The Physics of the “Seamy” Side of Baseball

The Preliminary Report of the Committee Studying Home Run Rates in MLB (December, 2019) released at the Winter Meetings in San Diego makes the droll statement, “The aerodynamic flow over a baseball is complex…” Nonetheless, it has provided much more solid data on the effect of seam height on the flight of the ball but still must acknowledge “only 35% of the increase in home run rate attributable to greater carry is due to a change in the seam height.”

The seam height is a feature that clearly disturbs the surface smoothness of the ball. One would suspect, based upon “common sense,” that anything that disturbs the smoothness would cause the air flowing over the surface of the ball during flight to impede the progress of the ball. However, this is not always the case.  

A golf ball is the usual counterexample. The dimples on a golf ball allow it to travel through the air more easily than a non-dimpled ball. The data from the report clearly shows that for baseballs at game speeds and spins, the “common sense” idea applies–the lower the seams, the further the ball flies. Thank goodness.

The report states researchers can detect changes in the yearly mean values to “0.0016 inches for seam height.” Say again? They can measure to an accuracy of 1.6 thousandths of an inch. For crying-out-loud, many human hairs are about the same thickness. Let’s go step by step and try to see how much farther a ball will travel if its seams are 0.0016 inches lower.  

Let’s start with a dime–a simple 10-cent piece. A stack of about 20 dimes is roughly an inch high. So, each dime is about 0.05 inches thick. So far, so good. The average seam height of an MLB baseball is about 0.03 inches, a bit over half the thickness of the dime. If you are lucky enough to own an MLB ball (or a dime for that matter), check it out yourself.  

Doing some quick arithmetic, the average seam height is equivalent to about 20 human hairs. Consider this for a moment. The red waxed thread used to stitch up the ball is composed of finer sub-threads in the same way as dental floss. If the sub-threads are about the size of a human hair, and one happens to be missing in the section of the red thread used on a particular ball, it will become a “good ball to hit.” If there is an extra sub-thread, it is now a good ball for the pitcher.  

The quality control for the red wax thread must be exceptional to produce uniform baseballs. In addition, the stitches are done by hand because attempts to mechanize the process have been unsuccessful to this point. Isn’t it reassuring that there are still some things humans are better at than machines? Anyway, more on the stitching process in a bit.

Let’s look at the seam height data from the report. Below is a plot of the drag coefficient versus the seam height. It is completely understandable if you need to take a moment to be sure you understand the drag coefficient. Perhaps The Physics of the MLB Report on Home Run Rates will help. Basically, if a ball has a higher drag coefficient, it is less aerodynamic and will not travel as far.

These data were built using 65 dozen MLB baseballs for 2013 through 2019, and there certainly is a lot of scatter in the results. The drag coefficients on this plot range from 0.30 to 0.39, or roughly plus or minus 13%. The seam height varies quite a lot as well–from 0.27 to about 0.37 inches.

Some of that variation is from the changes in the average from year to year (see figure 3 in the report), and some is ball-to-ball variation. Some of the ball-to-ball variation is associated with seam height, as can be seen by the correlation between the drag coefficient and the seam height. The report points out that much of the ball-to-ball variation is not associated with seam height, and its cause is still unknown.

The blue line through the data is the best-fitting line (“regression line”). Examining this line carefully, one can discern the drag coefficient is related to the seam height by the following equation.

drag coefficient = 3.14 * (seam height) + 0.236

This means a change in the seam height of 0.0016 inches (one sub-thread) causes a change in the drag coefficient of 0.005. Since the drag coefficients of the balls average about 0.34, this is about a 1.5% change. Previously, we noticed the drag coefficient is bouncing around between plus and minus 13%. So, the scientists and engineers can now detect a consistent 1.5% change in a data set that shows 13% variations. Small wonder they needed lots of data, like the nearly 800 baseballs they used here.

The next question is, how would a missing sub-thread change the distance of a well-hit ball? The report also contains a plot of fly ball distance versus the drag coefficient shown below.

The regression line is given by this equation:

distance = -456 * (drag coefficient) +527.

We can combine the regression line from the drag coefficient-versus-seam height plot with the line from the distance-versus-drag coefficient plot to get an equation for the distance versus the seam height. Note, this is a bit sloppy because the drag coefficient-versus-seam height plot was created in a lab, presumably using spinning balls at one speed, while the distance-versus-drag coefficient graph used Statcast data at a variety of speeds and spins, then normalized it.

To avoid this concern to a degree, let’s focus just on changes in distance due to changes in seam height. The result is the following equation:

change in distance = -1430 * (change in seam height)

Now, let’s get back to our 0.0016 drop in the seam height due to a missing sub-thread. Our new equation gives us an increase in distance of about 2.3 feet. This number is a bit scary–a very small change in seam height, one that is barely detectable from year to year, can change the distance of a fly ball by a measurable amount.

The reality of the situation, which you may have noticed when you compared the height of a seam to a dime, is that in addition to the red wax thread, a portion of the seam height is due to how much leather has been pulled into the stitch. Recalling that baseballs are indeed sewn by hand, it is in fact quite unremarkable that seam heights vary from ball to ball. It is actually impressive they are this consistent.

Does the fact that there are ball-to-ball variations really matter to the game? There are arguments both ways, but it is hard to complain about a variation of a couple of feet due to a single missing sub-thread when there are much larger park-to-park variations in the distance to fences.

That said, consistent year-to-year variations that appear to continually increase the number of home runs are radically changing the game. From 2013 to last season, the seam height has dropped by about 0.005 inches. In addition, according to the report, the seam height problem is only 35% of the total decrease in drag.  Until there is a good explanation for seasonal changes, some will continue to claim there is a “seamy” side to baseball.