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Wednesday, June 08, 2011
Testing the binomial distribution theory in baseball
Ichiro has had 802 games where he came to bat exactly 5 times. His OBP was .413.
The expectation of him getting on base 0 or once, using the binomial distribution, is 252 times. In reality, it was 262 times.
Ichiro had 671 games where he came to bat exactly 4 times. His OBP was .326.
The expectation of him getting on base 0 or once, using the binomial distribution, is 406 times. In reality, it was 399 times.
If you add the two above:
- the expected number of times he would get on base 0 or once, based on the binomial, is 659 games
- the actual number of times he actually did get on base 0 or once, based on the binomial, is 661 games
Ichiro was the first guy I looked at. That it ended up this close was fantastically fortunate for me. But, it’s not a surprise.
So, there’s my challenge to anyone else: select 10 hitters. I dunno… Rickey, Boggs, Gwynn, Raines… whoever. Whoever you are interested in (though preferably not guys with lots of IBB).
Report the results. You’ll find something close to what I found.
***
For those wondering why the OBP are so different for 4 and 5 PA: the PA was selected after the fact. If he came to bat 5 times, chances are, his team (and him) were hitting pretty well. In order to not have this issue, I would instead only look for the FIRST FOUR PA of each game. Then you wouldn’t have this problem.
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