It seems to me that it is human nature that the closer we get to achieving a particular goal, the more we focus our energy on realizing it. Examples of this "push to the finish" mentality can be seen in many facets of life, including the time leading up to a looming deadline at work or an exam at school.
In the context of a plate appearance, one way to gauge this phenomenon is to observe the average fastball velocity reached by pitchers depending on the number of strikes in the count. While not everyone believes in the benefits of the strikeout, the behavior of the average pitcher as a potential strikeout nears in a plate appearance is a good indication that he is certainly targeting such a result.
Max Marchi at Baseball Prospectus produced a brilliant two part series last year where he documented the difference in velocity for pitchers based on count, base-out state as well as batting opponent. I recently discovered the same relationship between fastball velocity and number of strikes in the count, but wanted to explore a potential relationship that I do not believe that I have seen investigated before.
One common belief surrounding pitching mechanics is that a consistent delivery is more desirable than not for preventing injuries. While in many respects, in terms of PITCHf/x data we think of release points as the closest proxy for testing a repeatable delivery, it seems plausible to me that reaching back for a little too much extra as the strike count mounts in a plate appearance may be another way that a delivery could be considered to be inconsistent. In other words, if the velocity increase is too much, could all those little extra oomphs accumulated over many plate appearances be harmful to your body?
To test this, I looked at the average four-seam fastball velocity by strike count for all pitchers in the years 2010, 2011 and 2012. Since velocity stabilizes very quickly, I did not have to concern myself with minimum batters faced in this study. Of course not every pitcher throws four-seam fastballs, but the exceptions are few. I calculated a "slope" for each pitcher, which is basically the fastball velocity increase per additional strike in the count of the plate appearance.
I then looked at the number of trips to the DL in each season for each pitcher. I wanted to see whether there is any weak relationship between the slope and the number of DL instances across the set of major league pitchers.
To start, here is the average four-seam fastball velocity of all pitchers by number of strikes in the count over the past three seasons:
|Year||0 Strikes||1 Strike||2 Strikes||Slope|
Average Four-seam Fastball Velocity by Strikes in Count, 2010-2012
We see overall average fastball velocities are on the rise across the league. We also see that consistently the average fastball velocity increases by around 0.4 MPH per additional strike in the count. This tends to break down into about a 0.3 MPH increase on strike one counts and another 0.5 MPH increase on strike two counts.
After calculating the slope for each pitcher individually, I wanted to check is how repeatable it was for a pitcher year-over-year, to get a feel for whether this is something that a pitcher tends to control.
|Year N||Year N+1||r|
Year-to-Year Repeatability for Increased Velocity by Strike Count Slope
Pitchers do appear to have some control over how much they amp up as the strikes mount in a plate appearance, but there is also a good amount of year-to-year random variability.
In breaking down the velocities by count for starters and relievers and then grouping them based on DL trips, we see a pattern forming in particular with relief pitchers.
|DL Trips||0 Strikes||1 Strike||2 Strikes||Slope||Sample|
Average Starting Pitcher Four-seam Fastball Velocity by Strike Count and DL Trips, 2010-2012
|DL Trips||0 Strikes||1 Strike||2 Strikes||Slope||Sample|
Average Relief Pitcher Four-seam Fastball Velocity by Strike Count and DL Trips, 2010-2012
While the table for starting pitchers looks inconclusive, in looking at the table for relievers we see that the number of DL trips increase as the slope of the fastball velocity rises. This relationship was seen for relievers in each of the last three years independently, which perhaps suggests something at play here more than just randomness.
Certainly I would not expect any such relationship to be very strong, as something as complex as injury prevention is not likely to have one variable of this nature make a large contribution. In running a linear regression for slope versus number of DL trips, I got a miniscule R^2, with a P-value of 0.09. I also tried running a binary logistic regression on just injured/not injured, but again did not see any significant association.
So while it was possible to look at the numbers in the table and believe there could be a positive relationship between the calculated slope and DL trips, simple regression tests could not really detect such a correlation. There are simply too many healthy pitchers who also amp up their fastballs during a plate appearance for a simple model to detect any significance of this one variable.
One problem with using DL trips as our response is that there are cases where pitchers appear to be injured, but are essentially "day-to-day" and recover without ever being placed on the DL. Glen Perkins, Kameron Loe and Aroldis Chapman are examples of relievers with very high slopes year-to-year that experienced these "day-to-day" injuries (as per Baseball Prospectus Injury History beta) that did not require DL time. Perhaps if all missed days could be used instead of DL trips, the relationship could be stronger.
Despite the apparent failure, as for a possible next step for this idea I could see this slope variable as potentially being useful as an input along with other PITCHf/x variables into a neural net that looks to predict injuries for relief pitchers. That type of model would be better at flushing out any real relationship between this slope in conjunction with other variables and injuries. Josh Kalk and Kyle Boddy have both published works based on neural networks attempting to predict injuries to starting pitchers, but I have not seen a model attempted for relievers. Whether the slope calculated here ends up being significant when put alongside deviations in movement and release point remains to be seen.
With injury prevention being one of the major areas where a lot of work can still be done, any little bit helps.
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Credit and thanks to Baseball Heat Maps for PITCHf/x and injury data upon which this analysis was based.