## Sunday, October 18, 2009

### Score of the game and pitcher performance

Continuing my previous post, I will now briefly analyze the association between the score the game and some pitching stats. I certainly expected to see some statistical significance here as I used more data - a pitcher with a big lead will probably throw more strikes, giving up more home runs and fewer walks, to limit the probability of a big inning. I was interested in seeing just how big this effect is. Perhaps the FIP for pitchers with a big lead is actually lower than for those with a smaller lead, and pitchers should consider throwing more strikes all the time? Anyway, I'm sure a more detailed study on this, and the associated win probabilities for different pitching strategies has already been done.

I fit binomial logistic models (one each for HR, BB, and K) accounting for team at bat and for the pitcher (and number of pitches in the previous inning). The other factor was either lead^2 or just lead of the team pitching. With lead^2, I got coefficients and p-values:
 HR 0.0032 8.53e-05 *** BB -0.0027 1.14e-05 *** K -0.0011 0.017213 *

Lead^2 is significant for HR, BB, and K, but each translates to less than half a percent multiplicative change in the odds of the associated counting statistic for each increase of one in lead^2. There are indeed more HR and fewer BB (and fewer K) when the game is not close, but for every 200 HR you see with lead^2 = x, you'll see less than one extra HR for lead^2 = x+1. This works out to about 10% more home runs in 5 run games than in tie games.

I fit the same model with lead instead of lead^2, and the effects were in the same direction but not as large, and the lead effect in the K model was not significant at all. This implies that pitchers on both sides throw more strikes when the game isn't close.

The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at "www.retrosheet.org".