Weather Biases in the NFL Totals Market* Richard Borghesi Texas State University McCoy College of Business Administration Department of Finance and Economics 601 University Drive San Marcos, TX 78666 (512) 245-1733
[email protected]
* I thank an anonymous referee for helpful comments and suggestions. Electronic copy available at: http://ssrn.com/abstract=2149710
Weather Biases in the NFL Totals Market Abstract I examine outcome predictability in the National Football League totals betting market using data from the 1984 through 2004 seasons. Results suggest that while weather is an important determinant of scoring, the market does not accurately incorporate the effects of adverse conditions into totals bet prices.
Specifically, I
demonstrate that heat, wind, and rain reduce point production, and provide evidence that bettors underestimate this effect. I also present a betting strategy that accounts for expected weather conditions and produces an out-of-sample win rate significantly above the 52.38% profitability threshold.
Electronic copy available at: http://ssrn.com/abstract=2149710
I. Introduction Betting markets are, in general, effective at gathering and incorporating complex and diverse information into bet prices.
However, researchers document several
anomalies that together suggest such markets are not perfectly efficient. For instance, in horserace markets, there is a bias against longshots late in the day because losses realized on earlier bets make late-day risk-seeking the norm (Asch and Quandt, 1987; Thaler and Ziemba, 1988).
Furthermore, Kuypers (2000) finds that English soccer lines are
inefficient, possibly because bookmakers seek to exploit bettor biases. As in equities markets, prices in sports betting markets are determined by buy and sell demand at each price level. So, findings such as these are potentially valuable in quantifying efficiency in more traditional financial markets.
This paper studies the
National Football League (NFL) totals betting market to determine if it is subject to a weather bias.
That is, the relationship between weather and bet outcome may be
systematically misvalued by gamblers. The most common sports bet is the sides wager in which gamblers bet on the difference (spread) between the number of points that two teams will score. In studying the NFL sides (point spread) market, researchers find a pronounced reverse favoritelongshot bias that makes betting on home underdogs attractive (e.g., Golec and Tamarkin, 1991; Gray and Gray, 1997; Dare and Holland, 2004), especially late each season (Borghesi, 2007). There is also evidence that bets on particular teams having specific characteristics may be misvalued by bettors. For instance, Lacey (1990) and Vergin (2001) find that gamblers overbet on teams that have recently exceeded performance expectations, while Boulier, Stekler, and Amundson (2006) find that differences in the
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playing surfaces of opponents are not fully reflected in closing lines. While each of these studies focuses on the sides betting market, the totals betting market also provides a good laboratory for testing efficiency. A totals wager is one in which a gambler bets that the combined scores of both teams in a contest will be over or under the total posted by a sports book. While the outcome of a sides bet is determined primarily by the strength of one team relative to another, the outcome of a totals bet depends primarily on how capable both offenses are against the opposing defenses. Anecdotal evidence suggests that weather conditions are important in determining game outcomes. 1 Further, it seems plausible that game day weather conditions affect absolute offensive effectiveness while relative team strength, on the other hand, is less likely to be systematically related to such conditions.
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therefore propose that weather may significantly affect the total amount of points scored in a football game, and that bettors may underestimate the impact of weather on game outcome. Totals markets have received somewhat less attention than sides markets, possibly because fewer dollars are wagered on totals than on sides. 2 Notable studies of totals markets include Brown and Abraham (2002), Gandar, Zuber, and Dare (2000), and Paul
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For instance, from 1976 to 2002 the Tampa Bay Buccaneers, a team located in a hot and humid region,
lost 21 straight games in which the kickoff temperature was below 40°F. From 1992 to 2002 the Green Bay Packers were quarterbacked by Brett Favre, who won 35 consecutive games when kickoff temperature was below 34°F. 2
Using data from Tradesports.com, an online exchange listing futures contracts on NFL and other sporting
events, I find that during the 2002, 2003, and 2004 NFL seasons, the ratio of dollars wagered on sides bets to that wagered on totals bets is 9.3 to 1.
