"Subconsciously, Athletes May Play Like Statisticians"

There's some evidence that people everywhere are actually intuitive statisticians, at least with things that have been around long enough to be hard-wired in through evolution.

See Steven Pinker's "How the Mind Works" for some good examples.

Probably off-topic, but humans (and all animals, actually) tend to hone in on mathmatically near-perfect solutions to problems such as foraging and hunting and etc.

 

Years ago, I read Jim Bouton's book, "Ball Four."

If you haven't read it, you should. Many amusing anecdotes.

One of Bouton's teammates in his travels was Mike Marshall, a relief pitcher who had his best seasons with the Dodgers. He was considered a bit of flake since he was actually quite a smart guy, and got a PhD in exercise physiology while he was playing in the majors. He has a pretty interesting web site and take on developing younger pitchers. See:

http://www.drmikemarshall.com/

The school of thought in pitching in those days, and today, was that you find a batter's weakness and attack it. In Ball Four, in contrast, I distinctly remember Marshall telling Bouton something I will never foget:

"A random pattern of pitches is best."

Compare that view with Ted Williams approach to hitting. He said a batter has to "guess."

By that, I think he meant that since you have to little time to react to a ball thrown at you, don't try to determine what the pitch is when it's thrown. Rather "predict" what it will be, thus allowing you to be completely prepared before the pitch is delivered.

That gives you, the batter, a probabilistic "edge" in the confrontation. The "events" where you "predict" correctly will be that much more likely to result in the a desired outcome -- thus outweiging the consequences of the negative events when you "guess" incorrectly.

 

http://hera.ucl.ac.uk/sml/publications/media/NYT-Jan-04.htm

You can read it here without going to the Times site.

It would be interesting to see how this relates with cognitive dissonance.

On the one hand you have with Bayseian

With CD you have

I think this is where the battleground lies that causes coaches to feel like they are banging their heads against a brick wall It also may explain why in the example of the tennis matches, they didn't mix the serves as randomly as the computer models would suggest.

 

I'm not sure if this article has already been posted on the forum or not... anyway, here's a journal article that shows that PK taking is better explained by game theory than other statistical models. The data is from French and Italian leagues in the late 90's.

From the Crooked Timber blog.