The Effects of Atmospheric Conditions on Pitchers

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1 The Effects of Atmospheric Conditions on Rodney Paul Syracuse University Matt Filippi Syracuse University Greg Ackerman Syracuse University Zack Albright Syracuse University Andrew Weinbach Coastal Carolina University Jeff Gurney University of South Carolina Corresponding Author: Rodney Paul David B. Falk College of Sport and Human Dynamics - Syracuse University Syracuse, NY, USA, Abstract Bahill, et al. [1] studied the physics of the flight of a baseball and found that the speed and movement of individual pitches and the distance traveled of a batted ball are impacted by air density. Air density is influenced by altitude, temperature, humidity, and barometric pressure. Using these findings, we calculated air density for each game of the 2012 MLB season to analyze the effects of atmospheric conditions on baseball in two distinct manners. First, we established the link between pitch selection and air density. We discovered that pitchers throw fewer breaking pitches on days with high air density and throw more breaking pitches on days with low air density. These choices by pitchers may stem from a hanging curve effect on high air density days. These results are statistically significant, mainly influenced by temperature and humidity, and are independent of the opposing team. Second, we used these results to investigate the MLB betting market to compare pitcher performance to market expectations. We discovered that pitchers who throw a high percentage of breaking pitches outperform expectations on low air density days, while pitchers who throw a low percentage of breaking pitches outperform expectations on high air density days. 1 Introduction In a physics study about the flight of a baseball, Bahill, et al. [1] showed that air density played an important role in both the speed and movement of individual pitches and the distance traveled of a batted ball. Air density is influenced by altitude, temperature, humidity, and barometric pressure (formula for air density is shown in appendix I). In their analysis, the authors reveal in relation to thrown pitches that a 10% decrease in air density will lead to a 1% increase in the speed of a fastball and a 4% decrease in the rise of the fastball. For breaking pitches, a 10% decrease in air density will increase the speed of the ball by 1% and reduce the drop in the breaking pitch by 9%. A priori, the impact on pitches due to air density is not straightforward. In high air density, breaking pitches will decrease in speed, but will have a greater drop. In low air density, breaking pitches will travel faster, but their drop will not be as large. Higher air density conditions could create the classic hanging-curve effect, where the breaking pitch is moving slower, is more recognizable to the hitter, and is likely easier to hit. Low air density, on the other hand, does not create as much of a drop in the breaking pitches, but the pitch does travel faster and still moves laterally, possibly making the breaking pitch in these conditions more difficult for the batter to identify and successfully hit. These findings regarding the physics of baseball may play a key role in performance analytics of individual pitchers and may generate profitable gambling strategies. We aim to test and establish the relationships that may exist between air density and pitcher performance. We will attempt to establish this relationship in two distinct manners. First, we will test if air density affects pitch selection. Then, once this relationship is established, we will turn to the betting market to determine if high and low air density conditions impact overall starting pitcher performance based upon their betting market returns. To test these relationships, we use all games played in the 2012 Major League Baseball season. The game results and starting pitchers were gathered from the Major League Baseball website. The weather data was taken daily from for each major league city. Pitch type was gathered from through their Pitchf/x section. Game odds for all Major League Baseball games were gathered from the online betting site BETUS.

2 2 Establishing the Link between Air Density and Pitch Selection For ease of exposition, we used the pitch type information from Fangraphs and calculated a Breaking Pitches category by taking the sum of curveballs, sliders, and knuckle-curves. To establish if air density truly impacts each individual pitcher s pitch selection, we calculated the average percentage of breaking pitches thrown by each starter in the majors. Then, we created a variable that is the difference between the percentage of breaking pitches thrown by the starting pitcher in each individual start minus his average percentage of breaking pitches thrown for the season. A positive value indicated that he threw more breaking pitches on that start than normal, while a negative value implied that he threw fewer breaking pitches in that individual start. A simple regression model was then established that used the individual pitcher change in breaking pitches thrown as the dependent variable. The independent variables consist of an intercept and the air density in the city for that game. If air density plays a role in pitch selection by pitchers (or catchers/coaches) then the coefficient on the air density variable should be statistically significant. The result of the simple regression revealed the following: Δ(Breaking Pitches by Starting Pitcher) = (Air Density). (1) This relationship can also be seen in appendix II as a simple scatterplot of the data relating change in breaking pitches to air density (zoomed for emphasis) with the downward linear trend highlighted. Basic results could be skewed by the opposing team, as certain opponents may have lineups that perform better vs. breaking pitches than others. To account for this possibility, we include dummy variables for the opposing team in the regression model. The results are shown below with all opposing teams compared to the Los Angeles Angels (omitted dummy variable category). Table I: Regression Model Result Air Density and Percentage of Breaking Pitches Dependent Variable Change in Breaking Pitches Thrown by Starter Intercept ** (2.2734) Detroit (0.2149) Pittsburgh ( ) Air Density ** ( ) Houston ( ) San Diego (1.2901) Arizona ( ) Kansas City (0.1293) Seattle (0.9030) Atlanta (0.2701) LA Dodgers ( ) San Francisco ( ) Baltimore (0.2616) Miami * ( ) St. Louis (0.5881) Boston ( ) Milwaukee (0.7783) Tampa * (1.7311) Chi. Cubs * (1.9150) Minnesota ( ) Texas (0.3977) Chi. White Sox (1.3139) NY Mets ( ) Toronto (1.6052) Cincinnati ** (2.0850) NY Yankees ( ) Washington (0.5702) Cleveland ( ) Oakland * ( ) Colorado ( ) Philadelphia ( ) Note -*-notation is statistical significance at the 10% (*) and 5% (**) levels. As seen in table I, on the average, pitchers change their pitch selection based upon air density on a given day. The results show that on days with higher air density, pitchers throw fewer breaking pitches. On days with lower air density, pitchers throw more breaking pitches. If high air density truly does creates the hanging-curve effect, it logically follows that pitchers would throw fewer breaking pitches in this environment and more breaking pitches when the air density is low. Given the results above, it is useful to know what components of air density pitchers (and/or catchers/coaches) respond to on a given day when they choose their pitch selection. Table II shows the result of the regression model with the change in breaking pitches thrown by the starter as the dependent variable and the

