In comparing starting pitching in a playoff series, one should NOT
use season averages (BB/9, K/9, SNLVAR, ERA, etc.) to compare the pitching
rotations of two teams that are facing each other in the playoffs. Because
pitchers only pitch once or twice per series, there is little chance that
a pitcher's performance will lie close to his regular season average in
an individual game.
For example, Pedro Martinez struck out about 28 percent of the batters
that he faced (prior to his injury in late June), but on some days he was
red hot (like when he struck out 11 of the 25 batters he faced in San Diego
on 22 April). On other days he was not so hot (like when he only struck
out 3 of the 25 batters he faced in Washington on 12 April).
Averages are important, but when comparing the pitchers in an individual
game, it's far more important to look at a pitcher's variance.
Intuitively, a rational manager would like to start a pitcher who gives
up few walks and few home runs and such a rational manager would also like
to be reasonably certain that the number of walks and home runs that the
pitcher gives up will lie close to his (low) average. (A similar statement
can also be made for strike outs).
To that end, I calculated a pitcher's probability of striking out a
batter, walking a batter and giving up a home run to a batter and I also
calculated the standard deviation around those averages.
Before getting into the specific details of how the probabilities were
calculated, let's have a little fun and look at the probabilities for each
starting pitcher in the Mets, Cardinals and Tigers rotation.
Technical Notes
Now, the more technically minded among you probably want to know how
I computed these probabilities and standard deviations.
First, I computed the ratio of strike outs to the number of batters
faced* for each game that the pitcher started, the ratio of walks to the
number of batters faced and the ratio of home runs to the number of batters
faced. This yields estimates of the probabilities of striking out a batter,
walking batter and giving up a home run to a batter (in each game).
Since we're dealing with percentages, so a probability has to be converted
into the natural logarithm of its odds ratio to obtain a continuous variable:
ln odds ratio = ln(prob) - ln(1-prob)
Then, I computed the average and standard deviations of the natural
logarithms of the odds ratios, computed the 90% confidence interval and
converted those intervals back into percentages:
* I took the raw numbers from MLB game logs, so I didn't get the precise
number of batters faced in each game. Instead, I had to add: outs + hits
+ walks to get the approximate number of batters. The trouble here is that
a batter who reaches first base and then gets caught stealing is counted
as two batters.
