The Physics of Cheating Baseball’s Humidors

The fabulous history of the National Pastime includes the disreputable efforts to find an edge often referred to as cheating. Cheating in baseball has taken myriad forms over the decades, some more sophisticated than others. Hitters have tried corking the bat and taking performance-enhancing drugs; pitchers have applied substances to the ball like spit, pine tar, and Vaseline, and sometimes even abused the ball with sandpaper, sharpened belt buckles, or thumbtacks. Teams have stolen signs with technology such as telescopes, video cameras, and even Apple watches.

Given any tool, substance or gadget offering the possibility of gaining a competitive advantage, the history of baseball shows players and teams will try it. As the use of humidors to control the properties of baseballs has spread over recent years in the major leagues, perhaps it’s time to consider the additional opportunities they may provide to the “black arts” of the game.

Humidors in the Majors

In 2002, MLB hoped some of the problems associated with mile-high baseball at Coors Field could be addressed by controlling the temperature and humidity in which the balls were stored. The humidors installed at Coors maintain 50% humidity at 70 degrees Fahrenheit, while the typical humidity in Denver is about 30%. The balls stored in the humidor thus have a higher water content than they would if they were stored in the dugout, making the balls “mushier” and slightly heavier. As a result of these changes, the balls will come off the bat with smaller exit velocities and, therefore, won’t travel as far. Home run production in the mountain air of Colorado did indeed drop after the introduction of the humidor, and the Coors humidor remains in place to this day.

The next humidor experiment began in Phoenix last season, the effects of which are summarized in “The Physics of Humidors: A Second Case Study at Chase Field.” Since the laws of physics are the same in both Phoenix and Colorado, the results were similar.

According to a report by Tom Verducci, MLB began requiring teams to store their baseballs in enclosed, air-conditioned rooms at the beginning of the 2018 season. Over the course of that season, MLB supposedly collected data to decide whether the air-conditioned rooms would suffice or if all teams should be required to use humidors. There is no evidence a decision has been made at this point.

The Physics

Imagine wadding up one of your socks into a crude ball. Think about hitting it with a bat. Would it go farther if it was dry or soaking wet? Go try it, and you will find the sock-ball goes farther when it is dry.

This holds true for baseballs as well. Controlling the temperature and humidity at which the ball is stored affects the ball’s Coefficient of Restitution (COR), which is a physicist’s way of saying “the bounciness of the ball.” The water in the air (the humidity) surrounding the ball allows water to enter or leave the ball. Hence, storing the ball in dry air (low humidity) will dry out the ball, while a ball in wet air (high humidity) will cause the ball to absorb water. So not only is a high-humidity ball less bouncy, but it weighs more as well – meaning it won’t travel as far when it is hit.

The temperature of a baseball also will affect its COR. The warmer the ball, the higher the COR. A warmer ball thus will come off the bat at a higher speed than a cooler ball, though the effect due to the temperature is smaller than the changes from the humidity.

The COR of a ball kept in the humidor for enough time is about 0.52. The best data we have on the variation in COR due to humidity and temperature is from a 2011 paper by Alan Nathan and several others. They found the COR of a baseball drops 1.2% for every 5% increase in humidity and 0.50% for every 5-degree decrease in temperature, showing that the temperature effect is indeed less than half the humidity effect.

The Cheating

Suppose you are a West Coast team with a solid pitching staff but few power hitters. Imagine you’re about to get a visit from a team known for the long ball. It certainly would be to your advantage to be able to reduce the COR of the baseballs used for the games against that team because the balls coming off the bats of the power hitters wouldn’t travel as far.

Let’s further assume the league requires the balls to be stored in a humidor at 50% humidity and 70 degrees Fahrenheit, and the local weather is predicted to be 80% humidity and 60 degrees Fahrenheit for the next few days. If the balls could sit out in the weather, they would have a smaller COR, thereby reducing the chances of your pitching staff getting bitten by dingers.

The question is, then, how quickly does the humidity and temperature of the ball change? In order to get an edge on your dinger-happy foes, do you need to take the balls out of the humidor a month early, a week, an hour, or just a few minutes prior to the game?

