A Test for Inherent Characteristic Bias in Betting Markets ABSTRACT. Keywords: Betting, Market, NFL, Efficiency, Bias, Home, Underdog

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1 A Test for Inherent Characteristic Bias in Betting Markets ABSTRACT We develop a model to estimate biases for inherent characteristics in betting markets. We use the model to estimate biases in the NFL betting market. We find biases for several team characteristics, including home, favored, and underdog teams as well as for the combined effects of favorites and underdogs playing at home. We show that the well documented NFL home underdog bias is specifically a bias favoring home underdogs and not a bias against the away favorites. An understanding of these biases may help in understanding financial market biases, such as the value versus growth anomaly. Keywords: Betting, Market, NFL, Efficiency, Bias, Home, Underdog JEL Classification Codes: G10, G14, G19, Z00

2 A Test for Inherent Characteristic Bias in Betting Markets I. Introduction Financial markets have been shown to exhibit bias. Fama and French (199x) report two significant biases in equity prices the superior returns of value versus growth stocks and the superior returns of small versus large stocks. 1 Betting markets have been shown to exhibit similar biases. The most prevalent investigation into bias in betting markets is in horseracing. It is the general case that favorites tend to have higher proportional payouts than longshots, when in an efficient market they should be equal. This favorite-long shot bias has been shown by many studies to exist in many different countries. Alternatively, the evidence in which markets suggests a reverse favoritelongshot (cheesecake) bias A key issue in the debate concerning growth versus value stocks and large versus small stocks is that our measure of risk may be inadequate. That is, value stocks and small companies may have more risk than we can measure with current methods. The reverse could be true; the measured risk of growth stocks and large stocks is smaller than their actual risk. As we don t know the actual risk-return relation, the debate may continue for a considerable length of time. Betting markets allow us to circumvent the risk measurement issue because the actual risk of betting is known once the bet outcomes are determined at the end of the event. That there is a favorite-longshot bias in horseracing indicates that rather than risk, behavioral tendencies may be the cause of the larger risk-adjusted returns for small, value stocks. We propose a method of investigation that will allow us to go deeper into the 1 Value and growth are defined in Fama and French (199x) as low market-to-book value and high book-to-market value, respectively.

3 analysis of bettor bias. We do so in the hope that this aids in our understanding of investors behavioral tendencies. We begin by recognizing there is there is a significant difference between horseracing pari-mutual pools and sports betting markets. Pari-mutual pools are zero sum. If one entry is underbet (overbet), the other entries must be overbet (underbet). There is an off-setting negative effect among over/underbetting on the horses. For sports betting markets, this negative relationship need not hold. Bookmakers set betting lines and maintain the betting pool with the amounts wagered on either side of the proposition known only to them. It is generally assumed in the literature that bookmakers set betting lines to equate the total monies bet on both sides of a proposition. If bettors bet more on one side of the proposition, bookmakers would move the line to balance the betting. Therefore, we should not see biased betting lines. Most of the literature has found little consistent evidence of biased betting lines, except for bets on NFL home-underdogs. Bets on NFL home-underdogs consistently win more than fifty percent of the time (Dare and Holland (2004)). However, the book balancing assumption concerning bookmakers may be severely erroneous. Using actual wagers on NFL games, Levitt (2004) finds that bettors bet favorites by a substantial margin (upwards of 68 percent on a sub-sample of bets). Further, he finds that bets on favorites win less than fifty percent of the time (roughly 48%). This suggests that bookmakers frequently have unbalanced books and that they potentially bias lines intentionally. Levitt concludes that bookmakers are better than bettors at predicting game outcomes and use their advantage to increase profits by biasing

