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June 20, 2011 Resident Fantasy GeniusWhen Pitchers' Stats StabilizeLast week in this space, I updated a study originally run four years ago by former BPer Russell Carleton (then monikered “Pizza Cutter”) at the nowdefunct 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 secondever live BP chat tomorrow afternoon at 1 p.m. EST to answer all of your fantasy questions.
Methodology 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 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 (20052010). 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 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 hitbypitch rate takes over two years.”
Note 1: The stolenbase figures are not a perfect (or anywhere near perfect) gauge of the pitcher’s stolenbase 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 battedball data this week. Colin Wyers informed me that Retrosheet actually uses MLBAM battedball classifications with a little tweaking, so I’ve only included the one set this week.
What These Findings Teach Us The fact that fly balls stabilize quickly and home runs stabilize quickly on a percontact basis but slowly on a perfly 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 hitbypitch 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 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 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 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 9 comments have been left for this article.

The HBPcontrolledbyhitter observation makes perfect sense if you consider the role of the hitter's setup distance from the plate and his reaction tendencies. A guy who hangs over the inside corner and simply twists away instead of leaning back is bound to get hit much more often than the with the open stance off the plate.
Further, we know that certain hitters get pitched inside more than others due to their skills as a hitter. I'm guessing that power hitters tend to be pitched away more than slap hitters. Maybe that's why a guy like Biggio got hit more often  pitchers were more willing to come in on him because they weren't afraid of him jerking the ball over the fence. Perhaps it's similar to HRs and FBs. Guys who see more pitches inside get hit more often.
Biggio "got hit" more often because he crowded the plate and ducked into pitches. That's why he got thrown at a lot, too  pitchers figured if the umps were gonna let him get away with that crap, they might as well just plunk him.
And Biggio had very respectable pop  291 career dingers and a career .433 Slug despite having the Astrodome as a home park for 12 years.
I'm not sure i'd ever be able to find it, but I remember that a previous article here on BP had also found that HBP were controlled by the hitter. I had commented at the time because I was surprised by the result... is there a way for me to search for article's I've commented on?
I think this is the article you were remembering:
http://www.baseballprospectus.com/article.php?articleid=10533