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and Weinbach (2002). Brown and Abraham use Major League Baseball as a laboratory setting and find that, in general, this totals market is efficient. However, they also offer evidence that streaks exist in outcomes, and that uncertainty caused by expansion, realignment, and the introduction of interleague play resulted in outcome predictability. Gandar, Zuber, and Dare examine line changes in the National Basketball Association totals market and show that closing totals lines are more accurate forecasts of realized scoring than are opening totals lines. Their evidence suggests that at least some traders in the totals betting market have highly specialized information that, through trading, causes opening lines to move towards observed outcomes. Paul and Weinbach study the NFL totals market using data from the 1979 through 2000 seasons, and find that a strategy of taking the under in games characterized by high totals produces a win rate significantly greater than 50%. Thus, market efficiency is rejected. I propose that the market for NFL totals is inefficient largely because the effects of weather on game outcome are mispriced. This idea has roots in financial markets, where weather has been demonstrated to affect stock prices. For instance, Hirshleifer and Shumway (2003) propose that when the level of sunshine is higher than normal, investors are more likely to have a positive bias in estimating the future prospects of firms. In addition, Goetzmann and Zhu (2005) find that the behavior of market makers may be affected by weather conditions. In outdoors sports contests, however, weather has a much less subtle effect on outcomes, as game day conditions can directly affect play outcomes. Research conducted by the medical and military industries supports this idea. Studies find that exposure to extreme temperatures can have adverse physical, cognitive, and emotional effects. For
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example, gross and fine motor skills, muscle strength, information processing accuracy, reaction time, and awareness are significantly reduced when players are exposed to low temperatures (Phetteplace, 2000).
The most significant physiological responses to
exercise in extreme heat are increased heart rate and decreased endurance (Goldman, 2002; Parkin, Carey, Zhao, and Febbraio, 1999). The presence of significant levels of wind potentially increases the difficulty of passing and kicking, while precipitation and snow may decrease the quality of traction on the field and/or increase the turnover rate as the football becomes more difficult to grasp. In sports markets, bookmakers adjust lines in response to changes in betting preferences so that, at the close, there is a relative balance of dollars placed on each side of the line. 3 Line movements generally occur gradually, and participants usually have time to respond to observed movements by buying or selling additional bets. Occasionally, however, critical new information is revealed just prior to kickoff (e.g., updated injury status of a star player or elimination of a team from playoff contention). Totals lines are potentially more exposed to such information shocks than are sides lines because game day weather conditions, which are potentially important determinants of totals outcomes, are known with relative certainty only hours before kickoff. So, bookmakers may not have an opportunity to change totals lines quickly enough to prevent profit-taking. Thus, bettors can make informed trades just prior to 3
While this has been the traditionally accepted mechanism, Levitt (2004) suggests the possibility that
bookmakers have an incentive to leave the book unbalanced in order to maximize their profits. This and other similar findings do not detract from the main point that the line may move slowly enough that profits can be captured because weather conditions are rapidly revealed with increasing certainty as kickoff times approach.
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kickoff, when the likely effect of weather on game outcome can be much more accurately estimated than in days prior. 4 Alternatively, bettors may not realize the magnitude of the weather effects, and thus bookmakers need not alter the line in response to changing game day conditions. In this paper, I provide evidence that outcomes in totals markets are predictable and that a profit-taking opportunity exists. The proposed betting strategy produces an out-of-sample win rate greater than 52.38%, the hurdle required for demonstrating economic inefficiency. Section II of this paper describes the data, Section III provides the analysis, and Section IV contains conclusions and closing remarks. II. Data The sample set used in the analysis consists of 5,008 NFL regular- and postseason games from the 1984 through 2004 seasons, and includes yards rushing and passing, turnovers, team scoring, and closing totals lines. This data comes from Pro Football Edge, which records the lines posted at the Stardust Casino in Las Vegas. Game day weather conditions for each contest are obtained from the website of the National Climactic Data Center. These fields include temperature (in degrees Fahrenheit), wind speed (in tenths of a mile per hour), precipitation (in hundredths of an inch), snow (in tenths of inches), and humidity (in percent). 5 Each data field represents the average value of the weather variable over a 24-hour period (from midnight to midnight). III. Analysis 4
Sides and totals lines are typically posted five to six days in advance of each event.
