THE BOOK--Playing The Percentages In Baseball

Wednesday, August 18, 2010

Understanding DIPS

Even though everyone who has ever written about DIPS in a responsible fashion explains it in terms of something like this:

“Pitchers have little or no control over their BABIP (emphasis mine)...”

Many people construe that as “no” (rather than “little or no") control, which leads to criticisms like (I am making these up to illustrate a point) this:

“Come on, one of the greatest pitchers in the history of baseball, Mariano Rivera, has a career BABIP of .277.  Any idiot can see that he induces weak contact, therefore he surely has a lot of control over his BABIP.”

Well, here’s the thing:

First of all, when someone says, “Little or no control,” they are not referring to any individual pitcher.  What they mean is simply that the spread of true BABIP talent among MLB pitchers is small.  Whether that wording, “Little or no control” is to your liking is up to you I suppose.  That is always one of the problems in trying to use “English” to describe or explain a mathematical concept.

I suppose that one could easily say, “All pitchers absolutely have control over their BABIP.  It is just that there is also a lot of noise or random variation in any sample of BIP that is less than enormous.”

The words, “Little, a lot, good, bad, great, etc.” have very little meaning without context and can generate an awful lot of controversy when used to describe or explain mathematical concepts.  One could on one hand say that Jason Kendall is a great baseball hitter, as compared to all baseball players at all adult levels, while on the other hand one could say that Kendall is an awful hitter, as compared to the population of major league baseball players.

Anyway, I digressed a little.

OK, let’s assume that DIPS is correct in that the spread of true talent (for those of you who don’t know what that means - it is the “fill in the blank” that a player will accomplish if given an infinite number of opportunities, thus eliminating any random fluctuation or luck if you will.  That number is also exactly equal to the best estimate of what that player will accomplish at any time in the future, assuming that that true talent “X” does not change with age, injury, etc.  For example, the “true talent batting average” for a fair coin flip is .500) is very small.  Again, using the word “small” in that context is almost meaningless, since we are not comparing it to anything in particular.  But, we’ll stick with that characterization.

In fact, let’s say that by “small” we mean that the standard deviation (SD) of true talent BABIP for pitchers is 7 points or .007.  That basically means that virtually all pitchers have a true talent BABIP of .279 to .321, assuming that the mean is .300 (even though we can assume that the talent distribution is normal, there are practical limits such that even though technically a normal distribution has no limits at either end, when it comes to human endeavors and characteristics, there likely are limits).

Now, because this talent distribution is so “small” (say, compared to batting average, which probably has a SD of around 20 points or so), what this means is that for most samples of BIP, even multi-year ones for starting pitchers, we must regress their sample (actual) BABIP a lot - probably in the 90+% range - in order to estimate their true talent BABIP.

And that is where the trouble often starts.

Let’s say that we have some really good pitchers in a season or two and they are “consistently” posting BABIP’s of .270.  The sabermetrician will quickly tell you that those .270 BABIP’s are likely mostly luck and he will estimate those pitchers’ true BABIP at something close to league average, or .300.  And that is when the ***t starts to hit the fan!  People start screaming, “What about Mariano Rivera, or Billy Wagner?  Or Nolan Ryan or even Tim Wakefield?  Surely great pitchers have low BABIP!  Why are you assuming that pitcher’s X, Y, and Z, are really .293 or .295 pitchers when they have posted .270 BABIP’s for 2 straight years?”

Well, here is the deal. There ARE some pitchers who are true .280 pitchers.  And some that are even true .275 pitchers.  And possibly even .270 pitchers.  We already told you that when we told you that the SD of BABIP true talent among MLB pitchers was 7 points!  That means by definition that there likely are some of these pitchers in existence (not necessarily at the present time of course).  It is just that we don’t know who they are!  And there are so few of them, as compared to the many, many more who are near average, that if we find a pitcher who posts a low BABIP in 1 or even 2 or 3 seasons, it is much more likely that he is near average and got lucky than he is a true low BABIP guy.  So we just automatically assume that he is somewhere in between, but much closer to average.

Even though we might call him a .293 pitcher (say, .270 heavily regressed toward .300), what we really mean is that there is a 20% chance he is a .300 pitcher who got lucky, 15% chance he is a .299 pitcher who got lucky, a 10% chance he is a .298 pitcher who got lucky....all the way down to a 1% chance he is a true .280 pitcher, and a .1% chance he is a true .270 pitcher, exactly equal to his sample BABIP.”

So yes, he could be another Mo Rivera, who is likely 2 or 3 SD’s from the mean in BABIP.  But we simply don’t know that yet until we have 15 or 20 years from the guy at a .270 or .280 clip, and even then we are not 100% sure what he is.  At that point, the numbers will change to, “20% chance he is a .275 pitcher, 15% chance he is a .280 pitcher who got lucky, 10% a .285 pitcher who got lucky, etc.”

One final thing.  If we know something else about the pitcher other than his BABIP numbers, we can and should certainly change the way we do the math - at least change the mean we are regressing toward.  If he throws 95 mph like a Nolan Ryan, maybe the mean BABIP for all pitchers like that is .295 rather than .300 (I don’t know).  If he throws a knuckleball, like Wakefield, the mean BABIP is probably lower too.