Unpredictable, rare, and occasionally effective…but always entertaining.

Count Dependent Game Theory

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Jeremy Greenhouse at Baseball Analysts wrote an interesting piece regarding how the count relates to pitch selection and swing rates.  His takeaway:

The rate at which pitchers throw strikes aligns perfectly with the average run expectancy in each count. However, batters’ swing rates are not likewise dictated by run expectancy. Instead, batters like to swing more the deeper they get in the count.

The big question is, How much do batters learn from pitch to pitch? The deeper into his repertoire a pitcher must go, the greater the advantage is for the batter. There are probably advantages to taking pitches besides drawing balls. I don’t think this applies to the full count, though, which might be why the swing rate is too damn high.

He also made his data available, and I’m going to steal it and re-organize it.

Count FB% Zone% Swing%
0-0 68.1% 50.2% 26.7%
1-0 68.6% 52.0% 40.7%
2-0 81.6% 55.3% 40.0%
3-0 95.2% 58.5% 6.6%
0-1 55.3% 41.8% 46.1%
1-1 56.4% 46.5% 52.9%
2-1 68.5% 52.6% 58.7%
3-1 85.0% 57.5% 54.3%
0-2 52.4% 29.0% 49.4%
1-2 49.2% 35.7% 57.8%
2-2 54.0% 43.8% 65.4%
3-2 69.4% 54.0% 73.7%



  • It seems like the FB% tells us what I think most of us know; pitchers throw more fastballs to avoid walks when there are 2 or 3 balls in the count (exception being 2-2, which makes sense because they aren’t behind in the count in this situation).
  • The zone % also makes sense to me.  With no strikes, it’s within 8 percent from 0 balls to 3 balls – very little change.
  • With one strike, it ranges from 41 to 57%, and a hitter is just as likely to see a strike 3-1 as he is 3-0.
  • The interesting data is with two strikes.  At 0-2 and 1-2, there’s really not much incentive to throw a strike; see if the hitter will get himself out.  But get to 3 balls and 3-0, 3-1, and 3-2 are within 3 percent of one another.
  • With the swing %, a hitter is more likely to swing with each additional strike.  Wouldn’t that just be due to the batter knowing he might HAVE to swing in that count (particularly with two strikes)?
  • I suppose the 3-2 swing % is highly correlated with the increase zone % from pitchers; that is, a pitcher is more likely to throw a strike with three balls and a hitter is more likely to swing with two strikes, so this is a perfect storm.

Anyway, it’s an interesting experiment in game theory that I thought I would share.


Written by Dan Hennessey

October 20, 2010 at 11:06 PM

Posted in Uncategorized

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