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For games played in domed stadiums, I set temperature, wind, rain, snow, and humidity to 72°F, 0, 0, 0,
and 50% respectively. I also repeat each analysis dropping from the sample all games played in domed stadiums. Results remain intact.
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I begin the analysis by examining the overall win rate of totals bets, and find that the proportion of over bets that win is 48.92%. The associated p-Value of 0.0635, obtained using a binomial test, suggests that the win rate produced by a simple strategy of betting the under is greater than 50%. So, consistent with Paul and Weinbach, I find the presence of a statistical inefficiency in this market. I propose that this anomaly is at least partly caused by the effects of weather on game outcome. To quantify the role of weather, I begin by isolating the effect of each weather variable on the win rate of a strategy that always bets the over. In general, adverse conditions should decrease offensive performance, so I expect over bets to cover less frequently as weather conditions worsen. Tables 1A through 1E illustrate that win frequency varies significantly with several of these variables. In general, win rates decrease as the values for temperature, wind, and rain increase. To capitalize, one would bet the under when these factors are particularly pronounced. A strategy of taking the under only when game day conditions are in the hottest, windiest, or rainiest quartiles produces win rates of 56.13%, 53.32%, and 59.37% respectively, each of which are greater than 52.38% at the 1% level using a binomial test. 6 This implies that bettors underestimate the impact of each of these variables on scoring. ---Insert Table 1 Here--To examine the combined effect of all weather variables on game outcome, I next specify an OLS regression as follows: Vi = α0 + α1TEMPi + α2 WINDi + α3 RAIN i + α4SNOWi + α5HUMDi + ei,
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Panels C and D include only those games in which measurable amounts of rain or snow are present.
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(1)
where Vi is a performance variable in game i (the combined total rush yards, pass yards, turnovers, or scoring of the two teams), and the weather variables are as described in Section II. Regression results, shown in Table 2, indicate that weather is a significant determinant of game events. 7 Rushing performance is reduced when temperature is high while passing is reduced by strong wind and rain. In addition, the number of turnovers increases with rain. The net effect is that scoring is reduced significantly by temperature, wind, and rain. Furthermore, since teams that regularly play in regions prone to harsh weather conditions are likely to gear their roster towards players that are adept at playing in such conditions, the magnitude of these effects are likely be understated. ---Insert Table 2 Here--Using a probit specification, I next examine the relationship between each of the weather variables and the outcomes of totals bets. 8 The specification is similar to that in (1) except that the dependent variable becomes Wi, which is set to 1 when a bet on the over wins and to 0 otherwise. In addition, I include LINEi, the value of the closing total, as an independent variable to account for any biases associated with the magnitude of the line. Results, shown in Table 3, suggest that totals lines are biased, and that bets on the under are most likely to win when totals lines are highest. In addition, high values of heat, wind, and rain significantly reduce the frequency at which over bets win. ---Insert Table 3 Here---
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Test results indicate that multicollinearity is not a problem in this specification.
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Here a probit specification is preferable to an OLS specification because the number of points by which a
bet covers is relatively unimportant compared to whether it covers.
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To demonstrate the feasibility of a betting strategy based on game day weather conditions, I next test out-of-sample predictability. I use games from 1984 to 1999 to generate coefficient estimates, and apply these estimates to calculate Pri, the likelihood that betting the over will produce a win in game i, for each game in the 2000 through 2004 NFL seasons. I then test the win rate of wagers placed within varying confidence levels as in Gray and Gray. Whenever the probit model predicts that the likelihood of an over is less than the cutoff, I take the under and calculate the observed frequency at which the strategy wins. The procedure is then repeated taking the over in games in which the calculated Pri is greater than the cutoff. I examine only those strategies that produce at least 100 bet opportunities. Results are presented in Table 4. ---Insert Table 4 Here--A strategy of betting the under when Pr < 0.50 produces 764 bets, and the resulting win rate is 53.67%, which I find to be statistically greater than 50% using a binomial test. The win rate of this strategy improves as Pr decreases, and the top two strategies (bet the under when Pr < 0.46 and when Pr < 0.44) produce win rates statistically greater than 52.38%, suggesting that this market may be economically inefficient. I am cautious about this claim, however, because it is implausible to assume that bettors know in advance the precise weather conditions that will be present during the roughly three hour span from the start to end of each game. However, in generating estimates for the effect of each weather variable, the ex post regression uses a noisy estimate of prior game time conditions since the value of each variable is a calculated as a 24-hour average. For instance, if a game is played while skies are clear but after the
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game it begins to rain, the model erringly accounts for this game as rainy. So, while bettors may clearly observe that no rain will occur during the game, the model does not make this distinction. Thus, results from the model presented above likely understate the true magnitude of the weather bias.
