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February 17, 2005

Crooked Numbers

Playing With the Lineup

by James Click

On the radio in Boston yesterday, the hosts of the show asked me if I thought that Edgar Renteria would be a good fit for the second spot in the Red Sox lineup. My response was that yes, Renteria would make for a good candidate for the two spot because he has a good OBP; their theory was that he would make a good #2 hitter because he hits for contact. We briefly discussed the idea that the batter in the two hole should be a contact hitter, able to get the leadoff hitter into scoring position for the big bats behind, and the general theories that higher OBP players should bat higher in the lineup to get them more plate appearances.

The more I think about it, though, I’m not sure that we know how much difference the lineup makes most of the time, or whether some of those conventional theories about lineup structure make sense. There has been work on lineup theory out there, from Keith Woolner’s efforts to more advanced research using Markov models.

The lineup is the part of the game over which the manager has the most control. Like the recent trends in bullpen management, however, it’s so ruled by convention that managers really can’t do anything that contradicts with mainstream thinking without drawing the ire and consternation of fans and writers alike. When Tony LaRussa starting batting his pitcher eighth instead of ninth to “get more guys on base in front of Mark McGwire," he was lambasted. When the A’s put Jeremy Giambi--who was as good at stealing as Tommy Williams--in the leadoff spot, the outcry from the media was even greater. Writers stacked soapboxes on top of soapboxes to scream about the essential skills that a leadoff hitter must have, conclusions drawn from years of experience watching and playing baseball.

A lineup's construction has two ramifications: how many times each player bats, and how those plate appearances interact with each other (for the time being, I’m going to disregard tactical matters such as alternating left-handed and right-handed hitters to mitigate platoon issues). The first effect is quite simple and can easily be estimated by average team performance and lineup position. If Barry Bonds bats first, he’s going to get significantly more plate appearances over the course of the season than if he bats lower. Usually, that’s a good thing, but the reason that Bonds doesn’t bat first is the second ramification. Conventional wisdom teaches that the value of those extra plate appearances will be nullified by the fact that Bonds will frequently come to the plate with no one on base by virtue of batting leadoff or, later in the game, after the weaker hitters at the bottom of the lineup. His ability to advance baserunners with long hits is wasted.

In order to start to tackle the problem of lineup optimization from a more theoretical and mathematical standpoint, I’ve written a program that simulates games from a probabilistic perspective. This program is quite similar to something like Strat-O-Matic; it is given a large set of probabilities for game situations and it “plays” out the games, going through each batter and determining the outcome based on the given probabilities. A basic example would be the following:

• Single: .232 (23.2%)
• Double: .035
• Triple: .012
• Home Run: .002
• Walk/HBP: .069