Several years ago Alan Nathan, Jeff Kensrud, Lloyd Smith, and Eric Lang brought an air cannon and a few boxes of brand new baseballs to Minute Maid Park. If you’re anything like me, you like where this is going. They set up their cannon to fire balls roughly 96mph on a 28° angle and used Trackman to measure their distance and spin rate. They tested four groups of balls, two groups composed of MLB balls, one MiLB, and one NCAA. One group of MLB balls, group A, were tested using reasonably low spin rates, about 1800. The other, group B, had variable spin rates, ranging from 2100 to 3300. The results of their study were published in an article titled How Far Did That Fly Ball Travel (Redux)? on Baseball Prospectus, although it can also be found here. I encourage you to read the piece, but today I want to focus on the MLB-A and MiLB groups.

Measured Ball Distance and Spin Ball Lot Distance (S. D.) Spin (S. D.) MLB-A 390 (8) 1806 (58) MiLB 362 (8) 1583 (49) SOURCE: http://baseball.physics.illinois.edu/FlyBallDistance.pdf

The major league ball traveled 28 feet further than the minor league ball. Albeit with a higher spin rate. Presumably, the higher spin rate should translate to increased distance, but it is difficult to imagine that a difference of 200 rpm could bridge a gap of 28 feet. More on this in a moment.

I plugged the information from this study into my distance calculator. I set the ball park to Minute Maid, Exit Velocity to 96 mph, launch angle to 28 degrees, 1800 rpm backspin and I found the average air pressure of Houston, 30.03 inHg and relative humidity, 75%. So that leaves temperature. Well, I don’t know what temperature it may have been that day in Houston. So I guessed and put in 75 degrees.

With these numbers, the home run distances were a little short, but with a little poking and prodding I found that an exit velocity of 97.5 mph just about perfectly matches the average distance result for the study.

For those following along at home with the calculator: In the two hidden sheets, change the variables controlling the standard deviations from .912 and .889 to .956 and .945 for the high end. For the low end change it from 1.088 and 1.111 to 1.044 and 1.056.

With these changes, the print out of the calculator matches the numbers from the study just about perfectly. The blue line shows the mean distance, and the red and green show one standard deviation above and below the mean, respectively.



Next, I changed the spin rate to 1580, and adjusted the Cd0, the coefficient of drag, to match the results from the study. The standard MLB ball had a Cd0 of .301, but the Minor League ball appears to be closer to .360.

So, I managed to get my calculator to spit out very similar numbers as those presented in the original study by setting the exit velocity to 97.5 mph, temperature to 75 degrees, the MLB ball to a Cd0 of .301, and the MiLB ball to a Cd0 of .360. I am happy with this, and you can see the data in a table below. I’ve also included the results calculated by giving the minor league ball the increased spin rate.

Estimated Distance Group Distance (S.D) Spin Major League 390.3 (8.4) 1800 Minor League 361.8 (8.5) 1580 Minor League 362.0 (8.3) 1800

Now that I have a model for the coefficient of drag that matches the results of field testing, I can apply the model to real game results. Since I don’t have access to minor league data, I can’t easily convert minor league data into major league data. But I can go in the other direction and see how major leaguers may have faired using a minor league ball. I don’t have time to run the data for every major league player, but I do have a name you might be interested in. Trey Mancini.

In 2016 Mancini hit 13 home runs in AAA and 3 more in the majors. In 2017, he hit 25 home runs in the majors. Some question whether these power figures are legitimate, others argue he doesn’t carry enough fantasy value to be drafted. Regardless of where you stand, he is an interesting name for this sort of analysis. How much did Mancini benefit from the MLB ball?

I ran every batted ball he has produced through my distance calculator four times.

Using the MLB Cd0 of .301 Using the Minor League Cd0 of .360 The distance to where the ball last had an altitude of 8 feet with a Cd0 of .301. Where the ball last had an altitude of 8 feet with a Cd0 of .36.

I haven’t entered a large number of stadiums into my database, but I found the average wall distance for the stadiums I have entered. You can see them in the following table. The true average may be higher or lower, but they are a decent estimate. I am also declaring that an average MLB stadium has an 8 foot fence. The true average is higher, but this is good enough.

Avg Wall Distances Area Avg Distance Right Field 359 Center Field 399 Left Field 362 Only includes a limited number of stadiums, this is incomplete data only to be used as a rough estimate

Furthermore, I have assumed 2500 rpm backspin, -900 rpm side spin. As I wrote about last week, this 2500 rpm backspin is far too high for line drives and ground balls, but it is sufficient for fly balls.

Finally, I found the average temperature and pressure for each stadium during the summer months, so every batted ball was given the average values for whichever stadium it was produced in.

In all, there are 418 batted balls in this data set, and I have produced average figures in the table below.

Mancini Calculated Distances Ball Type AVGft, 20°+ Angle LF >362 ft CF >399ft RF >359ft “Over Fence” Expected HR MLB 321 20 15 32 67 MLB 8ft 314 18 9 29 56 28 Minor League 301 14 4 21 39 Minor League 8ft 294 12 3 14 29 15

The two highlighted cells are the most important ones. Note that this calculation should be finding the average distance for these batted balls. Half should fly longer, half should go shorter. In order to find the expected home run rate, we would divide these totals by 2. With the major league ball, there are 56, divide that by 2 and we have 28. Mancini actually hit 28 home runs, so that is a pretty good sign. Now look at the minor league ball, there are 15 expected home runs.

Mancini hit 13 home runs in AAA in 2016 through the majority of a season. Perhaps he may have hit one or two more at that level if given the extra 20 or so plate appearances. Instead, he jumped to MLB and hit three home runs there. Then he hit 25 home runs in the majors in 2017. This ratio of major league home runs to minor league home runs just about perfectly matches the ratio the physics model predicted. Which is pretty cool, considering the assumptions being made. These results point towards a consistent underlying skillset, though. Mancini’s power didn’t appear to vary between the minors and majors, rather his environment changed around him.

Also, take note that the research this model is based on was published in 2014. We have a lot of evidence that the coefficient of drag was altered in 2015, making the MLB ball fly even further. I have not encountered any evidence for the minor league ball being altered in a similar manner. So, in fact, the difference in the MLB ball may be even greater than these results suggest. The current major league ball may in fact have a Cd0 closer to .290 than .301, adding about 5 feet to fly ball distance.