Much has been made this season of Willie Randolph's questionable lineup construction, specifically his inability (or unwillingness) to acknowledge who his best hitter was, amongst other things. Very early on it was clear to anyone who watched the games, read the boxscores, or looked at the statistics that David Wright, in just his first full season in the big leagues, had blossomed into the best hitter on the team.
Randolph took much longer than everyone else to make this discovery, and as a result Wright lost plate appearances while batting sixth and seventh for much of the season. The old adage is that your best hitter should bat third, which provides ample opportunity to:
a) Come to the plate plenty of times, and
b) Come to the plate plenty of times with runners on base
For all of the seemingly-obvious benefits of ideal (or close to ideal) lineup construction, we have also heard in the past few years that any advantage gained by such construction, while real, is largely overrated and is not nearly as critical to a team's success as, say, bullpen management, another of Randolph's weaknesses this season.
I thought I would run a little experiment to see how much it has cost the Mets having their best hitter batting somewhere lower than third in the lineup. For starters, I had to establish a measure of value that I could apply to any plate appearances that David Wright "lost". I decided to use Runs Created, since it is fairly universal and is readily available for a good variety of splits at ESPN.com.
To this point in the season David Wright has created 102.1 runs in 602 plate appearances, which works out to .170 RC/PA. Wright's 102.1 RC is good for 12th in the National League. Derrek Lee (146.8 RC, .229 RC/PA) and Albert Pujols (138.6 RC, .213 RC/PA) are pacing the NL.
Now that we've established a per-plate-appearance value for Wright's season, let's see how many extra plate appearances he likely would have had if he had batted third all season.
Mets PA Diff % Diff
Batting #3 659 0 0.0%
Batting #4 642 17 2.6%
Batting #5 628 31 4.7%
Batting #6 605 54 8.2%
Batting #7 589 70 10.6%
The above chart indicates the number of plate appearances the Mets have had at each lineup spot 3 through 7 as well as the difference between that spot and #3 expressed in both raw plate appearances as well as percentage-wise. For instance, players batting third for the Mets this season, collectively, have had 10.6% more plate appearances than those players batting seventh.
Now here is a breakdown of David Wright's plate appearances this season from each spot in the lineup.
PA RC
Batting #4 11 2.4
Batting #5 220 45.1
Batting #6 127 28.3
Batting #7 130 19.8
Wright has come to the plate a total of 257 times as either the #6 or #7 hitter, amassing 42.7% of his plate appearances in those two spots. We would all have preferred he seen all of those pitches in the three-hole, but exactly how much of a difference would it have made? Let's put all of the above information together and have a look.
Batting #4
11 PA * 2.6% = 0 extra PA * .170 RC/PA = 0 extra RC
Batting #5
220 PA * 4.7% = 10 extra PA * .170 RC/PA = 1.7 extra RC
Batting #6
127 PA * 8.2% = 10 extra PA * .170 RC/PA = 1.7 extra RC
Batting #7
130 PA * 10.6% = 14 extra PA * 1.70 RC/PA = 2.38 extra RC
Overall Difference
34 extra PA, 5.78 extra RC
The general rule of thumb is that 10 RC = 1 Win, meaning that the difference between David Wright batting in all of those other places this season as opposed to batting third is a little more half a win. Now a half a win is something, but it's a lot less than I thought it would be. In fact, the difference isn't even as much as the 5.78 calculated above, since we also have to account for the plate appearances that Wright would be replacing (i.e. the value provided in those 34 extra PAs by the person who actually did bat). Whatever that value is, it would surely push the additional value of Wright's extra plate appearances to something less than five runs.
This is nothing close to an exhaustive study, but it certainly has revealed a few things. For one, despite Randolph's butchering of the lineup card on a seemingly daily basis, his refusal to bat his best hitter in the optimal spot has apparently not cost the Mets much in the way of wins or runs. This does nothing to support the absurdity of playing Miguel Cairo at first base, in right field, or anywhere else for that matter, but it does let Willie off the hook, at least a little bit.
For another, it does lend credence to the belief that, in general, advantages gained from ideal lineup construction are marginal at best. For the most part, your typical gameday lineup is something not too dissimilar from the ideal one. That is to say that the best hitters tend to be clustered around the #4 spot, the worst hitter is almost always last (i.e. the pitcher doesn't bat leadoff), etc., so the difference between the perfect lineup and the average lineup is only a win or two over the course of a season. That is something, but it isn't very much.