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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. 
Click here to see Eric's other articles. You can contact Eric by clicking here

Related Content:  Velocity,  Rest

26 comments have been left for this article. (Click to hide comments)

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Jamey
(208)

I'm not clear what value this data has. Given that relatively few pitchers started on short rest, I expect that the data is skewed towards their pitch velocity and movement. It would be much more meaningful to see an average weighted difference from each pitcher's average velocity/movement on normal rest.

Apr 02, 2009 10:55 AM
rating: 0
 
BP staff member Eric Seidman
BP staff

Jamey... 3 days is short rest... and I literally mentioned that nothing should be gleaned from short rest in any of the three groups, and that the more interesting discussion is on standard rest (4 days) and one extra day (5 days). In fact that's the bulk of the article.

Apr 02, 2009 10:56 AM
 
thegeneral13

Yeah but Jamey's point, with which I concur, is that the proper way to test this is to look at the average velocity and movement differentials (i.e. Pitcher A fastball velocity on 3 days rest minus Pitcher A fastball velocity on 4 days rest, etc.) within each cohort rather than the absolute numbers. That would eliminate any bias within the cohorts (e.g. those with the highest velocity might happen to be the ones who threw on short rest most often). You need paired data to do that, which reduces degrees of freedom, but it is really the right way to do this test. Just a suggestion.

Apr 02, 2009 11:11 AM
rating: 2
 
BP staff member Eric Seidman
BP staff

Ah, okay, I misunderstood that point. I'll calculate that out now and report it in a few minutes.

Apr 02, 2009 11:15 AM
 
John Kearns

It strikes me that the sample size for the 3 days' rest data is irrelevant, because this data isn't useful to begin with. Even if we had data for 200 years, if usage patterns remained relatively constant over that time, then the pitchers likely to throw on three days' rest are virtually always going to be the better pitchers, and not at all the same ones represented in the four- and five-days' (and certainly six-days') rest categories.

It seems what we really should be doing, rather than lumping pitchers into arbitrary categories, is comparing velocity on differing days' rest for the *same* pitchers. What matters isn't the difference in the average velocity, it's the average of the differences between the velocities of individual pitchers. I can't think of any situation in which it's useful to compare the data we're presented with here, as the 3-day and 4-day groups don't represent the same pitchers. Some of them will be the same, but the representations are skewed as pitchers of Sabathia's caliber will be grossly over-represented in the first group no matter how many years of data we collect.

Also, while looking at game-by-game information like this is useful in determining who gets an important start, it ignores what I think is really the larger question of pitchers' rest, which is how the pitchers' arms hold up *after* these games - how do they fare in the next game? Over the next month? Year? The rest of their career? This article seems to imply that looking at these statistics will answer all of our usage questions, but if I'm Joe Girardi, I don't care whether Sabathia throws a no-hitter every time he pitches on three days' rest if doing so means his arm will break down in a few months and lessen his effectiveness for the rest of his career.

Apr 02, 2009 11:03 AM
rating: 4
 
BP staff member Eric Seidman
BP staff

Which is pretty much why I suggested skipping the 3-day and comparing the 4 day and 5 day data, as in each group these two areas featured the same pitchers, making the data more meaningful. Of course the short rest will be skewed by the better pitchers... but the sample sizes were irrelevant there to begin with so there was no need to mention that.

Apr 02, 2009 11:10 AM
 
BurrRutledge

I'm reminded of a quote a classmate once uttered in one of my statistics-based classes in grad school, "The "n"s justify the means."

Apr 02, 2009 12:12 PM
rating: 1
 
jlefty

even when comparing pitches thrown on 4 days rest to pitches thrown on 5 days rest.. it seems that more of the pitches thrown on 5 days rest will be by a larger proportion of back of the rotation pitchers. I'm very interested in the data that would result in comparing pitchers against _themselves_ but as mentioned before, small sample size or not, there seems to be bias in all of these numbers (not just the short rest column).

