## RBIs with Two Outs July 4, 2011

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

Sunday’s Subway Series game between the Mets and Yankees ended with a bang – Jason Bay hit a single off Hector Noesi that brought home Scott Hairston. The tenth inning should have been over, but Ramiro Pena committed an error at shortstop that put Daniel Murphy on base for Boone Logan. Hairston’s run was unearned, but no matter – Noesi took the loss and the Mets won the game.

The final score was 3-2, and the interesting thing about the game was that all three of the Mets’ runs came with two outs. (My fiancée, Katie, suggested that this was unusual, and motivated most of the rest of this post.) In fact, so far, the Mets have had 347 RBIs (of 375 runs scored), and 147 of them have come with two outs. That’s about 42.4% of their RBIs. By contrast, only 1070 of 3274 plate appearances – 32.7% – come with two outs. (Less than a third of plate appearances come with two outs because of the double play, among other reasons.) The majority come with no men out (about 34.8%) with the remainder coming with one out. It seems like the high concentration of 2-out RBIs should be explained by the use of the sacrifice bunt, but the Mets have only had 31 sacrifice bunts this season – not nearly enough to account for the difference between 32.7% of plate appearances and 42.4% of RBIs.

Is that pattern common across baseball? So far, there have been 10,037 RBIs in Major League Baseball in the 2011 season. 3686 of them – about 36.7% – came with two outs. Excluding the Mets’ numbers, that’s 3539 out of 9690, or 36.5%. For the National League only, there were 1928 two-out RBIS of 5212 total, or 37%, with 1781 of 4865 (36.6%) of National League RBIs coming with two outs if you exclude the Mets. (Note that I’m defining ‘in the National League’ as ‘in National League parks,’ since what I’m interested in is whether the Mets’ concentration of RBIs can be partially explained by the rules requiring pitchers to bat.)

Assume that the Mets’ RBIs are drawn from the same distribution as all others’. Then, 95% of the time, I’d expect the proportion of RBIs that come with two outs to be within two standard errors of the National League’s proportion, excluding the Mets. (The ‘two standard errors’ comes from the fact that a t-distribution’s critical value for a large number of trials for 95% significance is 1.96. For less than an infinite number, two standard errors is a handy approximation.) For the Mets’ 347 RBIs, the standard error would be

$\sqrt{\frac{p(1-p)}{n-1}} = \sqrt{\frac{.366(.734)}{346}} = \sqrt{\frac{.232}{346}} = \sqrt{.000671} = .026$

Thus, 95% of the time, the Mets should be within the interval of (.366 – .052, .366+.052), or (.314, .418). Since, again, the Mets’ proportion is .424, the Mets are slightly outside the 95% confidence interval. That’s pretty close, and certainly could happen by chance, but it’s surprising nonetheless. The question then is whether this is due to some sort of strategy employed by the Mets’ management or to some sort of clutch playing ability by the Mets. Again, there’s more data to collect and crunch (as always).