Back in 2011, I wrote an article the primary focus of which was an attempt to postdict the effect of the humidor on home run production at Coors Field. The article was based in part on a piece of academic research I had done with my collaborators a few months earlier in which we did careful laboratory measurements of the effect of humidity on the weight and coefficient of restitution (COR, or the “bounciness”) of the baseball. The essential idea is that when a baseball is stored in a humid environment, it absorbs water, which has the dual effect of decreasing the COR and increasing the weight, both of which should result in a reduction in exit speed, all other things being equal.
It might be helpful to review the basic facts about Coors Field, which long has been viewed as a batter’s paradise and a pitcher’s nightmare. Because the air density in Denver is approximately 80 percent of that at sea level, fly balls carry farther and pitches have less movement, both of which contribute to an increase in a variety of offensive statistics, particularly home runs.
For the first seven seasons at Coors, there were 3.20 home runs per game compared to 1.93 per Rockies away game. However, starting in 2002 the Colorado Rockies began to store their baseballs in a humidor at a constant 50 percent relative humidity and 700F, as opposed to the more typical 30 percent humidity in Denver. During the period from 2002-2010, the Coors ratio decreased to 2.39, a reduction of 25 percent, while the away game ratio stayed essentially constant at 1.86.
To calculate the expected decrease in home run production at Coors required a three-step process. First, it was necessary to estimate how the elevated relative humidity (from 30 percent to 50 percent) affected the properties of the baseball–primarily COR and weight–resulting in a reduced exit speed. That was accomplished using laboratory measurements of the effect of humidity on the COR and weight, along with a physics model of the ball-bat collision to calculate the effect of these quantities on the exit speed.
Second, using the reduced exit speed, an aerodynamics model for the flight of the baseball was used to calculate the reduction in flyball distance. Finally, actual home run data, courtesy of ESPN Home Run Tracker, were used to calculate the reduction of home runs expected from the reduced distance. Amazingly, the calculated reduction in home runs at Coors, 27±4 percent, agreed essentially perfectly with the actual value of 25 percent.
In the course of this work, there were stories reported that the Arizona Diamondbacks were considering installing a humidor at Chase Field. So we decided to use the same technique to extend our calculations to Chase, where the relative humidity is even lower, about 20 percent, than at Coors. Therefore, we expected and found an even greater reduction in home runs, 37±7 percent, than at Coors. Interestingly, the plans to install the humidor subsequently were abandoned. I realize correlation is not necessarily causation, but it is very tempting (not to mention flattering) to think there was a causal connection with our article.
Now we fast forward to the 2017 season, where reports abound that the D-backs are reviving their plans to install a humidor, and it will probably happen within a month or so. D-backs CEO Derrick Hall is quoted as saying regarding the humidor, “Again, I don’t know if it’s going to make a difference. It hasn’t made a huge difference at Coors Field, I don’t think.”
With all due respect, Mr. Hall, it has made a huge difference at Coors, at least with respect to home run production. Moreover, if our previous analysis is even close to being correct, it will make an even larger difference at Chase. To prove that, I decided to dust off my old calculations and come up with an updated prediction. And unlike our earlier postdiction for Coors, the new prediction soon will be tested. In other words, I am really sticking my neck out here.
I am going to approach this problem a bit differently than last time in that I want to rely as much as possible on publicly available data from Statcast from the 2015 and 2016 seasons, including exit speeds, launch angles, and outcomes. I will be using two categories of data:
- Data Set 1: All home and away batted-ball data for the D-backs
- Data Set 2: All batted-ball data from Chase Field
I first use Data Set 1 to compare home and away mean exit speeds for D-backs batters. The essential idea is that higher exit speeds would be expected for the home games at Chase Field due to the elevated COR in the drier climate. A home/away comparison is shown in Figure 1, where the histograms have been scaled so that the same number of batted balls appear in each plot.
Since I am considering only home runs, only events in the launch angle range 20-35 degrees — encompassing about 90 percent of total home runs at Chase — are included. The left plot shows the full distribution, the right plot a blowup of the region above 90 mph, which is the region most relevant for home runs. The mean exit speed is 91.9 and 89.9 mph for home and away, respectively, a clear-cut two-mph shift to higher speed for games played at Chase. The shift is particularly apparent for exit speeds above 100 mph, as the right plot most clearly shows.
At this point I want to digress briefly to comment on how compatible a 2-mph shift in exit speed is with expectations based on how the baseball properties depend on relative humidity. In fact, based on a starting point of 20 percent and elevating to 50 percent (both at 700F), the physics-based calculation predicts a shift of about twice that, or 3.8 mph, which is essentially identical to the 4.1 mph shift we found in 2011, despite the improved ball-bat collision model. I am puzzled by this discrepancy and wish I understood it better. But I don’t and will proceed with the analysis assuming a two-mph shift, but also realizing the effect on home runs could be even greater. I will return to this point shortly.
Given the two-mph shift in exit speeds, the analysis now proceeds along the same lines I used in an article I wrote last year about the increase in home runs starting with the 2015 All-Star break. Using Data Set 2, which are batted balls at Chase Field (both home and away teams), and once again restricting the analysis to balls hit in the range of launch angles between 20 and 35 degrees, I plot in Figure 2 the distribution of exit speeds — both the actual exit speeds (red) and the same exit speeds shifted downward by two mph (blue), the latter simulating the effect of the humidor.
The dotted curve shows the home run probability as a function of exit speed, which varies between zero and one and is a smooth fit to the Statcast data. Given that the exit speed distribution is falling rapidly in just the region where the home run probability is increasing rapidly, it is not hard to imagine how a seemingly small shift in exit speeds can have a very large effect on the number of home runs.
This is further apparent by the curves in Figure 3, which were obtained by multiplying the exit speed distributions by the home run probability for each 2 mph bucket of exit speed. The resulting curves are the distribution of exit speeds for balls hit for a home run.
The area under each curve is the expected number of home runs, which is 312 for the actual data and 232 for the shifted data, a 26 percent reduction. If the actual shift in exit speeds were four mph, as the physics-based calculation predicts, the expected number of home runs would be 164, a reduction of 47 percent. Interestingly, the average of these two results is 37 percent, exactly the value found in the 2011 analysis. However, this perfect agreement is surely fortuitous, given the very different techniques and data utilized back then.
So what do we conclude? I am very comfortable saying that, with the humidor running at 50 percent and 700F, there will a reduction in home run production at Chase by 25-50 percent. While it would be nice to come up with a more precise prediction, we should not lose sight of the principal takeaway that the installation of a humidor will reduce the number of home runs substantially.
References & Resources
- Statcast; Baseball Savant
- ESPN Home Run Tracker
- Alan Nathan, Baseball Prospectus, “Baseball ProGUESTus: Home Runs and Humidors: Is There a Connection?”
- Alan Nathan, Lloyd Smith, Warren Faber and Daniel Russell, American Journal of Physics, “Corked bats, juiced balls, and humidors: The physics of cheating in baseball”
- Nick Piecoro, The Arizona Republic, “Arizona Diamondbacks exploring ways to make Chase Field less hitter friendly”
- Nick Piecoro, The Arizona Republic, “Arizona Diamondbacks back off idea of using humidor this year”
- Vince Marotta, ArizonaSports.com, “Get a grip: Arizona Diamondbacks to install humidor at Chase Field”
- Alan Nathan, The Hardball Times, “Exit Speed and Home Runs”