Apr 02, 2009 12:47 PM
rating: 0
 
BP staff member Eric Seidman
BP staff

Joe, look below, as I posted that data here in the comments.

Apr 02, 2009 12:53 PM
 
Ben Solow

Still, Eric, I don't understand how you can avoid the endogeneity problem in this sort of analysis. It seems really hard for me to imagine that even 4/5 day rest periods would be assigned randomly to pitchers. We have all sorts of anecdotal evidence confirming that it's not assigned randomly, as managers skip bad starters to keep good starters "on normal rest", or assign extra rest conditional on performance. For example, if a pitcher has a bad fastball in a given start, they're more likely to get an extra day; additionally, if the team has performed extremely well or badly (in context of playoff race) they're more likely to get an extra day. Given that previous start performance and team record are both likely to be correlated with both your performance measure and your independent variable, your results will be biased. I don't know anything about time series analysis, but if you're just looking cross-sectionally, there's all sorts of selection bias that really limits your ability to make causal statements about the effects of rest.

Apr 06, 2009 08:04 AM
rating: 0
 
BurrRutledge

99% agreement from me regarding paragraphs 1 & 2. Long term effects of such pitching patterns are an equally important question, but shouldn't diminish the value of what Eric's put together.

I do think there is some value in grouping some of the data in order to get a larger sample size, but you're right that the comparison may be skewed because it
s 3-days rest of a small sample of SPs vs. the 4-day/5-day rest of a much larger sample of SPs. The guys called on by their managers to throw on 3-days rest are almost certainly going to be of higher caliber than the majority of guys throwing on 4 and 5 days rest.

Eric, can you isolate this data only for those SPs who pitched on 3-days rest? Toss out all the guys last season who never pitched on 3-days and let's see what the numbers show for these same few SPs on 3-days, 4-days, and 5-days rest. Yes, it'll reduce the number of pitches being analyzed, but it might be more useful data nonetheless.

Thanks!

Apr 02, 2009 11:32 AM
rating: 0
 
BP staff member Eric Seidman
BP staff

Burr, the issue there is that these guys only made like 1-2 starts on short rest and it isn't even worth reporting. The more interesting data would be the paired samples deltas, which I posted here in the comments section as it compares the 4 day vs 5 day data for each individual pitcher and then takes the weighted average.

Apr 02, 2009 11:46 AM
 
BurrRutledge

I see your point, and I agree with the improved analysis using the differences in paired samples. Thanks for re-running it on that basis.

Even though the data is miniscule over one season, how will we ever know whether there's a short-rest effect if we don't run the analysis? I'd also be very interested in seeing the paired samples data if you analyzed only the pitchers who were called on for short rest. I'd also be curious of an analysis on their pitch velocity/movement during their next start after pitching on short rest. There's the potential that this might actually show something more significant.

Yes, the sample for '08 will be small/miniscule, but you gotta start somewhere. If you don't think it's "valuable" or "reliable" enough to publish with such a small sample, that's your call. Thanks again!

Apr 02, 2009 12:08 PM
rating: 0
 
BP staff member Eric Seidman
BP staff

Okay, so I just re-ran the numbers based on the suggestions and got the following deltas from 4 day to 5 day:

Hard-Throwers: -0.13 velo, 0.07 horiozntal, 0.24 vert
Medium-Throwers: -0.11 velo, -0.14 horizontal, -0.03 vert
Soft-Tossers: -0.05 velo, 0.21 horizontal, 0.04 vert

Apr 02, 2009 11:30 AM
 
thegeneral13

Thanks for doing that, Eric. It would be interesting for a future article as you get more data to do a regression of the paired differences to see whether they are significantly different from zero. Hard to tell from the raw numbers whether there is anything to be gleaned from the numbers. At first glance nothing jumps out at me as "looking" significant, but that doesn't really mean anything. I do find it curious that average velocity was down in all 3 groups with an extra day of rest, though again, it may not be statistically significant. Thanks for the follow-up to the comments, though. Much appreciated!