Furthermore, the win rate of a weather-based
strategy may improve were one to bet based on conditions observed immediately prior to kickoff. While it is unreasonable to suggest that bettors could perfectly forecast game time weather conditions, a reasonable assumption is that they would be capable of assessing into which quartile each realized game day condition will fall, with the possible exception being SNOWi. I therefore repeat the analysis specifying TEMPi, WIND i, RAINi, and HUMDi as dummy variables, setting each to 1 when a corresponding condition falls into the highest quartile, and to 0 otherwise. Results, shown in Table 5, indicate that even after significantly relaxing the forecasting assumptions, the out-of-sample weather-based strategy remains profitable. ---Insert Table 5 Here--Evidence suggests that the market for NFL totals bets is both statistically and economically inefficient. A profitable opportunity exists because closing totals lines fail to fully reflect the effects of adverse weather on game outcomes. In addition, the closing line is upwardly biased even after correcting for weather. A plausible explanation offered by Paul and Weinbach for the latter bias is that bettors gain nonmonetary benefits by taking a position in which they can root for scores. If this were true, then bookmakers could profit by intentionally setting the line too high, thus taking a naked position on the under. Above I offer evidence that bookmakers’ profits may increase further when
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adverse weather conditions materialize because bettors fail to lower totals expectations sufficiently. IV. Conclusions I examine the relationship between game day weather conditions and the accuracy of NFL closing totals lines and find evidence suggesting that significant statistical and economic inefficiencies exist. Results show that when games are played in hot, windy, or rainy conditions, offensive performance worsens, and that this information is not fully incorporated into closing totals lines. I also demonstrate that there is an opportunity to capitalize on this mispricing by placing bets just prior to kickoff when weather conditions are known with relative certainty. The out-of-sample win rate of a betting strategy based on weather variables and closing totals lines exceeds the 52.38% breakeven threshold.
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References Asch, Peter and Richard Quandt, 1987. Efficiency and Profitability in Exotic Bets. Economica 54(251), 278-298. Borghesi, Richard, 2007. The Late-Season Bias: Explaining the NFL’s Home Underdog Effect. Applied Economics, forthcoming. Boulier, Bryan, H.O. Stekler, and Sarah Amundson, 2006. Testing the Efficiency of the National Football League Betting Market. Applied Economics 38(3), 279-284. Brown, Kenneth and Fred Abraham, 2002. Testing Market Efficiency in the Major League Baseball Overunder Betting Market. Journal of Sports Economics 3(4), 311-319. Dare, William and Steve Holland, 2004. Efficiency in the NFL Betting Market: Modifying and Consolidating Research Methods. Applied Economics 36(1), 9-15. Gandar, John, Richard Zuber, and William Dare, 2000. The Search for Informed Traders in the Totals Betting Market for National Basketball Association Games. Journal of Sports Economics 1(2), 177-186. Goetzmann, William and Ning Zhu, 2005. Where is the Weather Effect? European Financial Management 11(5), 559-578. Goldman, Ralph, 2002. Medical Aspects of Harsh Environments, Volume 1, Office of the Surgeon General. Golec, Joseph and Maurry Tamarkin, 1991. The Degree of Inefficiency in the Football Betting Market: Statistical Tests. Journal of Financial Economics 30(2), 311-323. Gray, Philip, and Stephen Gray, 1997. Testing Market Efficiency: Evidence from the NFL Sports Betting Market. Journal of Finance 52(4), 1725-1737. Hirshleifer, David and Tyler Shumway, 2003. Good Day Sunshine: Stock Returns and the Weather. Journal of Finance 58(3), 1009-1032. Kuypers, Tim, 2000. Information and Efficiency: An Empirical Study of a Fixed Odds Betting Market. Applied Economics 32(11), 1353-1363. Lacey, Nelson, 1990. An Estimation of Market Efficiency in the NFL Point Spread Betting Market. Applied Economics 22(1), 117-129. Levitt, Steven, 2004. Why Are Gambling Markets Organised So Differently from Financial Markets? The Economic Journal 114(April), 223-246.