4 lines. Americans love an underdog, but in the NFL betting market, Americans bet favorites, and bookmakers know it. As pointed out by Golec and Tamarkin (1991), there are several inherent team characteristics in NFL betting. A game can involve a favorite playing the underdog, the home team playing the away team and combinations of those characteristics, such as home underdogs that play away favorites. The flip side of such a combination would be home favorites playing away underdogs. It is these individual characteristics that we want to investigate for bettor bias. With unbalanced betting occurring, bettors can overvalue (undervalue) the potential scores of favorites, underdogs, home or away teams resulting in a bias specific only to that characteristic. For example, both the favorite and the underdog can be over or underbet. If both are overbet (underbet), the negative relation between the characteristics forces the measured biases to zero for bets on the differences in points scored between the two teams (sides bets). That is, the forecast bias for favored teams can only be measured as the difference of two potential biases, that for favored teams and that for underdog teams. Bettors may prefer to bet favorites, upwardly biasing their scoring expectations for favorites, but with no bias for scores of underdog teams. This relation is also possible for home teams versus away teams. As a result of this differenced estimate of bias, the current methodology in this area cannot determine specific bettor biases. To return to our financial market example, both growth and value stocks could be misvalued by the market, or just one group could be misvalued. The model we propose allows us to investigate each characteristic individually.

5 Our results indicate that there are biases for favorites, underdogs, home teams, and teams with the combined characteristics; home-favorites, home-underdogs, and away-underdogs. Additionally, we are able to conclude that the well known NFL bias against home-underdogs is strictly related to undervaluation of home-underdog teams, with no bias indicated against the opposing away-favorite teams. Our method can be used to examine for characteristic biases in other sports markets. There need be only a sides line (point spread) and a totals lines (over/under). Specifically baseball, basketball, hockey, and soccer are all candidates for examination using this method. We have confined our analysis here to the NFL, where the homeunderdog bias is known to exist. II. The NFL Betting Market Literature Pankoff (1968) is the first article to examine market efficiency for betting in NFL games. The study found that the market was weak-form efficient in that using past performances did not produce profitable betting strategies. There was some weak evidence that using experts picks produced profitable strategies. Vergin and Scriabin (1978) found profits could be made in the period by betting on underdogs when the spread was greater than five points. They also reported evidence that profits could be made by focusing on teams that beat the spread by a great margin. 2 However, Tryfos, Casey, Cook, Leger and Pylypiak (TCCLP) (1984) could not 2 Lacey (1990) also finds evidence that a profitable betting strategy is to bet on teams that win by a large margin the previous week.

6 replicate the results in the NFL seasons. Badarinathi and Kochman (1996) could not find profitable trading strategies in the NFL seasons. 3 TCCLP (1984) were the first to show that the test for point spread betting efficiency must incorporate the eleven-for-ten betting rule. Woodland and Woodland (1997) modified the TCCLP (1984) test to exclude bets that end in ties. This method, a simple t-test against a null win percentage of percent, is the current standard of evaluation, and it has been used in some form by various authors. Zuber, Gandar, and Bowers (1985) examined weak-form efficiency by using the first half of the season to predict game outcomes in the second half of the season. They found that weak-form efficiency was violated and that profitable trading strategies existed. However, a follow-up article by Sauer, Brajer, Ferris, and Marr (1988) showed that similar strategies were not profitable in the following year. Gandar, Zuber, O'Brien, and Russo (GZOR) (1988) tested the Vergin and Scriabin and TCCLP betting strategies and found that they are not profitable for the seasons. However, they found a profitable strategy in betting the opposite of the public in the week following when the public does well. They also examined the movement of betting lines from open to close, suggesting that the line should move in the correct direction because the opening line is set solely by the bookmaker, but the closing line is set by all market participants. However, they found that the line moved toward the game outcome only 47% of the time. Golec and Tamarkin (1991) and Dare and MacDonald (1996) showed that the manner in which teams are differenced - home versus away or favorite versus underdog - 3 They find profitable trading strategies, but only where bets are placed in syndicates across the country. This requires placing bets in states where gambling is illegal.

