The Effects of Atmospheric Conditions on Pitchers
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, 13224-2238
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 www.weatherunderground.com for each major league city. Pitch type was gathered from
www.fangraphs.com through their Pitchf/x section. Game odds for all Major League Baseball games were gathered
from the online betting site BETUS.
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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) = 5.9163 – 5.1735 (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
Variable
Coefficient
Variable
Coefficient
Variable
Coefficient
(t-stat)
(t-stat)
(t-stat)
Intercept
6.1730**
Detroit
0.1792
Pittsburgh
-0.0752
(2.2734)
(0.2149)
(-0.0901)
Air Density
-5.5177**
Houston
-0.1307
San Diego
1.0758
(-2.3988)
(-0.1568)
(1.2901)
Arizona
-0.3672
Kansas City
0.1078
Seattle
0.7536
(-0.4387)
(0.1293)
(0.9030)
Atlanta
0.2259
LA Dodgers
-0.6961
San Francisco
-0.1637
(0.2701)
(-0.8346)
(-0.1963)
Baltimore
0.2182
Miami
-1.4631*
St. Louis
0.4913
(0.2616)
(-1.7541)
(0.5881)
Boston
-0.1971
Milwaukee
0.6495
Tampa
1.4439*
(-0.2363)
(0.7783)
(1.7311)
Chi. Cubs
1.5972*
Minnesota
-0.7347
Texas
0.7062
(1.9150)
(-0.8809)
(0.3977)
Chi. White Sox
1.0959
NY Mets
-0.6905
Toronto
1.3387
(1.3139)
(-0.8281)
(1.6052)
Cincinnati
1.7397**
NY Yankees
-0.0214
Washington
0.4756
(2.0850)
(-0.0257)
(0.5702)
Cleveland
-0.7456
Oakland
-1.5573*
(-0.8941)
(-1.8667)
Colorado
-0.2991
Philadelphia
-0.8269
(-0.3471)
(-0.9915)
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
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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
(t-stat)
(t-stat)
Intercept
-7.8506
Barometric Pressure
0.1228
(-1.5407)
(0.7427)
Temperature
0.0399***
Altitude
0.0002
(3.8906)
(1.1726)
Humidity
0.0165*
(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 Pitchers in Different Air Densities
Air Density
Betting Market
Air Density
Betting Market
Air Density
Betting Market
Grouping
Return per $1
Grouping
Return per $1
Grouping
Return per $1
(# Games)
Bet: Highest
(#Games)
Bet: Higher
(# Games)
Bet: High
Breaking Ball %
Breaking Ball %
Breaking Ball %
Pitchers
Pitchers
Pitchers
Highest Air
-0.1691
Highest Air
-0.1328
Highest Air
-0.0906
Density (32)
Density (275)
Density (513)
Lowest Air
0.0709
Lowest Air
0.0184
Lowest Air
0.0069
Density (32)
Density (275)
Density (513)
All (95)
0.0003
All (826)
-0.0448
All (1538)
-0.0504
Air Density
Betting Market
Games
Betting Market
Air Density
Betting Market
Grouping (#
Return per $1
Return per $1
Grouping (#
Return per $1
Games)
Bet: Lowest
Bet: Lower
Games)
Bet: Low
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Breaking Ball %
Pitchers
Highest Air
Density (28)
Lowest Air
Density (28)
All (84)
0.1861
0.0804
0.1078
Breaking Ball %
Pitchers
Highest Air
Density (289)
Lowest Air
Density (289)
All (868)
-0.0417
-0.1422
-0.0749
Breaking Ball %
Pitchers
Highest Air
Density (580)
Lowest Air
Density (580)
All (1741)
-0.0419
-0.0832
-0.0499
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. 109-128, 2009.
[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. 269-279, 1994.
[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): 1309-1317, 2002.
[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 Pitchers.” Oxford University Handbook of the Economics of Gambling. Oxford
University Press, USA, L. V. Williams and D. S. Siegel, editors, 2013.
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Appendix I:
Equation for Air Density in kg/m3 (Bahill, et al., [1])
Air Density = 1.045 + 0.01045{-0.0034(Altitude-2600)-0.2422(Temperature-85)-0.0480(Humidity50)+3.4223(Barometric Pressure-29.92)}.
Note – this equation is taken directly from pp. 119-120 in Bahill, et al., [1].
Appendix II:
2
1.5
1
0.5
diffbreak
0
0
1000
2000
3000
4000
5000
Linear (diffbreak)
-0.5
-1
-1.5
-2
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:
Variable
Intercept
Temperature
Humidity
Barometric
Full Regression Result – Individual Components of Air Density
Dependent Variable – Change in Breaking Pitches thrown by Starter
Coefficient
(t-stat)
-7.8506
(-1.5407)
0.0399***
(3.8906)
0.0165*
(1.9285)
0.1228
Variable
Cleveland
Colorado
Detroit
Houston
Coefficient
(t-stat)
-0.7710
(-0.9237)
-0.1810
(-0.2020)
0.1564
(0.1876)
-0.2162
Variable
Philadelphia
Pittsburgh
San Diego
Seattle
Coefficient
(t-stat)
-0.9686
(-1.1606)
-0.1874
(-0.2242)
1.0545
(1.2632)
0.7947
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Pressure
Altitude
Arizona
Atlanta
Baltimore
Boston
Chi. Cubs
Chi. White Sox
Cincinnati
(0.7427)
0.0002
(1.1726)
-0.2554
(-0.3034)
0.0099
(0.0118)
0.1143
(0.1370)
-0.2470
(-0.2958)
1.6503**
(1.9784)
1.0970
(1.3161)
1.6568**
(1.9834)
Kansas City
LA Dodgers
Miami
Milwaukee
Minnesota
NY Mets
NY Yankees
Oakland
(-0.2691)
-0.0709
(-0.0848)
-0.7239
(-0.8670)
-1.6619**
(-1.9852)
0.5849
(0.7005)
-0.8136
(-0.9743)
-0.7683
(-0.9208)
-0.0907
(-0.1088)
-1.5342**
(-1.8358)
San Francisco
St. Louis
Tampa
Texas
Toronto
Washington
(0.9523)
-0.0632
(-0.0756)
0.3741
(0.4478)
1.4658*
(1.7573)
0.5159
(0.6168)
1.2961
(1.5519)
0.3384
(0.4055)
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