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Parkin, J.M., M.F. Carey, S. Zhao, and M.A. Febbraio, 1999. Effect of Ambient Temperature on Human Skeletal Muscle Metabolism During Fatiguing Submaximal Exercise. Journal of Applied Physiology 86(3), 902-908. Paul, Rodney and Andrew Weinbach, 2002. Market Efficiency and a Profitable Betting Rule. Journal of Sports Economics 3(3), 256-263. Phetteplace, Gary, 2000. Integrating Cold Weather Impacts on Human Performance into Army M&S Applications. Proceedings of the 2000 Winter Simulation Conference, 10201024. Thaler, Richard and William Ziemba, 1988. Parimutuel Betting Markets: Racetracks and Lotteries. Journal of Economic Perspectives 2(2), 161-174. Vergin, Roger, 2001. Overreaction in the NFL Point Spread Market. Applied Financial Economics 11(5), 497-509.
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Table 1: The Effects of Weather on Totals Bets Panels A through E show summary statistics describing game day conditions and the associated proportion of over bets that win. The variables measured are temperature (in degrees Fahrenheit), wind speed (in tenths of a mile per hour), rain (in hundredths of an inch), snow (in tenths of inches), and humidity (in percent). The sample includes 5,008 regular season and playoff games from the 1984 through 2004 NFL seasons. The associated p-Values measure whether a strategy of betting the over in games within a particular quartile wins at a rate greater than 50%.
Panel A: Temperature Quartile High
Low All
N 506 2,040 1,267 1,195 5,008
Mean Temperature (°F) 78.76 69.51 54.47 35.15 58.47
N 1,234 1,296 1,229 1,249 5,008
Mean Wind (1/10th mph) 128.69 79.70 48.33 0.61 64.35
Over Win Rate 43.87% 48.87% 48.93% 51.13% 48.92%
p-Value 0.0029 0.1542 0.2241 0.7826 0.0635
Over Win Rate 46.68% 48.38% 51.18% 49.48% 48.92%
p-Value 0.0098 0.1217 0.7959 0.3565 0.0635
Over Win Rate 40.63% 48.57% 49.10% 47.46% 46.52%
p-Value 0.0013 0.3163 0.3819 0.2174 0.0121
Over Win Rate 43.33% 56.25% 53.66% 60.00% 52.85%
p-Value 0.2326 0.7602 0.6803 0.8145 0.7360
Over Win Rate 49.39% 48.75% 48.57% 49.06% 48.92%
p-Value 0.3457 0.0959 0.1187 0.8271 0.0635
Panel B: Wind Quartile High
Low All
Panel C: Rain Quartile High
Low All
N 256 280 277 236 1,049
Mean Rainfall (1/100th inch) 90.94 25.54 7.19 1.69 31.29
N 30 32 41 20 123
Mean Snow (1/10th inch) 41.20 10.41 3.41 1.00 14.06
N 1,073 1,399 1,256 1,280 5,008
Mean Humidity (%) 98.98 92.77 77.05 45.84 78.16
Panel D: Snow Quartile High
Low All
Panel E: Humidity Quartile High
Low All
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Table 2: The Effects of Weather on Offensive Performance This table shows the results of an OLS regression analysis in which the dependent variable is either rush yards, pass yards, turnovers, or scoring. The independent variables are temperature (in degrees Fahrenheit), wind speed (in tenths of a mile per hour), rain (in hundredths of an inch), snow (in tenths of inches), and humidity (in percent). The sample set includes 5,008 observations from the 1984 through 2004 NFL seasons.
