*The post that follows is an academic exercise that I completed for grad school in 2016.* *This is a follow up to a previous post on pitcher height. In short, I found that taller pitchers tend to throw harder than shorter pitchers, but their superiority in velocity does not necessarily translate into performance. You can view the code here.*

**Introduction**

Analysis performed in Assignment #1 examined the relationship between height and pitching in Major League Baseball. Positive correlations were found between height and both perceived velocity and the downward plane of the ball as it travels towards home plate. However, assessing the impact of these variables on pitching effectiveness revealed inconclusive results. Thus, the question remains: why do professional baseball teams prefer taller pitchers?

As mentioned in the previous report, the theory is that taller pitchers use their size to throw the ball harder and create a greater downward plane when the ball is released (Greenberg, 2016). The difference between tall and short MLB pitchers has been studied before. Baseball analyst David Cameron wrote that teams often undervalue short pitchers due to a belief that their bodies will not hold up to a large workload (Cameron, 2003). Baseball writer Jeff Zimmerman suggests that shorter pitchers receive less credit for their ability and found that they actually outperform others (Zimmerman, 2014). Elliot Evans of the baseball research website Fangraphs.com examined tall and short pitchers from the perspective of performance per dollar and found that short pitchers are undervalued, despite no significant difference in performance (Evans, 2015). An investigation by Driveline Baseball, a training company specializing in the biomechanics of pitching, found that the mechanics of taller pitchers actually creates more stress on the arm than shorter pitchers (Boddy, 2016). While many believe that shorter pitchers may be undervalued, the trend in MLB has not changed.

The purpose of this analysis is to examine the prevalence of tall MLB pitchers from a different perspective, building on the previous analysis by using PITCHf/x data to compare tall pitchers to their shorter counterparts. Created in the early 2000s and used in every MLB stadium since the beginning of the 2008 season, PITCHf/x captures data on the release point, speed, and trajectory of every pitch that occurs in every game throughout the league (Marchi, 2013). The hypothesis for this study is that the data will reveal a significant difference between tall and short pitchers in at least one variable, shedding light on the reason behind MLB’s roster selection strategy.

**Methods**

PITCHf/x results data from the beginning of the 2008 season through the first half of the 2016 season for pitchers who threw a minimum of 50 pitches during the period was extracted from MLB’s Statcast database (Statcast Search, 2016). While the dataset used for Assignment #1 contained a record for every pitch thrown during the relevant period, the results data used for this study included one record for each pitcher who played during the period. The Statcast database summarized the pitch-by-pitch data into key performance metrics that indicate the average velocity, perceived velocity, and spin rate for each pitcher. It also included the average exit velocity and launch angle of all batted balls per pitcher, as well as a few rate measurements like batting average that indicate how well batters perform against each pitcher. Using results data rather than pitch-by-pitch data drastically reduced the size of the dataset, so historical data spanning the entire PITCHf/x era was gathered in order to generate as many observations as possible. A minimum of 50 pitches thrown was used to eliminate position players who occasionally pitch in blowout situations. They are typically untrained in pitching and would likely create outliers in the data. Finally, additional data was downloaded from the Baseball Prospectus Active Player tables to supplement the dataset with the pitcher’s height for each record (Baseball Prospectus | Active Players by Year, 2016). Each variable in the dataset is defined below in Table 1.

The player_id field is a unique identifier for each player and was used to join the PITCHf/x data to the Baseball Prospectus height data. Velocity, effective_speed, exit_velocity, and launch_angle were used in the previous analysis to investigate the correlation between height and pitching performance. Spin rate is an additional PITCHf/x field that represents the rate of spin on the ball after it is released by the pitcher. The general belief is that pitches with a higher spin rate are more difficult to hit due to the effect on the ball’s trajectory (Glossary, 2016). The batting average (ba), batting average on balls in play (babip), slugging percentage (slg), and isolated power (iso) metrics are commonly used today to quantity batter performance. In this case, these fields characterize the performance of all batters combined against each individual pitcher. As the initial step in the exploratory analysis, the descriptive statistics presented in Table 2 were calculated for the ratio level variables.

In total, there were 1653 observations in the results dataset. Note that there are 841 missing values in the trajectory-related PITCHf/x fields of effective speed, spin rate, exit velocity, and launch angle. There was no explanation for this upon downloading the data, but it was assumed that this was due to missing values in the underlying pitch-by-pitch data used by the Statcast engine to generate the results data (i.e. the PITCHf/x technology failed to capture a pitch). A closer examination of the data revealed that it mostly impacted pitchers who played during the early years of the PITCHf/x era. It is likely that the technology has improved over time and missing values are less common today. The mean height was 74.42 inches, which was used as a threshold to dichotomize the data into two categories and create the new variable tall_short. There were 814 tall pitchers and 839 short pitchers.

