Okay…maybe I overstated my case, but I do have a somewhat scientific way to show that left-handed power hitters hit relatively better with runners on base than with bases empty compared with right-handed power hitters.
Here’s my theory:
Due to the location of first base (the right side of the infield), teams employ large shifts for left-handed power hitters when it is possible, frequently placing three infielders on the right side of the diamond. However, when there are runners on base, it is more difficult to position infielders in such a way that minimizes the hitter’s chance of hitting safely if they hit the ball in play. The result is that for a given batting average, a left-handed power hitter is actually more likely to get those hits when runners are on base. These are naturally higher leverage situations in general. Hence, a given batting line for a left-handed power hitter is more valuable than the equivalent batting line for right-handed power hitters.
The process:
I don’t really know the details of the defensive positioning used against every hitter, so the numbers may not be the best reflection of the truth, but even with this noisy data, I was actually able to find significant results anyway.
I found the top 20 non-switch hitters in career slugging percentage who started their careers after 1956 (the era for which Baseball-Reference.com has data on splits) and who had over 3000 career PA. There were 12 righties and 8 lefties, and I checked their BABIP with runners on base and with bases empty. The 12 righties hit an average of .009 points better with runners on base than with bases empty (the fact that they hit better is unsurprising, considering batting with runners on is correlated with batting against poorer pitchers and batting against fielders who are not positioning themselves only to limit the chance that the hitter reaches base, but also to avoid stolen bases and complete double plays). However, the 8 lefties hit an average of .022 points better with runners on base than with bases empty. Given the number of balls in play that each group had, this difference was significant at the 95% level.
The 12 righties with their respective BABIP with runners on base, BABIP with bases empty are as follows, and difference)
Albert Pujols (.317, .321, -.004)
Manny Ramirez (.345, .332, +.013)
Mark McGwire (.265, .247, +.018)
Alex Rodriguez (.325, .319, +.006)
Vladimir Guerrero (.327, .312, +.015)
Albert Belle (.288, .299, -.011)
Juan Gonzalez (.304, .305, -.001)
Frank Thomas (.311, .298, +.013)
Mike Piazza (.316, .312, +.004)
Miguel Cabrera (.354, .336, +.018)
Jeff Bagwell (.325, .308, +.017)
Frank Robinson (.300, .290, +.010)
The 8 lefties:
Barry Bonds (.308, .267, +.041)
Todd Helton (.346, .327, +.019)
Larry Walker (.331, .332, -.001)
Jim Thome (.327, .317, +.010)
David Ortiz (.324, .283, +.041)
Ken Griffey (.297, .285, +.012)
Carlos Delgado (.303, .303, .000)
Jason Giambi (.327, .277, +.051)
The totals were that the twelve righties hit .314 on 30,470 balls in play with runners on and .305 on 31,796 balls in play with bases empty. The eight lefties hit .319 on 20,161 balls in play with runners on and .297 on 22,752 balls in play with bases empty.
Obviously, the story could just be that David Ortiz, Jason Giambi, and Barry Bonds are uber-clutch and happen to left handed, but I would think that the shift is the reason. To check whether they just happened to be better hitters with runners on base, I checked homerun percentage by the lefties and the righties—and the righties had 6.5% homeruns with runners on, and 6.6% with bases empty, and the lefties had 6.3% homeruns with runners on, and 6.8% homeruns with bases empty.
Maybe, I’m not using the right statistic, so for the sake of transparency, here’s how I developed the standard deviation I used to develop the t-statistic: the 20 hitters combined to hit .316 with runners on base and .302 with bases empty. This established the variance with runners on base as .316*(1-.316) and with bases empty as .302*(1-.302). I divided each of these by the number of balls in play that righties had with runners on base and bases empty, respectively. That was the variance for the righties. Then I divided .316*(1-.316) and .302*(1-.302) by the number of balls in play that lefties had with runners on base and bases empty, respectively. That was the variance for the lefties. I added these and took the square root and found that the standard error should be .0058. Given that the difference between the .022 that the lefties hit better with runners on base and the .009 that the righties hit better with runners on base was .014, this established a t-stat of .013/.0058=2.30. There is only a 2.2% chance this would happen by randomness—making this a statistical significant difference.
All in all, I think this is a sign that perhaps using purely sabermetric theories which assume that no hitter is significantly better than others at performing in the clutch, and thereby evaluating hitters’ cumulative numbers, is not accurate. This is not quite a testament to the glory of the RBI, but it demonstrates some of the value in looking at situational context hitters as different. I tend to doubt the impact of psychology on performance and mainstream sportswriters frequent use of antiquated ideas of clutchness, but there are probably characteristics that affect hitters’ abilities to succeed in important situations. The characteristic presented here may be one of them.