3 individual components of air density variables as independent variables (opposing team dummies are included in the regression full regression results are shown in Appendix III). Table II: Regression of Individual Components of Air Density on the Change in Breaking Pitches Variable Coefficient Variable Coefficient Intercept ( ) Barometric Pressure (0.7427) Temperature *** (3.8906) Altitude (1.1726) Humidity * (1.9285) Note -*-notation is statistical significance at the 10% (*) and 1%(***) levels. From these results, pitchers seem mainly to be influenced by temperature (statistically significant at the 1% level) and by humidity (statistically significant at the 10% level). With high temperatures and high humidity, pitchers throw more breaking pitches. Given that temperature and humidity have a negative relationship with air density, this corresponds to pitchers throwing more breaking pitchers on low air density days. Overall, the results show that air density (with temperature and humidity as the driving forces) impacts pitch selection in Major League Baseball. 3 Air Density and Betting Market Returns To determine how pitchers fared in different atmospheric conditions, we broke the 2012 MLB sample into distinct groups of pitchers and air density days with the goal of testing some basic betting market strategies. First, we calculated the mean and standard deviation of the percentage of breaking pitches thrown by each starter. We then used this information to create groups of the pitchers who threw the highest (lowest) percentage of breaking pitches (2 standard deviations above (below) the mean), higher (lower) percentage of breaking pitches (1 standard deviation above (below) the mean), and high (low) percentage of breaking pitches (1/2 standard deviation above (below) the mean). For each of these groups of pitchers, we took their starts and divided them into three equal groups of atmospheric condition days: high air density days, medium air density days, and low air density days. For each grouping, we calculated the betting market return of placing a $1 wager on that starting pitcher in those atmospheric conditions. Returns to each betting market strategy are expected to be negative due to the commission charged on wagers by sports books. In academic studies, the Major League Baseball betting market has generally been shown to be efficient, with some exceptions in the tails of the distribution (i.e. Woodland and Woodland [2], Gandar, et al. [3], and Paul, et al. [4]). The general results of overall market efficiency help us test the impact of atmospheric conditions on pitcher performance because the betting market odds will already incorporate the relative strengths and weaknesses of both starting pitchers (in addition to differences in overall team quality) and where the game is played (home-field advantage). If we assume that the impact of air density is not included in the betting market odds, differences in pitcher performance between high and low air density days may reveal a simple betting rule which could yield positive returns. Alternatively, if air density is already included in the market odds, then simple strategies based upon air density should earn the expected negative return. Returns for each category of pitcher in the high and low air density sub-samples are shown in Table III. Table III: Betting Market Returns for High and Low Breaking Ball in Different Air Densities Betting Market Air Density Betting Market Air Density Grouping Grouping Bet: Highest (#Games) Bet: Higher (# Games) Air Density Grouping (# Games) Betting Market Bet: High Highest Air Highest Air Highest Air Density (32) Density (275) Density (513) Lowest Air Lowest Air Lowest Air Density (32) Density (275) Density (513) All (95) All (826) All (1538) Air Density Grouping (# Games) Betting Market Bet: Lowest Games Betting Market Bet: Lower Air Density Grouping (# Games) Betting Market Bet: Low

