# Home Runs and Drag: An Early Look at the 2022 Season

The month of April is now complete and the verdict is in: The in-play home run rate for the 2022 season is down from recent seasons, as shown in Figure 1. Much has already been written about this feature by a variety of authors, including Jim Albert, Rob Arthur, Eno Sarris and Ken Rosenthal, and Bradford Doolittle, Alden Gonzalez, Jesse Rogers and David Schoenfield, and various reasons have been proposed for the relative dearth of home runs. Some argue that the baseball has been deadened, resulting in lower exit velocities and therefore fewer home runs. Others have suggested that the drag on the baseball has increased, perhaps due to higher seams. Yet others have argued that it is the effect of the universal humidor.

In this article, we will address the issue of reduced home run rates and hopefully add more light to the discussion. Specifically, we will examine home run rates during the month of April for the 2018-22 seasons, excepting the ’20 season for which there was no major league baseball in April. Here is our approach.

### The Carry Properties of the Baseball

We start by investigating the carry properties of the baseball using a technique described by the MLB Home Run Committee. With 2018 as our reference season, we fit a generalized additive model relating the probability of a home run to the launch parameters. Ideally, all the relevant launch parameters would be used, including exit velocity, launch angle, spin rate, and spin axis. In practice, that is somewhat problematic, since the batted ball spin rate and axis are not publicly available. Accordingly, for this analysis, we use only exit velocity and launch angle.

Having fitted a model based on the April 2018 data, we then apply that model to the April data from a subsequent season to arrive at a predicted home run rate histogram as shown in Figure 2, which also shows the observed home run rate. The observed home run rate for a particular season is determined by both the launch parameters and the “carry,” which is a measure of the distance of a fly ball for given launch parameters. The carry depends on the aerodynamic effects that govern the flight of a baseball, primarily the drag. The predicted home run rate distribution for a future season reflects the carry properties of the 2018 season and the launch parameters of the future season. If the observed future season home rate is in the middle of the predicted rate distribution, that indicates the ball carry is the same as in 2018. If the observed rate falls above the predicted distribution, it indicates better carry; if the observed rate falls below the distribution, then it shows worse carry.

From Figure 2 we draw the following conclusions:

- The predicted home run rate distributions in 2019 and ’22 (top and bottom graphs) are essentially identical and consistent with the ’18 rate, indicating distributions of exit velocities and launch angles are equally conducive to home runs in those seasons.
- The predicted rate distribution in 2021 (middle graph) is greater than in the other seasons, indicating exit velocities and launch angle were more conducive to home runs in ’21.
- The observed home run rate in 2019 is greater than predicted (indicating better carry), equal to predicted in ’21 (indicating the same carry), and less than predicted in ’22 (indicating worse carry).

We can therefore say that the reduced home run rate in 2022 relative to that in the ’18 season is primarily due to reduced carry. Since much of the recent discussion is about the reduction in the in-play home run rate in April 2022 relative to that in April ’21, we present the relevant numbers in the table below. These numbers show that there is a 21.7% reduction in the in-play home run rate in 2022 relative to ’21, of which 7.5% (or about one-third) is attributed to less favorable launch parameters and 14.2% (or about two-thirds) to reduced carry:

Year | Predicted | Actual |
---|---|---|

2021 | 0.0465 | 0.0465 |

2022 | 0.0430 | 0.0364 |

### Drag Coefficients

Since the carry is largely determined by drag, we next look at a property of the baseball known as the drag coefficient C_{D}. We use the technique described by Kagan and Nathan and apply it to the voluminous amount of data from pitched baseball trajectories. The primary thing you need to know about C_{D} is that a larger value means greater drag and therefore worse carry, and a smaller value means less drag and therefore better carry. The graph in Figure 3 shows monthly averages of C_{D} values for fastballs (red points). We see considerable year-to-year variation, indicating real differences in the aerodynamic properties of the baseball. The difference between the largest (April 2022) and smallest (June ’19) values is approximately 0.028, or about 8%.

However, more relevant for our purposes are the density-corrected C_{D} values (blue point), which is the product of air density and C_{D}^{*}, normalized to a fixed air density. For those of you who like equations, C_{D}^{*} = C_{D}ρ/ρ_{0}, where ρ is the actual air density and ρ_{0} is a fixed standard air density. The essential point is that the drag force is determined by the product of air density and drag coefficient, so the expectation is that the carry will be better related to the C_{D}^{*} values. Indeed, the variation of the blue points in the graph shows the expected seasonal variation, i.e., high in April when the temperature is low and low in the summer when the temperature is high. Comparing values only in April, the relative ordering of the values is consistent with the findings discussed with respect to Figure 2: Relative to 2018, the ’21 value is about the same, the ’19 value is lower, and the ’22 value is higher.

### Relating Carry to Drag

To investigate more fully the relationship between drag and carry, the April 2018 model was applied to each of the subsequent months through April ’22, allowing a determination of the ratio R of the observed to predicted home run rate. It is expected that R is a surrogate for the carry relative to that of the reference month, April 2018. In Figure 4, R is plotted versus the monthly average of C_{D}^{*} values, with the error flags equal to the standard error (i.e., one standard deviation or the 68% level).

We see that there is a linear relationship between R and C_{D}^{*}. The slope of the line is such that an increase in C_{D}^{*} by 0.01 results in a reduction in the in-play home run rate by about 19%, assuming the same launch parameters. For the reference month, April 2018, R is expected to be 1 and it is indeed 1. It is also 1 for April 2021, consistent with Figure 2. The highest values of R, and the lowest values of C_{D}^{*}, are for July-August 2019. The lowest value of R, and the highest value of C_{D}^{*}, is for April 2022, the very month that motivated this study.

### Summary

In summary, we have investigated changes in the in-play home run rates for the 2018-22 seasons, using April ’18 as our reference. We have developed a technique to separate the changes into those due to changes in launch conditions and those due to changes in carry. We have further shown that the latter are directly correlated with changes in the density-corrected drag coefficient. Finally we have shown that the significant reduction in the in-play home run rate for the 2022 season relative to April ’21 is due in part to changes in launch conditions (approximately one-third) and in part to changes in the drag (approximately two-thirds).

*Addendum: One of us (JA) has written a shiny app that allows one to create graphs such as those in Figure 2, where the model and predicted seasons are selectable by the user.*

Great article! Always enjoy Dr Nathan’s work (respect to JA too). Now do Cd* vs. pitch movement 🙂