THE BOOK--Playing The Percentages In Baseball

Friday, November 18, 2011

To pinch-hit or not?

MGL’s terrific guest piece at BPro:

In any case, it is easy enough to see how these starters pitched after they were allowed to bat. Remember that, on average, the starter pitched another 1.42 innings after his stint at the plate. What was the average TAv against over these 1.42 innings, again, after removing all pitcher batting? Remember, these were .258 pitchers for the season who had pitched to the tune of .221 so far in the game. They were also facing the lineup for the third time on the average; if there was no carryover effect, we would actually expect them to have pitched worse than their normal .258, all other things— like the park, weather, and opposing batters—being equal.

So how did they pitch? (We’re going to exclude the ninth inning for the reasons stated above.) They pitched to the tune of a .251 TAv against (after adjusting for opponent batter pool)—better than we expected, but quite a bit worse than their .221 prior to being allowed to hit. Coincidentally, .251 is almost exactly the same as the average reliever, who is a .250 pitcher. So leaving your “hot” starter in the game yields no advantage over replacing him with an average reliever, unless he is a considerably above-average pitcher.

What about when the starter was taken out of the game for a pinch hitter? How did the relievers pitch in the very next inning? They allowed a TAv of .243, which is around what you would expect from a late-inning reliever.

So let’s recap the last few paragraphs. When a manager allows his starter, who is an overall .258 pitcher but has thus far pitched at a .221 level, to bat in a high-leverage situation (LI > 1.5) after he has pitched at least five full innings, he pitches at a .251 level (TAv) for the next 1.42 innings, on the average. When the starter is removed in the same situation, relievers pitch at a .243 clip for at least the next inning. Clearly, there are some starters who are good enough to post a sub-.243 TAv later in the game, but remember we are asking the question, “What if we were to remove all starters when they have completed at least five innings on the mound and they are due to bat in a situation where the LI is greater than 1.5?” Whatever our answer is, we can perhaps leverage that one-size-fits-all strategy by letting some pitchers (aces) bat for themselves and continue to pitch. Of course, you are still giving up the value of using a pinch hitter, which is almost the whole point of the strategy. In other words, a pitcher would have to pitch a heck of a lot better than .243 or .250 in order to justify allowing him to bat. This brings us to our next, vitally important question:
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Also remember that each team averages around 28 of these decisions per season, and the starter ends up batting around 12 of the 28 times. Multiplying 12 times .032 wins yields a gain of .384 wins per season per team by virtue of this simple strategy.

If one were to argue that such a strategy might tax a bullpen or hurt the confidence or ego of a team’s starting pitchers, remember that the average subsequent IP whenever a starter is not removed for a pinch hitter is only 1.42. That means that we would be transferring a total of 12 * 1.42, or 17 IP, from the starters to the bullpen, an average of around three fewer innings per starter and perhaps one or two more innings per reliever. This hardly seems like a crisis.

A gain of 0.384 wins on 17 innings?  That’s a gain of +.200 wins per 9 IP, which is like replacing an average pitcher with Roy Halladay.