from Amazon
Tuesday, June 08, 2010
Game theory on 3-2 counts
David in a fascinating piece:
If you do the math, you find that hitters want to swing 74.5 percent of the time, which makes sense since pitchers will obviously just about always want to throw a strike given the high cost of throwing a ball when the batter is taking. In fact, hitters swing 73.2 percent of the time in 3-2 counts, which is just about what game theory would predict.
...
Do the math and you find that pitchers want to throw a strike 89.8 percent of the time. In actuality, however, they throw strikes on only 59.2 percent of their 3-2 pitches. Again, the hitters confirm our model’s predictions while the pitchers do not! What is going on?
My issue here is with his chart:
If the pitcher threw a strike and the batter went after it, for example, the hitter ended up with a .330 wOBA, on average. If the hitter didn’t offer, his wOBA was just .273. If the pitcher threw a ball and the hitter nonetheless took a swing, his wOBA was really pitiful—.188—but if he kept his bat on his shoulder, it was a hefty .688.
First, I don’t know how the wOBA can be .273 on strikes that the batter takes. It should be .000 (a strikeout). The wOBA on balls that that the batter takes should be close to .700, and it is (a walk).
When he’s working out his probabilities to get to the equilibrium point, he’s using these numbers as fixed. Well, the .188 wOBA on balls out of the strike zone that the hitter swings at is based on his expectation that the ball might be close to the strike zone. And similarly, his .330 wOBA on swings at pitches in the strike zone is based on his expectation of a decent pitch.
However, what happens if, as David’s model suggests, that the batter will take every pitch? The pitcher will throw easy strikes, and on the rare occasions that he doesn’t take, his wOBA on swings at pitches in the strike zone will be say .500.
So, unless I’m not following along correctly, we need a model that will float the values of the swings based on the ball/strike frequency.
Love this stuff.
Recent comments
Older comments
Page 1 of 344 pages 1 2 3 > Last »Complete Archive – By Category
Complete Archive – By Date