THE BOOK--Playing The Percentages In Baseball

Wednesday, March 31, 2010

A very good article by Sky A. on batter tendencies (ability to hit the fastball, curve, etc.)

Here is the URL of the article:

http://baseballanalysts.com/archives/behind_the_scor/

And here is the concluding paragraph:

Overall, this has been a somewhat sprawling piece on a tricky topic, so I’ll sum up. Looking at the evidence, it appears that when trying to identify a hitter’s strengths and weaknesses against particular pitches, looking at how he actually did against those pitches is not a particular useful measure. More indicative is the frequency which a batter was thrown each pitch. The better a hitter is against a particular pitch, they less often he will see it. This entire issue of selection bias is an important one to consider, especially when doing pitch f/x analysis or other pitch-by-pitch studies.

Basically, he starts out looking at the range (SD) of results for all batters against all different kinds of pitches, using a runs per pitch metric. He wants to see who is a good fastball hitter, who is not, etc., or at least what is the spread of talent among batters against each type of pitch.  If some batters are good fastball hitters, others are good curveball hitters, etc., we should see a spread in talent with respect to each of those pitches, right?  Uh, wrong…

First, here is how he found the spread of talent:  He used the wonderful method which Tango has been touting for years.  Take a sample of results, compute the variance (square of the SD) among players (say, weighted by opportunities per player) and then compare that to the expected variance by chance given the number of elements in your sample (number of batters), and the underlying sample size (number of pitches) for each element. The difference is the spread of talent, more or less (there are sometimes other small sources of variance besides talent and chance).

What sky found, and not surprisingly so, is that there was little or no spread of talent, when looking at runs allowed per pitch or per 100 pitches (or whatever) for each type of pitch.  Of course he explains why, which is same reason I wrote, “Uh, wrong...” above.  Those of you familiar with game theory and its implications already know why.  If in fact there IS a spread of talent among batters with respect to pitch type, according to the tenets of game theory pitchers will throw fewer and fewer of the pitches that a hitter hits well and more and more of the pitches that a hitter does not well (to that hitter of course) until the results of all those pitches are equal!  And that is why Sky finds virtually no spread of talent when he looks at the results of each kind of pitch.  There is a spread in talent but it “disappears” when pitchers adjust their pitch frequencies, as it should (if pitchers and batters are acting reasonably optimally).  The reason that this happens of course, is that the more a batter expects a certain kind of pitch, by virtue of how often it is thrown to him, the better he will do against that pitch, regardless of his “talent” at hitting that pitch.  If a batter is a great fastball hitter but not such a great curveball hitter, if hardly ever sees the fastball, he won’t be so good at it anymore.  Similarly, if he sees lots of curveballs, he is going to be better at hitting them.

Keep in mind that this “shifting in the quality of the results” against each type of pitch, according to how often (percent per pitch) the batter sees each type of pitch, is not because a batter gets used to certain pitches (or not) and thus improves his ability against that pitch (or not), although that is certainly true to some small extent.  It is the anticipation of a certain pitch at a certain count that drastically affects a batter’s results on that pitch.

Anyway, I spoiled Sky’s great article to some extent, but I really wanted to emphasize this point about game theory, because it is important and fascinating, in my opinion.  In fact, all batters, pitchers, coaches, and managers should take at least a basic primer on game theory…