Today's question: how does the number of runs scored depend on where in the batting order the inning starts?
My first guess was to look at the percentages of runs scored, but this is a clear error, as the #1 spot in the lineup gets so many more chances than the other positions. What we really want is the variation in scoring rate - how does the average number of runs scored when this hitter leads off compare to the average number of runs scored overall.
Now, one could look at offenses - but there's some concern that efficient offenses are shaped differently than inefficient ones. So for my baseline, I decided to turn the question about and look at runs allowed - facing an assortment of lineups over the course of a season is a rough approximation of facing an average lineup.
Obviously, the designated hitter looms as a distortion that we need to worry about. In collecting the data, I aggregated AL and NL results independently, but limited my tests to those years when the DH rule was in effect. Interleague play threatens to add another hobgoblin to the mix, but fortunately the dataset I obtained from retrosheet stopped at 1992 anyway.
An overview of the results:
The general curve of results is about the same shape in both leagues. The amplitude differs in that the NL is much higher and lower than the AL. The ranking of the lineup spots is almost identical - in the NL, the 8 spot is slightly below the 5 spot; in the AL, the 8 spot is distinctly higher.
| # | NL | AL |
|---|---|---|
| 1 | 1.189 | 1.109 |
| 2 | 1.169 | 1.089 |
| 3 | 1.133 | 1.069 |
| 4 | 0.962 | 0.982 |
| 5 | 0.884 | 0.912 |
| 6 | 0.816 | 0.892 |
| 7 | 0.798 | 0.881 |
| 8 | 0.873 | 0.945 |
| 9 | 1.004 | 1.035 |
The standard deviation is around 0.1585, which suggests that when looking at offenses, distinguishing between signal (true deviations from the distribution of talent in the lineup) and noise is going to be a bitch.
June 30, 2005 7:44 PM
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