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Saturday, August 14, 2004

Batting Barry First?

Earlier this season there was much discussion by folks advocating that the Giants bat Barry Bonds higher in the lineup, possibly even first citing the increased number of at bats he would get which would result in more runs and, as the theory went, more wins for the Giants.

I've heard arguments like this before with different people citing the number of extra at bats a player would garner at different spots in the order. In fact, Earnshaw Cook in his 1964 book Percentage Baseball advocated just such a strategy and claimed it would greatly increase run scoring if a team used a lineup in descending order by run production. Well, I finally had a chance to sit down today and see for myself just what the difference actually is and whether or not it would really matter.

To see what the difference in plate appearances actually is 1 through 9 in a typical season I loaded the 1992 (the latest season available) Retrosheet play-by-play data into SQL Server. I then wrote a couple queries to show how many plate appearances each spot in the batting order had. The results:

American League

Lineup PA PA/G PA/162

1 10621 4.68 758.64
2 10395 4.58 742.50
3 10161 4.48 725.79
4 9911 4.37 707.93
5 9661 4.26 690.07
6 9428 4.16 673.43
7 9176 4.05 655.43
8 8915 3.93 636.79
9 8619 3.80 615.64
National League

Lineup  PA  PA/G  PA/162

1 8995 4.63 749.58
2 8809 4.53 734.08
3 8616 4.43 718.00
4 8413 4.33 701.08
5 8205 4.22 683.75
6 7996 4.11 666.33
7 7766 3.99 647.17
8 7536 3.88 628.00
9 7322 3.77 610.17
So from top to bottom there was about 140 plate appearance difference and roughly 15 to 20 fewer plate appearances for each position lower in the batting order. So moving Bonds from fourth to first would provide somewhere between 45 and 60 extra plate appearances in which to do his damage. Since 2003 was a higher scoring season than 1992 each lineup position would get more at bats but I'm not sure that would change the difference between positions or the ratio. How would moving Bonds to leadoff then impact the Giants?

One way to try and answer this question is to look at how many more runs Barry would create with those 45 to 60 extra plate appearances. This is easy to do given Bill James' basic Runs Created formula ((H+BB)*(TB)/(AB+BB)). Since Bonds created an average of .283 runs per plate appearance, giving him 45 to 60 extra plate appearances would yield between 12.8 and 17 extra runs. Using the Pythagorean Formula (Winning Pct = (R^2)/(R^2+RA^2)) you can then estimate how many more games the Giants of 2003 would have won with those extra 15 or so runs. Since they actually scored 755 runs and allowed 638 adding 15 more runs gives them an extra 1.6 wins (a simple rule is that in most leagues a win is purchased with 10 to 11 runs). So moving Bonds would help but not by much.

A related question is whether a team should reorder its lineup in descending order by ability to maximize their production per Cook. To test to determine how many runs a team might gain by maximizing its plate appearances I simply calculated the Runs Created per Plate Appearance for the nine lineup positions in the 1992 AL and NL and then reassigned the plate appearances in descending order starting with the highest RC/PA. For example, in the AL in 1992 the third hitter in the lineup created the most runs per plate appearance at .1296. I therefore assigned the third position the 10,621 plate appearances that the leadoff hitters amassed and recalculated the Runs Created. Finally, I added up all the Runs Created for the new optimal lineup to see how it differed from the non-adjusted lineup. Here are the results:

1992 AL Non-adjusted Lineup = 694.2
1992 AL Optimal Lineup = 695.3

1992 NL Non-adjusted Lineup = 643.7
1992 NL Optimal Lineup = 645.2

In both cases the optimal lineup that gives plate appearances to its best run creators only created the equivalent of a little over 1 run for an entire season.

I then turned the tables and created the least optimal lineup by reversing the optimal order. This resulted in 684.8 runs for the AL and 625.4 runs for the NL a loss of 10 runs in the AL and 18 in the NL. The larger drop in the NL is accounted for by the fact that a much weaker hitter, the pitcher, would be getting the most plate appearances. This also highlights the fact that in any individual team the variance between lineup positions will be greater than the averages used for this analysis. That means that an average team could be expected to pick up more than a single run when their lineup is optimized and the amount would depend on the magnitude of the offensive differences between their players. For example, if a team in the NL in 1992 were to switch its 9th and 2nd hitters they would score 634.7 runs, only nine fewer than the normal lineup. This is a far smaller effect than I had previously supposed.

This analysis clearly vindicates the conclusion of Palmer and Thorn in The Hidden Game of Baseball when they said, "All the time managers put into masterminding a winning lineup is so much thumb twiddling, and they are hereby granted an additional hour's sleep a night."

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Kenji said...

I have a theory that the lineup should be 3-2, instead of 1-9. That is, the pitcher bats 7th. I don't want the pitcher to bat right before my traditional #3 batter. I like the theory of having the speed #1 guy, contact #2 guy, and power 3-4-5 guys. I'm just willing to sacrifice the first inning for the betterment of the other eight.

What happens when you re-align the lineup so it goes 3-4-5-6-7-8-9-1-2 instead of 1-9?

In your study, the best hitters hit more often, but every single time they hit, they hit behind the worst hitters. In mine, they hit more often, and still bat behind the same guys in the lineup as today's traditional system.