## Manny’s First 27 Games (or, the Marginal Product of Drug Use) June 4, 2010

Posted by tomflesher in Baseball, Economics.
Tags: , , , , , , , , ,

Last year, Manny Ramirez was suspended for 50 games on May 6. The suspension came after his 27th game of the season. On May 25th of this year, Manny played his 27th game of 2010. That means we can take a look at the first 27 games of each season, when he was using performance-enhancing drugs (in 2009) and when he wasn’t (presumably, this year). The differential line is behind the cut.

 Stat G GS Rslt PA AB R 2009 27 27 20-7 120 92 22 2010 27 23 17-10 104 82 13 ∆ 0 -4 -3 -16 -10 -9 Stat 2B 3B HR RBI BB IBB 2009 9 0 6 20 26 8 2010 6 0 2 21 18 2 ∆ -3 0 -4 1 -8 -6 Stat SO HBP SH SF GDP BA 2009 17 1 0 1 2 0.348 2010 13 1 0 3 1 0.329 ∆ -4 0 0 2 -1 -0.019 Stat OBP SLG OPS aLI WPA RE24 2009 0.492 0.641 1.133 1.02 1.674 17.11 2010 0.442 0.476 0.918 1 1.334 9.43 ∆ -0.05 -0.165 -0.215 -0.02 -0.34 -7.68

Obviously, comparing across these years involves making some assumptions, some of which are justified and some of which aren’t. They boil down to assuming that there isn’t any other factor that would explain Manny’s decline in performance. For example, I’m assuming that Manny didn’t play a tougher schedule in 2010 than in 2009, which may be suspect because the Dodgers were 20-7 in Manny’s games in 2009 but 17-10 in 2010. I’m also assuming that Manny’s position in the batting order didn’t change his numbers, which may or may not be a factor. Manny invariably hit third in 2009 and has more often been hitting 4th in 2010.

However, the line is very telling. In 2009, Manny hit 6 home runs in 120 plate appearances, or about .05 home runs per PA. This year, he hit 2 in 104 PA, or a little bit under .02 home runs per PA. This is a significant drop, and since he’s being intentionally walked significantly less (6.7% of the time in 2009 versus 1.9% of the time this year), it corroborates the idea that Manny is seen as less of a threat. This could also be a result of Manny being moved to the fourth slot instead of being protected by Andre Ethier, but Manny is often backed up by James Loney this year, so I’m not sure the protection issue is realistic.

Two of those home runs became sacrifice flies, and Manny is striking out slightly less this year, but overall his OBP and slugging average have fallen precipitously.

The margin of error for proportions is $\sqrt{\frac{p(1-p)}{n}}$ , so the margin for his OBP this year is $\sqrt{\frac{.442(.458)}{104}}$ , or about $\sqrt{\frac{202}{104}}$ , which is about $.044$. That means that we can be 95% confident that Manny’s “true” OBP is somewhere within $.442 \pm 1.98(.044)$. This interval puts the bounds at $.355$ on the low end and $.529$. In fact, the difference – $.05$ – is about 1.14 standard  errors. That means we can only be about 75% certain that the difference is not due to chance.

Still, as the year plays out, I’ll be very interested in seeing whether this is a temporary trend or whether Manny’s numbers take a permanent dive.

 G GS PA AB R H 2B 3B HR RBI BB IBB SO HBP SH SF BA OBP SLG OPS WPA RE24 27 27 120 92 22 32 9 0 6 20 26 8 17 1 0 1 0.348 0.492 0.641 1.133 1.674 17.11 27 23 104 82 13 27 6 0 2 21 18 2 13 1 0 3 0.329 0.442 0.476 0.918 1.334 9.43 0 4 16 10 9 5 3 0 4 -1 8 6 4 0 0 -2 0.019 0.05 0.165 0.215 0.34 7.68