What was your first thought? Mine was that it had to be either the second or third spot, and I think most analytically-inclined (but maybe not analytically experienced) observers would say the same thing. Like most of these ideas, how to form the question is equally as important as how to reach the answer. To me, the phrasing of this question is most objectively defined in the following way:
If you had a lineup of average players---which, as described in the link, produces an average number of runs---and you could make one of those players 10% better, which one should you pick?
By 10% better, I mean that the rate at which is they reach base in all forms except error (walks, hits, hit-by-pitch) is increased by 10%. Strikeouts are the same. Ground ball to fly ball ratio is the same, as is baserunning. This is actually a substantial increase in player ability: an increase from a wOBA of 0.330 to 0.363 is the transition from a slightly-above-average player to a near All-Star caliber hitter. But it's easier to see the difference when making the shift larger. Over the course of a 162-game season, how many extra runs (over the fully-average team) would this new lineup score? How many would they lose if the player were made 10% worse instead?
I put this scenario through the lineup simulator and reached the following results:
Two things jump out at you: (1) Putting the boost into the leadoff spot creates the most runs relative to all other lineup spots, and (2) the 3rd spot in the order is actually the least important spot of the top 5. Now, the differences between each of these spots isn't especially significant, but this is mostly an academic exercise anyway since the "average lineup" doesn't exist in reality. But even with those caveats, it is an intriguing result.
These results here are essentially echoed in the chapter in lineup construction in The Book[1]. The value in the third spot in the lineup is attenuated by the fact that this spot comes up with 0 on and 2 outs more than any other spot. The run expectancy of any event is at a minimum. One might argue that my "objective approach" for defining this problem over-inflates the value of the leadoff spot, since the guy in the 9th slot will reach base more than a typical bottom-feeder in MLB (especially in the NL), leading to more RBI opportunities than would normally exist. However, the leadoff hitter actually leads off in ~41% of all their plate appearances[2] (which translates into 19% of all innings--nearly twice as much as the next batter, the 4th slot), so what happens in the ninth slot isn't critical. Additionally, the run expectancy + Markov Chain approach in The Book comes to pretty much the same conclusion: once the number of PAs is factored in, run values for each type of batter event are maximal in the leadoff spot for most all events save home runs, where the number of men on base is minimal.
[1] If I do anymore reinventing of the wheel on this blog, I'll be driving a semi-trailer truck this time next week.
[2] h/t SportsAnalyticsBlog for tweeting this number.
It's ironic that the sabermetric revolution seems to be responsible for an increased idea that your biggest bat needs to hit third, rather than fourth[3]. Remember back to all the arguments about where Barry Bonds should bat? But now, third seems to be the slot of choice for the games top hitters: Cabrera, Votto, Cano, McCutchen, Goldschmidt, Braun... the list goes on. Teams would be better served moving them one slot up or down. And that's not even getting into the double play opportunities afforded to the guy in the 3rd spot. I think it's worth pointing out that the Detroit Tigers have underperformed relative to their weighted runs created (wRC) every single year since Cabrera came over from the Marlins (with the exception of 2009, where they were +1 runs). And not by small margins: usually minus 20 to 40 runs each year.
[3] That's at least how I remember it. However, looking back at lineups of yesteryear kind of proves me wrong-- historically, the wOBA of the 3rd and 4th spots appears to be about the same through most eras.
Of course not all of this difference can be attributable to Cabrera batting third-- they're a slow overall team with negative team "BsR" each year except 2010 (a year they were -19 with respect to wRC)-- but as a KC fan, I'll be glad to see him come up in the third spot in 2014.
If you had a lineup of average players---which, as described in the link, produces an average number of runs---and you could make one of those players 10% better, which one should you pick?
By 10% better, I mean that the rate at which is they reach base in all forms except error (walks, hits, hit-by-pitch) is increased by 10%. Strikeouts are the same. Ground ball to fly ball ratio is the same, as is baserunning. This is actually a substantial increase in player ability: an increase from a wOBA of 0.330 to 0.363 is the transition from a slightly-above-average player to a near All-Star caliber hitter. But it's easier to see the difference when making the shift larger. Over the course of a 162-game season, how many extra runs (over the fully-average team) would this new lineup score? How many would they lose if the player were made 10% worse instead?
I put this scenario through the lineup simulator and reached the following results:
 |
| Runs gained (or lost), when making one batter in a lineup of equal batters 10% better (or worse) than the other 8. Numbers are aggregates over a 162-game season. |
Two things jump out at you: (1) Putting the boost into the leadoff spot creates the most runs relative to all other lineup spots, and (2) the 3rd spot in the order is actually the least important spot of the top 5. Now, the differences between each of these spots isn't especially significant, but this is mostly an academic exercise anyway since the "average lineup" doesn't exist in reality. But even with those caveats, it is an intriguing result.
These results here are essentially echoed in the chapter in lineup construction in The Book[1]. The value in the third spot in the lineup is attenuated by the fact that this spot comes up with 0 on and 2 outs more than any other spot. The run expectancy of any event is at a minimum. One might argue that my "objective approach" for defining this problem over-inflates the value of the leadoff spot, since the guy in the 9th slot will reach base more than a typical bottom-feeder in MLB (especially in the NL), leading to more RBI opportunities than would normally exist. However, the leadoff hitter actually leads off in ~41% of all their plate appearances[2] (which translates into 19% of all innings--nearly twice as much as the next batter, the 4th slot), so what happens in the ninth slot isn't critical. Additionally, the run expectancy + Markov Chain approach in The Book comes to pretty much the same conclusion: once the number of PAs is factored in, run values for each type of batter event are maximal in the leadoff spot for most all events save home runs, where the number of men on base is minimal.
[1] If I do anymore reinventing of the wheel on this blog, I'll be driving a semi-trailer truck this time next week.
[2] h/t SportsAnalyticsBlog for tweeting this number.
It's ironic that the sabermetric revolution seems to be responsible for an increased idea that your biggest bat needs to hit third, rather than fourth[3]. Remember back to all the arguments about where Barry Bonds should bat? But now, third seems to be the slot of choice for the games top hitters: Cabrera, Votto, Cano, McCutchen, Goldschmidt, Braun... the list goes on. Teams would be better served moving them one slot up or down. And that's not even getting into the double play opportunities afforded to the guy in the 3rd spot. I think it's worth pointing out that the Detroit Tigers have underperformed relative to their weighted runs created (wRC) every single year since Cabrera came over from the Marlins (with the exception of 2009, where they were +1 runs). And not by small margins: usually minus 20 to 40 runs each year.
[3] That's at least how I remember it. However, looking back at lineups of yesteryear kind of proves me wrong-- historically, the wOBA of the 3rd and 4th spots appears to be about the same through most eras.
Of course not all of this difference can be attributable to Cabrera batting third-- they're a slow overall team with negative team "BsR" each year except 2010 (a year they were -19 with respect to wRC)-- but as a KC fan, I'll be glad to see him come up in the third spot in 2014.
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