The statistical model used to compare the two categories was Welch’s two sample t-test, a variation of the Student’s t-test that accounts for differences in variance between the two populations. Otherwise, the assumptions remain the same. The first assumption for the t-test is that the dependent variable(s) should be measured on a continuous scale, which is true in this case. Each item that was examined is a ratio level continuous variable. Next, the independent variable should be categorical with two groups. That is also true in this case, with the dataset split into tall and short pitchers. The third assumption is that there must be independence of observations between the populations or samples, which also holds true for this data. All pitchers are classified into only one group and there is no relationship between the observations in each group. The final two assumptions are that the dependent variable(s) follow a normal distribution for each group and that there are no significant outliers. These assumptions were assessed using histograms and boxplots. Figure 1 below presents the graphics for velocity, with short pitchers presented in light blue and tall pitchers presented in royal blue.

There is some obvious negative skew in the distributions for both tall and short pitchers, as well as a few extreme outliers based on the boxplots. One possible explanation of the outliers in the velocity field is knuckleball pitchers. These unconventional pitchers rely almost exclusively on a special pitch called the knuckleball, which is often thrown at a much lower velocity than most pitches. The focus of this study is on the traditional style of pitchers, so known knuckleball pitchers Tim Wakefield, Charlie Zink, Charlie Haeger, Steven Wright, and R.A. Dickey were removed (Wikipedia, 2016). This eliminated 5 observations, leaving a total of 813 tall pitchers and 835 short pitchers (1648 total observations). Figure 2 below presents the plots for a select few variables for discussion purposes.

Removing these extreme outliers improved the normality of the velocity distributions, but there are obvious issues with batting average (ba) and slugging percentage (slg) that violate the assumptions of the statistical model. This is also proven by the skewness and kurtosis values presented in Table 3 below.

There are a few variables that approach normality in both the tall and short groups. However, there are also several variables that show drastic deviation from normality, particularly the batting performance metrics batting average (ba), batting average on balls in play (babip), slugging percentage (slg), and isolated power (iso).

In addition to the apparent normality violations, the boxplots for batting average (ba), slugging percentage (slg), and several other variables show a large number of outliers. By examining the dataset in a spreadsheet view, it was discovered that many of the extreme values for these variables that lie near the maximum and minimum ends of range occur in observations where the number of at bats was relatively small. For these particular pitchers, it appeared that the sample size was not large enough to deliver results that are indicative of the typical MLB style of play. Therefore 216 observations with less than 50 at bats were removed from the dataset. Consequently, 721 tall pitchers and 711 short pitchers remained, for a total of 1432 observations. At this point, normality was checked again on the modified data. Figure 3 below presents the plots for a select few variables after outlier removal for discussion purposes.

A significant improvement in normality is obvious in the histograms for batting average (ba) and slugging percentage (slg). While the boxplots continue to show outliers, it appears that the volume has decreased significantly.

This improvement extends to other variables, as well, and the skewness and kurtosis values presented in Table 4. Many of the distributions for both tall and short pitchers exhibit some degree skewness and kurtosis. However, none of these values represent significant violations of the normality assumption, particularly when combined with the large sample size of over 700 observations in each group. After the removal of outliers based on unconventional styles and a minimum number of at bats, the assumptions for performing the t-tests have been met. Notably, the distributions for exit velocity diverge from normality more than any of the others. A non-parametric test may be necessary to properly evaluate this metric.

**Results**

The results of the individuals Welch’s t-tests are displayed in Table 5 below, with the statistically significant p-values highlighted in yellow.

The small p-values for velocity and effective speed denote a statistically significant difference in the mean values of each group. The mean value for both variables is higher in the tall group than in the short group. Therefore, this can be interpreted to mean that the tall pitchers in this dataset throw the ball harder than the short pitchers. The p-value for spin rate is not significant at the 95% confidence level, but would be significant at a 90% confidence level. The mean value is higher for tall pitchers, suggesting that they may achieve a greater spin rate than shorter pitchers. However, this conclusion does not share the same degree of certainty as seen with velocity and effective speed. All of the other variables exhibit p-values that are demonstrably insignificant at a 95% confidence level. From these results, it can be inferred that there is no difference between tall and short pitchers in regards to exit velocity, launch angle, batting average (ba), batting average on balls in play (babip), slugging percentage (slg), and isolated power (iso).

For the sake of thoroughness, the non-parametric Wilcoxon Rank Sum Test was also performed on each pair. The results were identical to those shown above, with statistically significant differences present on only velocity and effective speed. It was observed that a non-parametric test may be more appropriate for exit velocity, but both the Wilcoxon and the Welch test indicate that a difference between tall and short pitchers is not likely.

