The great home run mystery of 2015-17 has been solved. Maybe.Yesterday, former FiveThirtyEight writer Ben Lindbergh and prominent sabermetrician Mitchel Lichtman published a piece at the Ringer with evidence showing that alterations to the ball might partially explain the spike in home runs over the past two seasons. By physically testing the balls, they found that in addition to changes that make the ball come off the bat faster, the seams were made flatter in a way that could affect the ball’s aerodynamics. With their findings in mind, I examined the rate of home runs per fly ball and found further evidence suggesting that the ball itself may be the culprit.Just after the All-Star Break in 2015, MLB’s home run rate increased without warning or explanation. Since then, it has continued rising, and it now threatens the all-time record set in the heart of the steroid era. In a series of articles at FiveThirtyEight, Lindbergh and I ruled out various explanations for the home run surge, including weather, a wave of young talent, and steroids, leaving alterations to the ball as the most likely answer. It’s either that, or 750 MLB players woke up one morning in 2015 with more pop in their bats. Despite MLB’s repeated denials, Lindbergh and Lichtman reveal that the 2016-17 baseballs have different physical properties — and those changes could explain the record-breaking home run rates. The primary alteration to the ball affected its bounciness, making it come off the bat faster. But Lindbergh and Lichtman also uncovered evidence that the ball’s seams are lower and that its circumference has decreased. Those changes should decrease the ball’s air resistance, so that a new ball should go farther than an old ball that leaves the bat at the same speed.And it turns out the new balls do tend to travel farther. I built a model to predict whether a given fly ball would go over the fence in 2015, based on the launch angle, exit velocity and stadium.1I defined a fly ball as one hit with launch angle greater than 20 degrees. Then I used that model to predict how many home runs there were in 2016.2I used a random forest to produce the results discussed in this article. I also ran a logistic regression, which produced similar findings.If the ball stayed the same, the model should be able to forecast the right number of homers. Instead, the league hit about four percent (201 total) more home runs hit than expected in 2016, even accounting for the higher exit velocities and better launch angles. That’s significantly more than you’d see by chance.3The p value was less than 0.01. The changes can also be seen in the trends of the last few years: If you focus on balls hit with launch angles of between 20 and 40 degrees and exit velocities higher than 100 miles per hour (roughly corresponding to the league’s definition of “barreled balls”), 72.9 percent of those flies ended up over the fence in 2015, compared to 74.7 percent in 2016 and 76.4 percent so far this year. Of course, another possibility is that MLB recalibrated Statcast, the radar tracking system that maps the trajectory of every batted ball, which could cause the same ball to be listed with different exit velocities in 2016 to and 2015. But even if that did happen, it would not resolve the mystery, it would only shift responsibility for the home run spike to inexplicably harder hitting, instead of more favorable ball aerodynamics.It’s possible that weather (temperature, wind or humidity) could be affecting home run rates, but when I examined only domed stadiums, I found the same increase in dingers. I asked baseball physicist Alan Nathan to calculate what effect the new balls could have, and he found that the changes in the seam height and circumference would increase average batted-ball distance something like 1 or 2 feet, raising home run rates by approximately 4 percent — identical to what I observed.Reached for comment, Major League Baseball noted that the league regularly tests baseballs to ensure that they meet established standards, and that recent tests have found that the balls are within those standards. MLB also said that an outside consultant has examined their results and found no reason to suspect that the baseballs in use today would cause an increase in offense.To be sure, the league-wide impact of tweaking the ball’s aerodynamics is small. According to Lindbergh and Lichtman, who note that their experiments are not definitive, the seam height and circumference changes only appeared in 2016, well after the midyear adjustment in 2015 that kicked off the home run surge (that part of the increase is likely attributable to increases in the balls’ bounciness). It’s likely that many factors are contributing to the ongoing spike in home run rates, including hitters adjusting their approaches and favorable weather conditions, but we now have a compelling explanation for the bulk of the spike.