Crooked Numbers: In Need of Relief

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.

Here’s how the numbers shake out since 2000 comparing the performance of “Rested” relievers to “Tired” relievers:

YEAR   NET_ERA   NET_RA   NET_SOR  NET_UBBR   NET_HRR
2000    -0.07    -0.11     0.002    -0.001     0.000
2001     0.02    -0.07     0.000     0.004    -0.005
2002    -0.10    -0.26     0.013     0.000    -0.001
2003     0.26     0.22     0.007     0.003     0.001
2004    -0.26    -0.29    -0.002     0.000    -0.003
2005    -0.13    -0.26     0.013     0.001    -0.001

Let’s walk through this. The first two columns show the difference in “Rested” reliever ERA minus the difference in “Tired” reliever ERA. In 2000, “Rested” relievers were 7 points better than their weighted ERA than “Tired” relievers were compared to their weighed ERA. Thus, in every column except strikeout rate (NET_SOR), negative numbers indicate the “Rested” relievers were better. As we would expect, “Rested” relievers show a slight advantage in every column (except NET_UBBR where the numbers are very nearly a wash).

Of course, those numbers don’t tell the entire story–what numbers ever do?–so let’s look at how reliever do specifically on their third day of work. Because teams rarely resort to using a reliever on three consecutive days on the season, these inning totals are going to be low, but not so low that they can be considered unreliable.

YEAR    IP     NET_ERA   NET_RA   NET_SOR  NET_UBBR   NET_HRR
2000   420.3    -0.43    -0.50     0.022     0.002     0.001
2001   531.0    -0.05    -0.05     0.000     0.002     0.007
2002   521.0     0.20     0.27    -0.026     0.009     0.002
2003   488.7     0.36     0.55    -0.002    -0.012     0.000
2004   535.0     0.23     0.46    -0.012     0.011     0.004
2005   502.0     0.21     0.31    -0.007     0.004    -0.001

In this chart, each column is the comparison to the weighted average; we’re no longer comparing “Rested” to “Tired”, we’re looking for changes in performance at a specific workload compared to the season average. As mentioned, the innings totals are rather low, but the pattern–at least for the last four years–is consistent across the first three columns: relievers see their ERAs and RAs rise and their strikeout rates fall on their third consecutive day of use compared to their season averages. Walk and home run rates are generally a little higher as well.

Once we get to the fourth consecutive day, the inning totals get low enough to be considered fairly unreliable:

YEAR    IP     NET_ERA   NET_RA   NET_SOR  NET_UBBR   NET_HRR
2000   43.7      1.35     1.44     0.004    -0.029     0.009
2001   64.3     -1.78    -0.96    -0.005    -0.009     0.002
2002   50.0     -1.51    -1.64     0.001     0.016    -0.013
2003   64.7      0.11     0.06    -0.021    -0.015    -0.001
2004   65.7      0.37     0.85    -0.023     0.024    -0.012
2005   46.7     -0.75    -1.09    -0.021     0.000    -0.001

In this case, the numbers are fairly scattered; there’s little consistency to any column and, as a result, few conclusions to be drawn. It’s certainly possible that adjusting for the length of appearances or the month–consecutive appearances earlier in the season may not be as damaging as in September–would yield stronger results, but as we’ve seen with a fourth consecutive appearance, the sample size begins to get very small as the criteria continues to be restricted.

So what does this all mean for the Angels and the rest of the post-season combatants? There does appear to be some tangible degradation in reliever performance as appearances accumulate on consecutive days. However, even at the maximum, this decline appears to be no more than a quarter of a run in ERA during the third consecutive appearance. Over the course of a season, it’s much easier for teams to avoid this repetition, but unless there’s another reason to avoid calling the same fireman’s name three consecutive days, fatigue doesn’t appear to be major factor in reliever performance as measured by consecutive appearances.