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October 13, 2005

Crooked Numbers

In Need of Relief

by James Click

Post-season baseball is a wholly different animal. Teams play like there’s no tomorrow, which, for half of them each time, there isn’t. This attitude change manifests itself mainly in pitching usage; struggling starters are pulled immediately, marginal relievers are skipped, top relievers are used more often and for longer stints. In many respects, it’s the kind of baseball teams played long ago before the effects of pitching fatigue was appreciated or quantified.

But while the Angels struggle to overcome a travel schedule to rival Odysseus, it’s possible to quantify some of the effect this usage has on their--and their opponent’s--pitchers. Rather than looking at post-seasons past, let’s instead see how reliever performance changes as workload increases. As a simple beginning, here’s how relievers performed this past season broken into whether or not they pitched the day before. (If “Rested” is 1, then the pitchers did not pitch the previous day.)

YEAR  RESTED  ERA     RA    SO/PA   UBB/PA  HR/PA
2005    1     4.15   4.52   0.181   0.083   0.025
2005    0     3.94   4.46   0.180   0.079   0.024

Interestingly, relievers who pitched the day before performed 21 points better in ERA with a lower unintentional walk rate (UBB/PA), a higher strike-to-unintentional walk rate (SO/UBB) and a lower home run rate (HR/PA).

While it may initially appear that relievers have trouble getting back into the groove after a day off, there’s an inherent selection bias involved in these numbers. Joe Torre may use Mariano Rivera on consecutive days in tight games, but he may find any excuse to use Wayne Franklin as little as possible. Those relievers in the unrested group above are likely their team’s better firemen, so comparing the two groups is not an apples-to-apples match.

Instead, it’s important to compare each group’s performance to their weighed season averages before comparing the two groups to each other. For example, looking just at Francisco Rodriguez’s 2005 season, he threw 41.3 IP when he had not pitched the day before, allowing 12 runs for an ERA of 2.61. In 26.0 “Tired” IP, he allowed 8 ER for an ERA of 2.77. In this case, it’s easy to see that Rodriguez pitched slightly better when rested in terms of ERA. But if we needed to compare his rested performance to that of Danny Kolb, we must first adjust the “Rested” and “Tired” innings for how many runs we would expect those pitchers to be allow given their season averages. The “Rested” numbers are likely going to close to the season-average numbers because so much of the data overlaps (most reliever innings are thrown after a day off), but nonetheless, without this adjustment, we are left with a large selection bias. Better the former problem than the latter.