4 Highest Air Highest Air Highest Air Density (28) Density (289) Density (580) Lowest Air Lowest Air Lowest Air Density (28) Density (289) Density (580) All (84) All (868) All (1741) When observing the starts of pitchers who throw many breaking pitches, simple betting strategies of wagering on these pitchers on days of relatively low air density greatly outperformed wagering on these pitchers when air density was at its highest. In each grouping in this category of pitchers, bets on starting pitchers who throw the highest percentage of breaking pitches on low air density days earned positive returns, while betting on them in the opposite case (high air density days) earned significantly negative returns. For pitchers on the other end of the distribution who throw very few breaking pitches, the opposite (and consistent) result holds true. Starting pitchers who throw very few breaking pitches earn positive returns (or lose less depending upon group) on high rather than low air density days. It does not appear the betting market fully encompasses the impact of air density on pitcher performance. Bets on pitchers who rely the most on their breaking pitches earn positive returns on days with low air density and take substantial losses on days where the air density is high. In contrast, pitchers who infrequently throw breaking pitches earn more (or lose less) on days with high air density compared to low air density. The betting market results are consistent with the regression results of the previous section, which showed that higher air density days lead to pitchers throwing fewer breaking pitches. High air density days led to betting market losses (poor performance) for pitchers who frequently use breaking pitches. By substituting away from the breaking ball, they may improve their performance. 4 Conclusions In conclusion, air density influences pitch selection. Starting pitchers choose to throw fewer (more) breaking pitches when air density is high (low). Betting market returns illustrate that high-frequency breaking ball pitchers earn positive returns in low air density, while low-frequency breaking ball pitchers earn more (lose less) in the gambling market in high air density. Air density appears to play a role in how pitchers approach hitters and in terms of performance compared to expectations (betting market odds). We believe this serves as a starting point for further investigation into atmospheric effects on pitch selection, performance analytics, and betting market strategies. 5 Acknowledgements: Data for this study was gathered by members of the Baseball Statistics Club of Syracuse University. Students involved in data collection (besides those credited as authors) were: Andrew Sagarin, Justin Mattingly, Marcus Shelmidine, James DiDonato, Colby Conetta, Curt Baylor, Greg Terruso, Jeremy Losak, Zack Potter, Matt Russo, Matt Romansky, Sam Friedman, and Justin Moritz. We would also like to thank Chris Weinbach for helpful discussions and comments. 6 References: [1] T. A. Bahill, D. G. Baldwin, and J. S. Ramberg, Effects of Altitude and Atmospheric Conditions on the Flight of a Baseball. International Journal of Sports Science and Engineering, vol. 3, no.2, pp , [2] L. M. Woodland and B. M. Woodland, Market Efficiency and the Favorite-Longshot Bias: The Baseball Betting Market. The Journal of Finance, vol. 49, no. 1, pp , [3] J. M. Gandar, R. A. Zuber, R. S. Johnson, and W. Dare, Re-Examining the Betting Market on Major League Baseball Games: Is there a Reverse Favorite-Longshot Bias? Applied Economics, 34(10): , [4] R. J. Paul, B. R. Humphreys, and A. P. Weinbach, The Lure of the Pitcher: How the Baseball Betting Market is influenced by Elite Starting. Oxford University Handbook of the Economics of Gambling. Oxford University Press, USA, L. V. Williams and D. S. Siegel, editors, 2013.

5 Appendix I: Equation for Air Density in kg/m 3 (Bahill, et al., [1]) Air Density = { (Altitude-2600) (Temperature-85) (Humidity- 50) (Barometric Pressure-29.92)}. Note this equation is taken directly from pp in Bahill, et al., [1]. Appendix II: diffbreak Linear (diffbreak) Scatterplot of Change in Breaking Pitches (Zoomed for Emphasis): Vertical Axis Change in Breaking Pitch Percentage / Horizontal Axis Air Density (Low to High) Appendix III: Full Regression Result Individual Components of Air Density Dependent Variable Change in Breaking Pitches thrown by Starter Intercept ( ) Cleveland ( ) Philadelphia ( ) Temperature *** (3.8906) Colorado ( ) Pittsburgh ( ) Humidity * (1.9285) Detroit (0.1876) San Diego (1.2632) Barometric Houston Seattle

6 Pressure (0.7427) ( ) (0.9523) Altitude (1.1726) Kansas City ( ) San Francisco ( ) Arizona ( ) LA Dodgers ( ) St. Louis (0.4478) Atlanta (0.0118) Miami ** ( ) Tampa * (1.7573) Baltimore (0.1370) Milwaukee (0.7005) Texas (0.6168) Boston ( ) Minnesota ( ) Toronto (1.5519) Chi. Cubs ** (1.9784) NY Mets ( ) Washington (0.4055) Chi. White Sox (1.3161) NY Yankees ( ) Cincinnati ** (1.9834) Oakland ** ( )

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