Intercept TEMP WIND RAIN SNOW HUMID
Rush Yards Estimate p-Value 244.0361 0.0000 -0.2346 0.0001 0.0313 0.1621 0.0439 0.2265 0.0825 0.7147 -0.0596 0.2012
Pass Yards Estimate p-Value 404.8700 0.0000 0.0644 0.5756 -0.2989 0.0000 -0.2596 0.0002 0.0298 0.9456 0.3200 0.0004
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Turnovers Estimate p-Value 4.1396 0.0000 -0.0008 0.6817 -0.0004 0.5757 0.0035 0.0050 -0.0032 0.6837 -0.0016 0.3247
Scoring Estimate p-Value 43.6144 0.0000 -0.0252 0.0766 -0.0370 0.0000 -0.0190 0.0288 -0.0290 0.5916 0.0216 0.0524
Table 3: The Effect of Weather on Win Rates This table shows the results of a probit regression analysis in which the dependent variable, Wi , is set to 1 when a bet on the over wins and to 0 otherwise. The independent variables are temperature (in degrees Fahrenheit), wind speed (in tenths of a mile per hour), rain (in hundredths of an inch), snow (in tenths of inches), and humidity (in percent). The sample set includes 5,008 observations from the 1984 through 2004 NFL seasons.
Intercept LINE TEMP WIND RAIN SNOW HUMID
Estimate 0.6504 -0.0094 -0.0045 -0.0019 -0.0018 -0.0023 0.0013
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p-Value 0.0014 0.0260 0.0003 0.0000 0.0278 0.6356 0.1741
Table 4: Out-of-Sample Win Rates This table shows the success rate at various confidence level cutoffs of a betting strategy based on closing totals lines and weather variables. When the predicted likelihood (Pr) of the over winning is less than the cutoff point, the under is taken. When the predicted likelihood of the over winning is greater than the cutoff point, the over is taken. The estimates are produced by regressing 3,713 observations from the 1984 through 1999 NFL seasons. The out-of-sample success rates are produced by predicting the results of 1,295 games from the 2000 through 2004 NFL seasons. The associated p-Values, which measure whether the strategy produces a win rate greater than 50% and 52.38%, are calculated using a binomial test. Bet Strategy Under Under Under Under Over Over Over Over
Cutoff Pr < 0.44 Pr < 0.46 Pr < 0.48 Pr < 0.50 Pr > 0.50 Pr > 0.52 Pr > 0.54 Pr > 0.56
Bets 190 337 552 764 531 335 201 110
Win Rate 57.37% 56.08% 53.80% 53.67% 52.35% 53.13% 51.24% 55.46%
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p-Value (> 50%) 0.0211 0.0128 0.0369 0.0214 0.1390 0.1256 0.3622 0.1263
p-Value (> 52.38%) 0.0843 0.0867 0.2514 0.2385 0.5048 0.3911 0.6265 0.2594
Table 5: Quartile Dummy Out-of-Sample Win Rates This table shows the success rate at various confidence level cutoffs of a betting strategy based on closing totals lines and dummy weather variables. Each dummy (TEMPi , WINDi , RAINi , or HUMDi ) is set to 1 when game day conditions fall into the highest respective quartile, and to 0 otherwise. When the predicted likelihood (Pr) of the over winning is less than the cutoff point, the under is taken. When the predicted likelihood of the over winning is greater than the cutoff point, the over is taken. The estimates are produced by regressing 3,713 observations from the 1984 through 1999 NFL seasons. The out-of-sample success rates are produced by predicting the results of 1,295 games from the 2000 through 2004 NFL seasons. The associated p-Values, which measure whether the strategy produces a win rate greater than 50% and 52.38%, are calculated using a binomial test.
Bet Strategy Under Under Under Under Over Over Over
Cutoff Pr < 0.44 Pr < 0.46 Pr < 0.48 Pr < 0.50 Pr > 0.50 Pr > 0.52 Pr > 0.54
Bets 188 310 495 711 584 349 121
Win Rate 56.92% 57.10% 54.34% 51.34% 48.97% 51.29% 58.68%
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p-Value (> 50%) 0.0290 0.0062 0.0266 0.2381 0.6903 0.3150 0.0281
p-Value (> 52.38%) 0.1066 0.0482 0.1909 0.7113 0.9504 0.6583 0.0827
