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Friday, July 15, 2005

Lineup Construction

Before Corey Patterson was sent down to the minors the Cubs once again were struggling with lineup construction - even hitting Patterson leadoff by his own request and regularly placing Neifi Perez and Jose Macias near the top of the order. Lineup construction is interesting to me because it's one of those things that your intuition tells you must be one way when hard data shows something else. In other words, while it seems like it must be important to find just the right order to maximize runs, it turns out that almost any possible lineup scores just about the same number of runs.

This conclusion regarding lineup construction was reinforced this week in a study published on Retrosheet by Tom Ruane entitled "Evaluating Traditional Lineups". In the study Ruane used a Markov chain (Markov chains have been used many times over the years to study baseball since they work with state transitions such as those present in baseball where each at bat begins in one of 24 possible states and ends in one of 25 states) to model lineup construction using data from 1993 through 2004. Using this data he analyzed 362,880 difference lineup combinations and was looking to see if there were any non-traditional lineups that produced more runs than the traditional ones.

For the NL the top producing lineups over 8 innings turned out to be:


RUNS ----- LINEUP ----
4.143 1 3 2 5 4 6 7 9 8
4.142 1 3 2 5 4 6 8 7 9
4.142 1 3 4 2 5 6 7 9 8
4.142 1 3 4 5 2 6 7 9 8
4.140 1 3 4 2 5 6 8 7 9
4.140 1 3 4 5 2 6 8 7 9
4.139 1 3 2 5 4 6 7 8 9
4.138 1 2 4 3 5 6 8 7 9
4.138 1 2 5 3 4 6 8 7 9
4.138 1 3 4 5 6 2 7 9 8

Whereas the traditional lineup scored 4.127 runs. For the AL, where the traditional lineup scored 4.477, the top lineups were:

RUNS ----- LINEUP ----
4.488 5 2 4 3 1 6 7 8 9
4.488 5 2 4 3 1 7 6 8 9
4.487 5 2 4 3 1 6 8 7 9
4.486 1 2 4 3 5 7 6 8 9
4.486 5 1 4 3 6 2 7 8 9
4.485 1 2 4 3 5 6 7 8 9
4.485 1 2 4 3 5 6 8 7 9
4.485 5 1 4 3 2 7 6 8 9
4.485 5 1 4 3 6 2 8 7 9
4.485 5 1 4 3 6 7 2 8 9

Ruane then sums up what he found as follows:

"I must confess that this wasn't what I hoped to find when I began this investigation. I suppose the best-case scenario would have been to find a handful of counter-intuitive lineups that were significantly better than the traditional ones. As it was, the best lineup in the NL scored only 4.4% more runs than the worst, and in the AL the range was even narrower, as the best team scored only 2.4% more runs than the worst. And the difference between the best and the traditional lineup is negligible: in the NL it amounted to 0.38% more runs (or about 3 runs a season) and in the AL it was 0.24% more runs. These results seem to agree with the long-held belief that the ordering makes little difference."

This result concords pretty well with a quick and dirty estimate I did last year. In my study using runs created per plate appearance and factoring in the number of plate appearances the NL optimal lineup scored 0.16% more runs than the traditional lineup and the AL 0.23% more. The optimal lineup in the NL scored 3.07% more runs than the least optimal lineup and in the AL the difference between the best and worst was 1.51%. Either way you look at it lineup construction makes little difference. Further, as Ruane mentions, the cost of making radical changes to the lineup such as batting Barry Bonds first from angry players and bewildered fans would likely offset any gains you might see.

But alas, try as I might to force my reason to overcome my emotions, I still sense a viceral reaction welling up within me when I see Neifi the Terrible and in the on deck circle in the bottom of the first. I'll work on it.

3 comments:

Xeifrank said...

I agree that at the professional level lineup construction doesn't really matter, other than possible alternating lefty and righty hitters to burn more bullpen pitchers. Studies I have run show that lineup construction and the results it provides is very random when it comes to comparing one lineup with another. Only in extreme cases did lineup construction matter much and that test was done with one great hitter and 8 very very weak hitters. Run production did drop off slightly by moving that one great hitter down in the lineup. Major league hitters in general are too equal to make much of a difference as far as what order they bat in.
vr, Xeifrank

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