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March 3, 2004

Breaking Balls

Optimal Bullpen Usage, Continued

by Derek Zumsteg

I wrote a piece in the Baseball Prospectus Basics last week ("How to Run a Bullpen.") I got a lot of feedback that ran like this:

Hey, that table you ran shows that it's good to generally use the best reliever in tighter situations, rather than to protect three-run leads in the ninth...Facing a tie game in the eighth, wouldn't it make sense that a manager would save his best pitcher for the ninth, which would be even more important?

This is a fine question, and one I think deserves to be answered in some depth. Here's that chart again, for ease-of-reference:

    Home                                 Away
1) Top 9th, lead by 1 (.170)     1)  Bottom 9th, lead by 1 (.223)
2) Top 9th, tied      (.160)     2)  Bottom 8th, lead by 1 (.158)
3) Top 8th, lead by 1 (.123)     3)  Bottom 9th, tied      (.155)
4) Top 8th, tied      (.115)     4)  Bottom 8th, tied      (.122)
5) Top 7th, lead by 1 (.096)     5)  Bottom 9th, lead by 2 (.113)
6) Top 7th, tied      (.092)     6)  Bottom 7th, lead by 1 (.111)
7) Top 9th, lead by 2 (.080)     7)  Bottom 8th, lead by 2 (.108)

There's no simple answer to the question of whether it's better to pitch early or later. If you're the home team, faced with a tie game in the seventh, there's a possibility that if you can hold the other team down but are unable to score yourself, you'll have to fill in three innings: the seventh tied, the eighth tied, and the ninth tied. And each inning grows in leverage, so if you had to order your bullpen of one-inning-only relievers according to that chart, you'd want the best to pitch the ninth, the second-best to pitch the eighth, and so on.

The problem with that logic is twofold. First, you don't know and can't know in advance what the score will be in future innings, and suddenly we're into the kind of prediction theory that's better suited to meteorology and the advanced combinational work of game theorists. A tie game in the seventh is a high-leverage inning, no matter what happens later.

Baseball's not a game of vague theory, though. No team features nine league-average hitters, and that's what makes baseball interesting. Let's take this tied-in-the-seventh situation and look at it in detail from the home team's dugout. The manager should know:

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