The Challenge of Explaining the Home Run Explosion

Home runs were up in baseball in 2019, but the physical explanation for why isn’t exactly clear. (via slgckgc)

Well, it’s autumn. Time to start thinking about cleaning out the vegetable garden…oh, and the postseason, of course! When I planted my tomatoes last spring, I decided to stop spending so much money on the expensive fertilizer I bought in previous years. It was “guaranteed” to increase the size of my fruit. Over the summer, I thought I noticed smaller tomatoes–but then again, how could I really tell? After all, the natural variation in the size of tomatoes was much larger than any decrease in their average size.

This is the essential challenge of explaining the home run explosion over the last couple of years.  As the MLB Report on Home Runs states, “We find that the ball-to-ball variation in the drag and lift coefficients is large compared to the size of changes of average values that would lead to the home run surge.” There is little evidence the ball is coming off the bat faster, nor are there any telltale signs of PEDs. The most likely problem is an (as-yet unexplained) drop in the drag coefficient of the ball.

Since this is likely to be the most home-run-filled postseason ever, it might be time to try to understand why, a year and a half since the report, no one has found the definitive cause for the drop in the drag coefficient on today’s baseballs. (If the words “drag coefficient” start to raise that uncomfortable feeling known as “jargon-terrors,” and you want to start throwing “drag coefficient” around yourself, perhaps “The Physics of the MLB Report on Home Run Rates” will help.)

In simplest terms, the ball is gliding through the air more gracefully than before. It is acting less like a 16-wheel truck and more like a sleek sports car. In the case of these two vehicles, the cause of the difference is pretty easy to understand. The sports car has an aerodynamic design that allows air to flow smoothly around and over it. The truck has a huge flat front that just slams into the oncoming air. In the case of a baseball, the difference is far more subtle.

In Appendix D of the MLB Report, there is a graph for the home run probability for balls hit at greater than 90 mph with launch angles between 15 and 45 degrees. The report describes balls hit with these parameters as being in the “Red Zone.” The graph shows the probability versus distance for eight different spray angles.  For balls hit to center field, there should be 2.6% more homers for each foot of extra distance the ball travels. This has already been averaged over all the parks in the league. Wait a minute…there will be 2.6% more dingers for just a solitary foot? Wow.

So, how much does the drag coefficient need to change for a ball to travel that single extra foot? Let’s look at a 399-foot blast launched at 100 mph with a launch angle of 30 degrees by a right-handed batter directly toward center field.  The backspin will be about 2800 rpm and the sidespin a bit over 800 rpm. Doing the trajectory calculations, a drop in the drag coefficient of only one half of one percent is enough to allow the ball to go the extra foot.

The table below is based solely upon data from Statcast. The second column shows the number of home runs each year since 2014 (the reference year in the MLB Report). The next column is the number of balls hit in the Red Zone.  Note that Statcast was not in place to collect Red Zone data in 2014, although the MLB Report has an estimate for this year from other non-public sources (not included here). The final column shows the percent increase in homers over 2014. The 2015 season is ignored because the change in drag seems to have begun midway through that year.  

The number of hits in the Red Zone was relatively constant through 2017. Since the MLB Report was released in May 2018, it can safely be assumed the home run increase is due to the drop in the drag coefficient, not more balls hit in the Red Zone.  The uptick in Red Zone hits since 2017 requires some correction to the number of homers due to the drag decrease.

In the table below, the third column is the number of homers that might be expected because of the increase in the number of balls hit in the Red Zone based on the 2016 value. The fourth column is the total home runs, minus the homers that can be explained by the increase in Red Zone hits. (These are these bombs that are presumably due to the drop in the drag coefficient.) The final column is the percent increase in homers over 2014, corrected for the increase in Red Zone hits.

Now, we need to see how much the drag coefficient would need to change to explain the 29% to 52% increase in long balls between 2016 and 2018.  Let’s just use the mean of a 40% increase in home runs.  

Using the previous result of a 2.6% increase in homers due to a one-foot average increase in distance, the 40% increase in home runs requires a 15.4-foot increase in distance. Going back and doing some trajectory calculations reveals that a 15.4-foot increase in distance occurs if the drag coefficient drops by 3.1%. The report presents data showing a drop in the drag coefficient from 0.375 in 2014 to about 0.365 in 2017. That’s a 2.7% drop, which is pretty close to the 3.1% estimate.

The second relevant issue brought up in the MLB Repor is the ball-to-ball variation in the drag coefficient. The balls measured in the Washington State University Sports Science Laboratory for MLB authentication in 2017 had drag coefficients between 0.29 and 0.44, with a mean of about 0.365. That range is 40% of the mean.

Now we are prepared to get back to the original question: Why is it so hard to figure out the cause of the drop in the drag coefficient?  Back in my garden, I can’t easily detect a decrease in the average size of a tomato because the tomatoes themselves vary in size much more than any change in the average size. In the lab with a bunch of baseballs, we need to explain a 3% change in drag coefficient when the drag coefficient naturally varies over a 40% range.  

If I was really concerned enough to find out if the fertilizer was worth the money, I would need to measure the size of very large numbers of randomly chosen tomatoes both before and after the fertilizer.  That way, I would be very certain of the average size in both cases. Similarly, if you suspect some property of the ball (seam height, surface roughness, etc.) has changed, you need to know the average value of that property both before and after to a high degree of certainty.

The point is, you can’t just grab a few baseballs and test to see if some particular property of the ball is the source of the change in drag coefficient.  After all, you may have randomly grabbed some that have too high a drag coefficient and get really screwy results. The underlying issue is that we’re looking for a needle in a haystack–and you need to examine a lot of hay before you find the needle.

There have been many proposals for the source of the drop in the drag coefficient, with a number of them considered in the report. However, the bottom line is that anyone having found “the smoking gun” and claiming to know the reason for the drop had better have evidence from a collection of tests on a very large number of baseballs.

So, I guess we just won’t know the explanation behind all the postseason bombs this year.  We’ll just have to enjoy them anyway. Now I need to get back to the garden. I have to be done before the game starts.