**Implications**

The hypothesis that the data will reveal a significant difference between tall and short pitchers in at least one variable was true. Both velocity and effective speed presented a significant difference between tall and short pitchers at the 95% confidence level. In both cases, the mean value for taller pitchers was larger so it was concluded that taller pitchers do, in fact, throw harder than shorter pitchers. Furthermore, spin rate showed a significant difference between tall and short pitchers at the 90% confidence level. The mean spin rate for the tall group was higher than the mean value for the short group. As mentioned in the introduction, a greater spin rate is associated with a greater degree of difficulty for the batter. No difference was found in the metrics that indicate how batters fare against tall or short pitchers (e.g. batting average or slugging percentage).

The findings presented above imply that MLB teams prefer taller pitchers largely because of their ability to throw the ball harder than shorter pitchers. The tendency does not appear to be based on any performance because there was no difference between tall and short pitchers in opponents’ batting average, BABIP, slugging percentage, or isolated power. This offers an explanation for roster construction throughout the league that focuses on height. Also, in an era where the sabermetrics movement has provided more performance measuring statistics than ever before, the results suggest that teams still seek the raw skills of bigger, stronger athletes who can throw with greater velocity. Teams may be able to find market inefficiencies in shorter pitchers who achieve better results than taller pitchers who may throw the ball harder.

One limitation of the data was discussed in the Methods section in that the effective speed, spin rate, exit velocity, and launch angle were missing for over 800 pitchers. It was assumed that these missing values were caused by technological limitations in the early years of the PITCHf/x system. Also, this study did not distinguish between starting pitchers and relief pitchers. Often, these two types of pitchers have very different styles and goals and it may be wise to examine these relationships in that context. Likewise, the data could be further partitioned into left-handed and right-handed throwers. In addition, a value other than the overall mean height could have been used to distinguish between tall and short pitchers. This cutoff value was 74.42 inches, or roughly 6 feet 2 inches. While this may be the mean height of MPB pitchers, it is still much taller than the average human male, so many pitchers in the short group would be considered tall outside of baseball. Other pitching metrics, such as ERA or strikeouts, could have been included as well to look at performance.

An alternative to the t-tests performed in this analysis would have been an ANOVA model, which examines all dependent variables at once and indicates whether there is a difference in any of the variables. However, the t-test model was chosen because the tall and short populations do not contain an equal number of observations. In addition, the individual t-tests offer a more granular breakdown of the differences between tall and short pitchers that will hopefully identify the aspects of pitching on which taller pitchers perform better.

**References**

Baseball Prospectus | Active Players by Year. (2016). Retrieved July 10, 2016, from http://www.baseballprospectus.com/sortable/extras/active_players.php

Baseball Prospectus | Glossary. (2016). Retrieved July 10, 2016, from http://www.baseballprospectus.com/glossary/

Boddy, K. (2016, June 16). Tall Pitchers vs. Short Pitchers – Velocity, Elbow Injuries, and Mechanics. Retrieved July 31, 2016, from https://www.drivelinebaseball.com/2016/06/16/tall-pitchers-vs-short-pitchers-velocity-elbow-injuries-mechanics/

Cameron, D. (2003, July 3). Prospecting: Short Pitchers. Retrieved July 31, 2016, from http://www.baseballprospectus.com/article.php?articleid=2064

Evans, E. (2015, April 3). Six Feet Under: Evaluating Short Pitchers. Retrieved July 31, 2016, from http://www.fangraphs.com/community/six-feet-under-evaluating-short-pitchers/

Glossary. (2016). Retrieved July 10, 2016, from http://m.mlb.com/glossary/statcast/

Greenberg, G. P. (2010). Does a Pitcher's Height Matter? Retrieved July 10, 2016, from http://sabr.org/research/does-pitcher-s-height-matter

List of knuckleball pitchers. (2016, July 27). Retrieved July 31, 2016, from https://en.wikipedia.org/wiki/List_of_knuckleball_pitchers

Marchi, M., & Albert, J. (2013). Analyzing baseball data with R. Boca Raton, FL: CRC Press.

Rymer, Z. D. (2013, May 13). Do Taller Pitchers Throw Harder Than Average? Retrieved July 10, 2016, from http://bleacherreport.com/articles/1645950-do-taller-pitchers-throw-harder-than-average

Statcast Search. (2016). Retrieved July 10, 2016, from https://baseballsavant.mlb.com/statcast_search

Zimmerman, J. (2014, October 6). Should Short Pitchers Still Get Short Shrift? Retrieved July 31, 2016, from http://www.hardballtimes.com/short-pitchers-still-getting-short-shrift/