The Measurements

The rate at which humidity changes the ball was measured by placing a ball that had been sitting on my desk for years into a “desiccator.” A desiccator is a jar that contains a chemical called “Drierite” that removes all the water from the air inside, so the humidity in the desiccator is 0%.

Below is a picture of the ball in the desiccator.

The dry air in the desiccator will pull the water out of the ball, and the weight of the ball will drop with time as water comes out of the ball. The trick is to measure the weight of the ball at the beginning of the experiment and then at intervals as it dries out.

Below is the plot of the measured mass versus time. The red circles are the data, and the blue curve is the best-fitting curve through the data points.

The mass drops with time according to an exponential curve.

Now might be the time to tell the story of the Exponential Baserunner. The Exponential Baserunner makes it halfway to first base every second, so you might think he would make it to the bag in two seconds. You would be wrong. In the first second, the runner covers half the distance (45 feet), but in the second second he covers half the remaining distance (22.5 feet). During the third second, he travels 11.25 feet, and so on in the same manner.

If you make the mistake of asking how long it will take the runner to make it to first base, the answer is forever. He will get closer and closer to the bag by smaller and smaller amounts every second, but he will never actually get to the base. Instead, the correct question is, “How long does it take to get halfway to the base?” The answer to that is simple: one second. Physicists call this time the “half-life.” This idea of half-life applies to all exponential curves.

Here’s the point of our little tale: The ball adjusts to changes in humidity in the same way the exponential runner tries to get to first base. So the question isn’t how long it will take for a ball to change to the new humidity. Instead, we should ask: What is the half-life for a change in humidity?

The blue curve in the plot above is the best-fitting exponential curve. It shows a half-life of 4.2 days. Going back to our cheating hypothetical, the baseballs were originally in 50% humidity in the humidor and would be moved to 80% humidity. After 4.2 days, the balls would go halfway from 50 to 80%. In other words, the COR of the balls after 4.2 days would be as if they were in 65% humidity. Based on the findings of the paper cited above, this means the COR of the baseballs would drop by about 3.6%.

The half-life for temperature changes was found by placing a temperature sensor in the center of a ball and measuring the temperature after the ball was removed from my desk and placed in a freezer. The measured data is below. Again, the red is the data, and the blue is the best fitting curve.

The half-life for temperature changes turns out to be 30 minutes. In our cheating hypothetical, the ball started at 70 degrees Fahrenheit and would be moved to 60 degrees Fahrenheit. After 30 minutes, then, the ball would have a temperature of halfway between those two temperatures, 65 degrees Fahrenheit. The temperature drop of five degrees Fahrenheit, per the findings of Nathan et al, would lower the COR another 0.5%.

Let’s suppose we removed the balls from the humidor 4.2 days ahead of the first match-up. That would be only one half-life for the humidity. It would be a huge number of half-lives for the temperature, though, so in the same way the Exponential Baserunner would be extremely close to first base, the ball would be very close to the final temperature. The temperature drop would be very nearly 10 degrees Fahrenheit, so the COR would fall by 1%. Combining that with the 3.6% COR drop from the humidity would give a total change in COR of 4.6%.

The Conclusions

According to the research cited earlier, a 4.5% drop in COR will decrease the speed of a properly-hit ball by 2.5 mph, shortening the ball’s distance of travel by 14 feet and decreasing the number of home runs by 25%. So the 4.6% decrease in COR from the cheating scenario is large enough to have a significant effect. Thus, there is definitely motivation for our imaginary West Coast team to consider attempting this type of cheating.

MLB presumably has not implemented humidors in all ballparks yet, so the cheating situation described here is completely fictional but nonetheless possible. This type of cheating would require very early removal of the balls from the humidor, though, and thus could be remedied by careful implementation of humidor protocols. In addition to simply requiring the use of humidors, MLB also should establish rules as to when the balls can be removed prior to each game. Perhaps they already have.

A big thanks to Jaydie Lee of California State University, Chico for making the temperature measurements.

References & Resources

• Kagan, David. “The Physics of Humidors: A Second Case Study at Chase Field.” The Hardball Times, April 26, 2019.
• Nathan, Alan, et al. “Corked bats, juiced balls and humidors: The physics of cheating in baseball.” American Journal of Physics 79 (6), June 2011.