April 2, 2009

Checking the Numbers

Rest Up

by Eric Seidman

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"Too many pitchers, that's all, there are just too many pitchers. Ten or twelve on a team. Don't see how any of them get enough work."
-Cy Young

Cy Young pitched in an era vastly different than the one we're accustomed to, an era in which pitch counts sounded like futuristic Doc Brown inventions, and the idea of specialized bullpens with roles reserved for one inning or one batter seemed laughable. Complete games and pitching on very short rest were the norms, while being unable to succeed at either task would elicit emasculating commentary. Just ask Joe McGinnity, who pitched complete games in both ends of three different doubleheaders, all in August 1903! Take a DeLorean ride one century into the future and the short-rest dominance of CC Sabathia last season was taboo enough to appear in grocery store gossip magazines. Changes in the styles of gameplay are to be expected over time, but no aspect has undergone as intense a transformation as the usage of starting pitchers. Teams have become much more prone to prevent pitchers from throwing without proper rest, and they continue to build deeper rotations to prevent pitchers from burning themselves out. From a statistical standpoint, is pitching on short rest truly worthy of a negative reputation?

A premium has been placed on rest and recuperation, in large part due to aversions to risk and the responsibility of front offices to maximize returns on their investments. Baseball players cost plenty of money these days, and the act of pitching involves such an incredibly unnatural motion that repeating it too often can land you in a Will Carroll column. In deciding to run the numbers based on days of rest, I chose to look at Pitch-f/x data rather than performance metrics, as the defense and strength of opponents faced could prove problematic in the latter. Pitch data might be more immune to such factors, as it deals almost exclusively with the individual pitcher.

To begin, I queried for pitchers with at least ten starts last season who started in 75 percent or more of their overall appearances. The pitcher pool of around 150 players was then broken down into three sub-groupings based on overall fastball velocity. The group of 22 hard throwers boasted average velocities in excess of 93 mph. The middle group consisted of 57 pitchers that averaged between 90.5 and 93 mph. Finally, the group with velocity below 90.5 mph was comprised of 72 pitchers. As you can see, the numbers of unique pitchers are not particularly large, but an analysis like this should be treated similarly to last week's look at closers in and out of save situations: an appetizer of sorts that will eventually become an entrée once we add a few more years of data. Despite this disclaimer, the sample size of fastballs thrown in the rest periods of interest tend to be quite impressive.

The bulk of pitches thrown last year came on the standard four days' rest, though there were a fair number with five rest days. As expected, the number of fastballs thrown on three days' rest is much smaller. Five and six days of rest generally resulted from scheduled off-days or opting to skip the fifth starter. Here is the velocity and movement data for the group with average fastball velocities greater than 93 mph:

Rest   # FB    Velo    PFX    PFZ
 3      604   94.87   6.44   9.65
 4   18,720   93.83   5.77   9.72
 5   11,200   93.69   5.75  10.17
 6    1,394   93.87   5.99   9.75

The same data for the middle group:

Rest   # FB    Velo    PFX    PFZ
 3    1,402   91.57   6.94   7.60
 4   48,051   91.22   6.95   8.93
 5   26,094   91.28   6.23   9.24
 6    4,419   91.16   6.38   8.92

And lastly, the pitch data for the slow-tossers:

Rest   # FB    Velo    PFX    PFZ
 3    1,135   88.16   6.09   8.15
 4   48,569   88.03   6.66   9.03
 5   28,696   88.02   5.98   8.99
 6    4,508   88.13   6.53   8.38

As expected, there are very few appearances on short rest, and almost as few on extended rest, showing that teams are generally doing a very good job of structuring rest patterns for their pitchers. Due to the small sample sizes on short rest, it becomes very difficult to make any sort of definitive claim, so it would be statistically inaccurate to say that fastball velocity is greater on short rest for each group. However, the data does show interesting trends in velocity and vertical movement that may become relevant in the future as our sample sizes increase, as each group averaged their fastest velocity as well as their least amount of vertical movement on short rest. If I could hammer home just one notion in this article, it would be that the higher or lower averages are not born out of a large enough sample to show a concrete performance discrepancy. Essentially, though this may seem like a silly lesson in semantics, saying that the average velocity on short rest was greater than the average velocities in other rest periods in 2008 is vastly different from saying pitchers throw harder and with less vertical movement on short rest.

Looking at standard rest compared to an extra day of rest ends up being much more interesting and statistically significant. The group of hard-throwers experienced a very slight increase in velocity with an extra day, as well as a half-inch greater rise. With equal amounts of horizontal movement, slightly greater velocity, and a decent increase of vertical movement, hard-throwing starters appear to have benefited from an extra day off last year. Our middle group saw virtually no difference in velocity, but their movement components trended in opposite directions, with standard rest sporting approximately 0.75 inches greater horizontal movement, yet 0.3 inches less of vertical movement. They threw at the same velocity on standard rest and saw their heaters tail much more, with less rise. Considering that they sported more sinkerballers and pitchers with two-seam fastballs, the lower vertical movement actually worked in their favor, showing that the medium velocity group benefited more from pitching on standard rest.

The same can be said for the low velocity group; they threw fastballs at literally identical velocities on standard rest and one extra day's rest, with nearly identical vertical movement and much more horizontal movement. Again, this is all relative to last season since it was the first year of truly reliable data. A few years from now, these results may change, but hard-throwers in 2008 seemed to possess better pitch data on an extra day's rest, while everyone else worked better under the rhythm derived from structured rest periods. Another idea that I wanted to investigate dealt strictly with sinkerballers such as Brandon Webb and Derek Lowe, as the mainstream has adopted the theory that being tired equals more sink. Unfortunately, the short-rest sample sizes are non-existent in both of their cases, which is particularly annoying because the theory has apparently sprung up from nowhere and cannot yet be tested.

Tabs will definitely be kept on this data throughout the season, and I will be very curious to see if and how the results change with a larger pool of pitchers and pitches. Keep in mind that this study looked solely at starting pitchers, since relievers have different usage patterns and should intuitively produce different data. Josh Kalk took a look at this reliever data very early in the season, and showed that the overall group tended to throw with more sink as the rest periods became shorter. His study also showed that relievers with one day off in between appearances averaged a half-mph greater velocity than those appearing on back-to-back days. The group of relievers needed to be normalized in order to separate the different types, but this is also an area of pitch data worth investigating Though definitive conclusions cannot be gleaned from the data yet, it does appear that rest periods affect the velocity and movement of pitchers, and that some benefit more from an extra day off than they do from standard rest. Many wily old veterans are calling for a short-rest renaissance, and while nothing here would work to dispel their desires, if structured periods of rest would keep pitchers off of the disabled list and at their most effective, why mess with the setup? Pitch counts are an entirely different animal that could use some adjustment, but days of rest between starts seem to work just fine in their current form.

Eric Seidman is an author of Baseball Prospectus. 
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