7 leads to differing results concerning efficiency. Golec and Tamarkin (1991) differenced teams randomly and included dummy variables for home teams and favorites. They showed that in a model that randomly selects teams, home underdogs are the best bet. However, Dare and MacDonald (1996) critiqued Golec and Tamarkin (1991) and offered a more elaborate model specification that required no randomization of the data. The results of their study failed to reject weak-form efficiency. Gray and Gray (1997) found profitable trading strategies employing a probit model. Vergin and Sosik (1999) found that home teams (particularly home underdogs) are especially profitable on Monday Night Football games and in the playoffs. Paul and Weinbach (2002) found that a bet on the under was profitable when the closing totals line is above the mean by five, six or seven points. Dare and Holland (2004) later show that the Dare and MacDonald (1996) specification can result in biased coefficients estimates and, in so doing, develop another specification that alleviates the bias. The method involves estimation of only the sample of home favorite teams and then again on a sample of strictly favored teams playing away. They use their specification to show that the results found by Gray and Gray (1997) are actually driven by the home underdog bias. Most specific to our analysis, Golec and Tamarkin (GT, 1991) showed a bias favoring bets on home underdogs playing away favorites, but a bias for home favorites playing away underdogs. Later, Dare and McDonald improved on the GT analysis but did not find a bias. Dare and Holland (2004) again improved the method of analysis and confirmed that a home underdog bias existed during the GT sample period, which disappeared for a few years, only to resurface in recent seasons. Dare and Holland

8 showed that rather than the lagged game results Gray and Gray (1997) report as the source of inefficiency in the NFL, it was an improperly specified home underdog bias. These later works suggest that a home underdog bias exists and, if not correctly controlled, that it can bias research results and conclusions. Still, is the bias for the home underdog or is it for the away favorite? An answer to that question will aid us in our understanding of betting markets, and it might aid us in the investigation of behavioral finance issues. III. Methodology The data are 5,705 NFL games from the through seasons. The betting lines are the closing lines from the Stardust Race and Sports Book. Our method requires sides and totals data from the same game. A side bet is a bet that the difference between the teams scores will be more or less than a set number of points. A totals bet is a bet that the total scores will be over or under a set number of points. We assume that the bettors in the sides and totals markets are similar. To determine individual biases, we offer the following simple method: Solving for E ( S B ), we get: Solving for E ( S A ), we get: E( S A )= expected score of team A E( S B )= expected score of team B E S E E S + E Closing sides line (CSL) = ( A) ( S B ) Closing totals line (CTL) = ( ) ( ) A S B CTL CSL E( S B ) =. (1) 2 E ( S ) E( S ) CSL =. (2) A B +

9 To measure bias for teams A and B, the expected scores are subtracted from the actual scores S A and S B, respectively: Bias of Team A = E( ) S (3) A S A Bias of Team B = E( ) S (4) B S B Teams A and B could be Favorites (F) versus Underdogs (U), Home (H) teams versus Away teams (A), or the combined effects of Favorites playing at Home (FH) versus Underdogs playing Away (UA) or Favorites playing Away (FA) versus Underdogs playing at Home (UH). We can measure and test for the significance of a bias for each of the noted Team A or B characteristics. In the next section, we test for these biases using NFL betting market data. IV. Results The measured biases are contained in Table 1. It is quickly evident that there are several significant biases. The Underdog, Home, and combined Favorite-Home, and Home-Underdog biases are significant at the one percent level. The Favorite factor is significant at the five percent level. All of the biases are positive, which indicates that the market bias for each characteristic is an undervaluation of the actual scores. As both the favored and underdog biases are positive, undervaluation of both teams is likely the reason that we do not find an overall bias for favored teams using the traditional method of differencing the two characteristics. Subtraction of the positive underdog bias negates the positive favored team bias. In relation to the others, the bias for home teams is fairly large (0.563) and the bias for Away teams is relatively small (0.191). This suggests that there should be a

10 measured bias for the difference between home and away teams using the traditional differencing method of efficiency investigation. Adding the measured home and favored team biases gives a value of 0.86 ( ). However, the measured FH bias is 0.43, much less than the addition of the separate biases. Therefore, the home team bias must be strongest for home underdogs. Looking at the bias for home underdogs, we find the measured bias of 0.836, the largest of the measured biases. Home underdogs play away favorites, which have an insignificant measured bias of only This strongly indicates that the well known home underdog bias is precisely that: the scoring of home underdogs is significantly more than bettors expect. The home underdog bias is consistent with the behavioral idea of loss aversion. The home underdog team is expected to lose. Home town fans would be disappointed to have their team simultaneously lose the game and also lose their bet (they would lose twice). In sum, there are significant biases in the NFL betting market. Most of the biases are cancelled out because, when differenced, the bias of the opposing team s characteristics are of the same sign. This is not true for home underdogs. The number of significant biases found indicates that the addition of these effects in equation (2) likely leads to biased estimates of the total points scored. To examine this issue, we regressed the difference between the total points scored (TPS) and the Closing Totals Line (CTL) and regressed that on the Closing Totals Line (CTL). The results are as follows (t-values in parenthesis): TPS CTL = x CTL (5) (3.61) (-3.19) Both estimated coefficients are significant at the one percent level, suggesting a bias in the over/under closing line. The bias is positive at small closing line values, indicating

