The Physics of Humidors: A Second Case Study at Chase Field

The first case study on the effect of humidors on baseballs goes back to 2002. The vagaries of mile-high baseball at Coors Field drove the decision to control the temperature and humidity in which the balls were stored. The typical humidity in Denver is about 30 percent, while humidors maintain 50 percent humidity at 70˚F.

Balls stored in the humidor have a higher water content than they would if they were stored in the Rockies dugout. The higher water content means the balls are “mushier.” In addition, they weight a bit more. As a result, such a ball will come off the bat with a lower exit velocity and thus won’t travel as far.

While home run numbers in the mountain air of Colorado remain high compared to other parks, they dropped about 13 percent from 2001 to 2002, demonstrably due to the humidor. The reason the home run numbers remain stubbornly above MLB averages is due to the thin air, which is a more difficult challenge to address. The Coors humidor remains in place to this day.

The second case study was conducted in Phoenix last season when the Diamondbacks introduced their own humidor to Chase Field. The typical outdoor humidity there is around 20 percent – even lower than in Denver. So one might expect the change in homers could be even larger.

Alan Nathan has written about the connection between home runs and humidors. Perhaps the most complete description is here. That article includes a preliminary prediction of the effect of a humidor at Chase; a more complete prediction can be found here. For more technical readers, there are additional details about the effect of humidors here.

The humidor affects three properties of the ball: its bounciness, its mass, and its size. These changes drive the basic physics of humidors. You can probably imagine a crisp dry ball will bounce off the bat faster than a waterlogged ball. As a result, a ball stored in the ambient dry air of Denver or Phoenix will bounce off the bat better than a ball stored in the damper air of the humidor.

The technical term for the bounciness of the ball is the “coefficient of restitution,” or COR. The COR for a ball stored in the ambient humidity at Coors drops from around 0.537 to 0.513 when stored in the humidor. That’s a 4.5 percent drop in COR. If we compare a ball from the humidor with an exit velocity of 100 mph that would travel 400 feet to a ball with the reduced COR, the exit velocity would drop by 3.6 mph, and the distance it would travel falls by 15 feet.

The additional water in the ball increases its weight. This also decreases the exit velocity of a well hit ball. Using the Colorado situation, there is a 3.5 percent increase in the weight of the ball. This will reduce the exit velocity by 1.2 mph and the distance traveled by 5.6 feet compared to the humidor ball with a launch velocity of 100 mph, which would travel 400 feet. This is roughly one-third of the change due to the COR decrease.

The flight of the ball is not affected much because the added weight actually makes the ball harder to slow down, increasing the distance. Meanwhile, the swelling of the ball due to the added water causes the ball to interact with more air, slowing it down and reducing the distance. The two effects tend to cancel each other.

Enough about Colorado — let’s look at Arizona. Last year in the Diamondbacks’ 81 home games, there were 171 homers hit by both teams compared to 215 the previous year. This is a 20 percent decrease, as you might have predicted understanding the effects of the humidor from Coors.

Naysayers would point to the fact that Arizona parted with J.D. Martinez prior to the 2018 season. He hit 46 homers in 2017, although only 16 of those dingers were at Chase. However, the table below shows the Rattlers hit essentially the same number of homers away from Chase Field in both 2017 and 2018. Meanwhile, their production at home dropped dramatically, consistent with the Coors experience.

Granted, this is only one year of data, but since the Coors home run reduction has sustained over time, one would suspect no less from Chase. However, before we wipe our hands and say we’re done, take a look at the plot below of home versus away round-trippers for the Diamondbacks the last few years.

If it was the case that 2018 was the first year the Snakes had more dingers on the road than at home, then it would nearly clinch the case for the home run decrease at Chase in 2018 was due to the humidor. Alas, 2015 shows the same away versus home split. So more investigation might be warranted.

I tried to find any changes to Chase in 2015, such as a higher yellow line in center field or a taller fence somewhere. The only thing I could find that happened before the 2015 campaign was new sod in the outfield – hardly a cause for the D-backs’ power outage at home.

However, in the Report of the Committee Studying Home Run Rates in Major League Baseball, Chase Field was one of only five ballparks that experienced a drop in home run rate between the beginning of the 2015 season and its end, suggesting there was something a bit out of the ordinary at Chase that year. By the way, the conclusion of the report was that the drag on the baseballs was less for some unexplained reason. Thus, the balls traveled farther than would be otherwise expected. It’s possible Arizona didn’t get any of these baseballs for some reason.

In any case, instead of looking at homers, let’s examine exit velocity. That way, we don’t need to worry about the trajectory of the ball. Below is a plot of the number of balls hit with an exit velocity over 105 mph by year at Chase Field.

The data show the fewest number hit were indeed in 2018. This is consistent with the humidor theory because the reduced COR and larger ball mass would make it harder to launch a ball at a high exit velocity regardless of the resulting trajectory.

In fact, if we stop obsessing about the abnormal number of away versus home four-baggers in 2015 and just look at balls hit by the Diamondbacks at high exit velocity since 2015, we might further clarify matters. Below is a plot showing these data. The percentage shown is the difference between home and away high exit velocity hits for each year.

You can see the Rattlers consistently hit the dry balls in Arizona at a high exit velocity more frequently than the mushier balls used in the rest of the league. Not only was there a steep drop in the number of high-exit-velocity balls in 2018 at Chase, the decrease between home and away is dramatically smaller after the introduction of the humidor.

In summary then, the humidor in Phoenix has done what humidors do to dry baseballs. This conclusion is based upon the physics of humidors and the following data:

• The reduction in total home runs hit at Chase Field in 2018.
• The Diamondbacks, for just the second time since 2014, hit more round-trippers away from home.
• There were fewer very-hard-hit balls in 2018 than at any time in the Statcast Era.
• The difference between the number of very-hard-hit balls at home and away is as small as it has ever been.

It still remains a bit of a mystery why Arizona would want to have fewer hard-hit balls and home runs in their ballpark. Conspiracy theorists would probably argue that Martinez left and Paul Goldschmidt is gone, making the humidor something of an equalizer. According to MLB.com’s Steve Gilbert, the purpose was “improving the grip that pitchers are able to get on the baseball.” Now, does anyone have any data on pitcher grip?

References and Resources

• Alan M. Nathan, Baseball Prospectus, “Home Runs and Humidors: Is There a Connection?”
• Alan M. Nathan, The Hardball Times, “A Humidor at Chase Field: What’s Up With That?”
• David Kagan, The Hardball Times, “Some Physics of Humidors”
• Alan M. Nathan et al., American Journal of Physics, “Corked bats, juiced balls, and humidors: The physics of cheating in baseball”
• Report of the Committee Studying Home Run Rates in Major League Baseball
• Steve Gilbert, MLB.com, “D-backs installing humidor for ball storage”