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.  

Home Runs and Red Zone Hits, 2014-2019
Year Home Runs Red Zone Hits % Extra Homers
2014 4186 No data – 0 –
2015 4909 24200 – ? –
2016 5610 25056 34%
2017 6105 25094 46%
2018 5585 25862 33%
2019 6776 26577 62%

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.

Corrected Home Run Data, 2016-2019
Year Total HRs HRs due to Red Zone Drag Homers % Extra Homers
2016 5610 0 5610 34%
2017 6105 9 6096 46%
2018 5585 180 5405 29%
2019 6776 411 6365 52%

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.

David Kagan is a physics professor at CSU Chico, and the self-proclaimed "Einstein of the National Pastime." Visit his website, Major League Physics, and follow him on Twitter @DrBaseballPhD.
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3 years ago

I simply credit the hitters and think the education is better than ever. And, I do buy into the whole swing plane thing.

3 years ago
Reply to  JohnnyRingoFWC

That is certainly not it. These are the exact same players that were not hitting home runs before balls got juiced. Is pitcher education worse? These are the same players, its the game that was changed.

Cave Dameron
3 years ago
Reply to  RonnieDobbs

It’s a combination of both the ball and swing plane changes. Most of these players made swing changes and hit the ball in the air more to take advantage of the different baseballs. Look at the launch angles and flyball % of these new HR hitters. Ketel Marte went from hitting 29% flyballs last year to 35% this year. His launch angle went from 5.7 degrees last year to 11.5 this year. The juiced balls aren’t solely responsible for every player’s HR jump.

3 years ago
Reply to  JohnnyRingoFWC

Did you know that juiced balls were introduced to AAA this year and they instantly just started smashing records? Its hard to credit those players with better data/education.

3 years ago

“…nor are there any telltale signs of PEDs.”

I would just point out that there are rarely such signs. No one suspected Cano until he was caught. Same thing with Braun. Same thing with dozens and dozens of other such players.

And those that are caught likely represent only a small fraction of those who are actually taking PEDs since the cheaters are normally several steps ahead of the testers (see Armstrong, Lance; Rodriguez, Alex).

Not saying that PEDs are the cause, just that they’re nearly impossible to rule out.

3 years ago
Reply to  emh1969

I mean, Braun ripped his shirt off and had 13 abs, soo… I suspected something.

D.K. Willardson
3 years ago

One of the better articles on the subject. Given that there seems to be overwhelming evidence of a ball change in 2018 to a higher drag ball and then another (likely reactionary) change in the opposite direction in 2019, I think it is more instructive to view the data year-over-year in light of the ball changes. So looking 2019 vs. 2017, interesting that hitter improvement via the “Red Zone” is also a significant driver in addition to the reduced drag.

3 years ago

Go check out Nate Silver’s work on the subject. The change occurred prior to 2018. It was not coincidentally right as players stared hitting a ton more HR.

D.K. Willardson
3 years ago
Reply to  RonnieDobbs

Think you might have missed my point. The ball was changed back in mid 2015 that REDUCED drag. HRs increased as a result through 2017. For 2018 there was a definite change to the ball that INCREASED drag prior to the 2018 season – Distance, HRs all down last year. I did an analysis on this as did others who came to a similar conclusion.

For whatever reason (possibly attendance down 3 million last year), there was yet ANOTHER change to the ball prior to the 2019 season which reduced drag again – which contributed to the HR increase along w/ hitters making changes.

My point was that for an accurate analysis, you need to consider all the changes to the ball that can clearly be seen in the data (with the help of a distance model).

Green Mountain Boy
3 years ago

Logic says that there are only three major things that could be making the ball go further: 1) A tighter core, 2) A smaller ball, and 3) As the author says, a lowered drag co-efficient.

If 1) or 2) were responsible, we’d be seeing differences in the size (diameter) and/or weight of the baseball. Nobody is claiming either of these, least of all the pitchers, who would be the first to notice (and complain).

That leaves us with 3), lowered drag co-efficient. It would seem to me that the easiest way to lower the drag co-efficient would be to reduce whatever is the highest contributor to drag. I’m no rocket scientist, but common sense tells me that would be the seams. Lowering the seams would definitely lower the drag co-efficient. So is there any evidence of that being done? What do you know… pitchers have been complaining that the seems are lower on the 2019 baseball since… when? I remember hearing their complaints at least as far back as May.

So get on the horn and get this fixed, Rob.

3 years ago

1 is not as straight forward as you would think. In slowpitch softball the cores are absolutely manipulated and you can’t feel or weigh the difference.

3 years ago

Juiced balls and the fallout of that change. You can make it complicated if you choose.

3 years ago

I guess all those small, intimate parks have a tomato problem. Maybe we can say a can of tomatoes is a tougher sell than a can of corn.