11 significant undervaluation of the expected total scores at low expected total scores. The undervaluation slowly diminishes and becomes overvaluation at high expected total scores. Bettors underestimate how low a low-scoring game will be and overestimate how high a high-scoring game will be. Both instances indicate over reaction or over confidence on the part of bettors. V. Conclusions We have developed a model that allows for the simultaneous estimation of biases in betting markets. The model employs both the sides line (point spread) and the totals line (over/under) to determine estimates of both teams scores. Previous research has focused only on either the point spread or the over/under, but not both simultaneously. Our model allows for tests of bias in inherent characteristics, such as being a home or an away team, a favorite or an underdog. We estimate the model in the NFL betting market, which is the largest in the US. The NFL betting market has been shown to exhibit a bias against home underdogs, and our methodology allows us to dig deeper into this issue, finding that the bias is on the home underdog and not the opponent - the away favorite. We show that there are several forecast biases in the NFL betting market. Specifically, there are forecast biases of the scores of favorites, underdogs, and home teams, but the home team bias is more likely due to a specific bias for home underdogs. We also report a bias for closing totals lines that is related to the size of the betting line. Low totals lines are too low and high totals lines are too high. The method can be employed in the investigation of any betting market that has both totals and sides

12 closing lines. We intend to pursue investigation of potential biases within these other markets. Our hope is that we gain an understanding of behavior finance issues which may lead us to a better understanding of known biases in financial markets, such as the growth versus value bias and the small versus large company bias.

13 References Avery, C., J. Chevalier, Identifying investor sentiment from price paths: The case of football betting. Journal of Business 72, Dare, W., Holland, S., Efficiency in the NFL Betting Market: Modifying and Consolidating Research Methods. Applied Economics 36, Dare, W., S. MacDonald, A generalized model for testing the home and favorite team advantage in point spread markets. Journal of Financial Economics 40, Gandar, J., R. Zuber, T. O Brien, B. Russo, Testing rationality in the pointspread betting market. Journal of Finance 43, Golec, J., M. Tamarkin, The degree of inefficiency in the football betting market. Journal of Financial Economics 30, Gray, P., S. Gray, Testing market efficiency: Evidence from the NFL sports betting market. Journal of Finance 12, Lacey, N., An estimation of market efficiency in the NFL pointspread betting market. Applied Economics 22, Pankoff, L., Market efficiency and football betting. Journal of Business 41, Paul, R., A. Weinbach, Market efficiency and a profitable betting rule: Evidence from totals on professional football. Journal of Sports Economics 3, Sauer, R., V. Brajer, S. Ferris, M. Marr, Hold your bets: Another look at the efficiency of the gambling market for National Football League games. Journal of Political Economy 96, Tryfos, P., S. Casey, S. Cook, G. Leger, B. Pylypiak, The profitability of wagering on NFL games. Management Science 30, Vergin, R., M. Scriabin, Winning strategies for wagering on National Football League games. Management Science 24, Vergin, R., J. Sosik, No place like home: An examination of the home field advantage in gambling strategies in NFL football. Journal of Economics and Business 51, Woodland, B., L. Woodland, Efficiency in gambling markets involving spread: A corrected and simplified test. Applied Economics Letters 4,

14 Woodland, B., L. Woodland, Testing contrarian strategies in the National Football League. Journal of Sports Economics 1, Zuber, R., J. Gandar, B. Bowers, Beating the spread: Testing the efficiency of the gambling market for National Football League games. Journal of Political Economy 93,

15 Table 1 The Estimated Mean Biases for the NFL through Seasons Characteristic N Mean Bias t-value F * U ** A H ** FH ** UA FA UH ** ** indicate significance at the 1% level, * indicates significance at the 5% level

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