Apr 02, 2009 11:48 AM
rating: 0
 
BP staff member Eric Seidman
BP staff

Well, it would actually be the other way around... this was done as Data on Day 4 - Data on Day 5, meaning velocity was up on an extra day of rest for each pitcher. Though with the samples being 22, 57, and 72 respectively, I too would doubt the results as being overly significant. Definitely something to examine in the future.

Apr 02, 2009 11:58 AM
 
thegeneral13

Ah, makes more sense. I interpreted your "from 4 day to 5 day" comment too literally.

Anyway, the larger point is that it would be nice to see a regression for this type of study so we know whether the variation is statistically significant or not. I'm afraid we may otherwise draw conclusions (see havybeaks' comment below) without sufficient evidence.

Apr 02, 2009 12:35 PM
rating: 0
 
sockeye

Running these as a paired t-tests should allow you to generate a test statistic and a power value, thus assessing whether the sample sizes are sufficient or not.

But really, the effects on each group is only half the interest - the other half is the effect on each pitcher. The mean velocity may not differ for the whole group, but wouldn't it be interesting to know that Braden Looper had a decreased velocity on short rest, whereas Jeff Suppan did not? Etc.

Apr 02, 2009 14:01 PM
rating: 0
 
Jamey
(208)

Thanks Eric. This is exactly what I was looking to see.

Apr 02, 2009 13:32 PM
rating: 0
 
Richard Bergstrom

This slice of the data suggests that sinker-ball pitchers do not throw better when they are tired, contrary to baseball lore. Would that be accurate, or is it possible to do this kind of analysis solely based on pitch type and days of rest?

Apr 05, 2009 00:46 AM
rating: 0
 
Mat Kovach

What strikes me is why some pitchers were pitching on extra rest? There is probably a mix of younger pitchers where a team was hoping to shaving some innings off the yearly total. I'm sure there are some pitchers that were coming off injuries, "tweaked" something and were given an extra day. Probably a few pitching after a rain out two. Unless we it is known WHY they are pitching on extra rest, it makes looking at the data hard.

Pitchers pitching on short rest are typically going to be players that are really good(tm) and have special care taken when they are pitching on short rest.

What I think would be more telling is did they use their fastball the same? Throw in more breaking pitches and change-ups? Basically, did they pitch differently? Did they tire faster? Was there less separation between their secondary pitches and fastballs?

If fact, I would like to see that for the extra rest guys too.

Apr 02, 2009 11:35 AM
rating: 0
 
James Martin Cole

Days off, most likely. If you don't play every day, then someone's going to have a day off every so often.

Apr 04, 2009 15:35 PM
rating: 0
 
havybeaks

Awesome stuff, Eric.

What strikes me about this data is how vertical movement varied more than velocity. I'm no physiologist but I wonder if the effects are related to neurological fatigue, not structural weakness; i.e. less-rested pitchers are still able to launch their arms hard enough to maintain velocity, but aren't snapping the wrist as sharply to create spin.

Could this explain the reduced PFZ with "too much" rest by losing some muscle memory but also with "too little" rest by neurological fatigue? Just tossing out ideas; please let me know if I'm nuts.

Apr 02, 2009 11:38 AM
rating: 0
 
BP staff member Will Carroll
BP staff

I completely agree with beaks' point here.

Apr 02, 2009 12:13 PM
 
thegeneral13

I think it would be much more instructive to test this hypothesis with breaking balls since there is no discrete "wrist snap" involved in throwing a fastball.

Apr 02, 2009 12:38 PM
rating: 0
 
Dr. Dave

Would grip fatigue be an issue here? Grip fatigue would affect fastballs as well as breaking balls, without any wrist action required.

Apr 02, 2009 13:47 PM
rating: 0
 
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