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Sunday, July 24, 2011
Players who seemingly “lost their power” for no apparent reason.
Nick Markakis averaged 17.7 HR per 600 PA in his first 4 years in baseball. Since then (2010 and 2011), he has averaged 11. There has been much talk about him “losing his power.” Now, obviously that is not a huge drop in power, but let’s look at this from a statistical perspective and we’ll use a little Bayesian inference as well.
Markakis had 2660 PA in those first 4 years, with a HR rate of .029 per PA. One standard deviation in HR rate in 2660 PA, by chance alone, is around .0026 (assuming a true rate of .0183).
Let’s say that his true HR rate over his career was actually .022, or 13 HR per 600 PA. His performance in the first 4 years would be around 2.7 SD above his true talent HR rate, by sheer luck alone. That is going to happen around 1 out of every 385 times.
That may be a small number (1/385), but the fact that we are cherry picking Markakis (or some other player) means that there are lots and lots of players who did NOT seemingly lose their power over a similar time period. In other words, with all the players we can look at, a few of them will, by chance alone, significantly under-perform their true talent HR rate (or any other stat) for no articulable reason whatsoever.
I’m not saying that we know that Markakis’ true talent HR rate has not decreased. We don’t. I’m just saying that it should come as no surprise whatsoever that a few players would seriously under-perform after 4 full years of baseball, simply because during those first 4 years, they just got lucky. And that is not even taking into consideration those who got unlucky for the next year or two, or some combination of the two (lucky at first, unlucky later).
Just another example of how we often try and invent a story or figure out a reason for things that are merely the vagueries of chance.
How does Bayes come into play? When I looked at Markakis the other day, he just didn’t look like a HR hitter to me. Although he is listed as 6-1 and 200 pounds, he doesn’t look all that powerful - i.e. a prolific HR hitter. If that is true, it is much more likely that he got lucky those first 4 years, and that 11 HR per 600 is closer to his true talent rate than 17.7. If it were someone like Prince Fielder who all of a sudden had a power outage, that would be a completely different story, statistically and Bayesianly speaking…
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