/FB) OF FB [MLBAM] 1239 9.4 GB [MLBAM] GB+OF+IF+LD 105 0.2 OF FB [MLBAM] GB+OF+IF+LD 205 0.4 IF FB [MLBAM] GB+OF+IF+LD 288 0.6 LD [MLBAM] GB+OF+IF+LD 2026 4.3 SB+CS 36 2.3 SBA 1B+UIBB+HBP+ROE+FC 161 1.2

Note 1: The stolen-base figures are not a perfect (or anywhere near perfect) gauge of the pitcher’s stolen-base prevention skills because we’re also correlating on the catcher, who will be the same for the majority of plate appearances in each half of the sample.

Note 2: I’ve only included MLBAM batted-ball data this week. Colin Wyers informed me that Retrosheet actually uses MLBAM batted-ball classifications with a little tweaking, so I’ve only included the one set this week.

What These Findings Teach Us
There are some very interesting things to note in these findings. The first, and most obvious, is just how long it takes for BABIP and HR/FB to stabilize. We’ve always known that they take a long time, but now we see just how long it takes. They actually take much longer than I expected, but I’ve checked and don’t think I’ve done anything wrong in arriving at these figures, especially when all the others are what we’d expect and when they seem to mesh with Harry’s results.

The fact that fly balls stabilize quickly and home runs stabilize quickly on a per-contact basis but slowly on a per-fly ball basis essentially confirms that most of a pitcher’s ability to prevent home runs is wrapped up in his batted ball profile, as we’ve long assumed. This just reinforces it to a much greater extent.

One minor but incredibly interesting thing to note is that hit-by-pitch rate actually stabilizes quicker for hitters (501/0.8) than it does for pitchers (1346/2.1). Normally we’d think that the pitcher has more control over HBPs since he’s the one throwing the ball, but that doesn’t appear to be the case. Hitters actually appear to have nearly three times as much control over them than pitchers do.

Like we’d expect, ground balls and outfield flies stabilize very quickly, with line drives bringing up the rear. Infield flies also stabilize quite quickly, much quicker than many assume. Considering that they turn into outs nearly 98 percent of the time, infield flies are perhaps the most overlooked stat when analyzing a pitcher.

Correcting Misconceptions about the Use of these Numbers
Note: This section is, again, copied directly from last week’s article, just in case anyone missed it and is jumping in this week.

While Russell’s original study was linked all over the place, people who use these numbers are sometimes confused about what they truly mean and how to use them properly.

First, note that these numbers are not magic. Once a hitter reaches 100 TPA-IBB-HBP, his strikeout rate doesn’t suddenly become a perfect representation of his talent. 99 TPA-IBB-HBP 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 this season, 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.

Special Thanks
I wanted to give a special thanks to Bryan Donovan and Harry Pavlidis from The Hardball Times, who helped me out with some of the coding a while back.

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