The financial consequences of unbalanced betting on NFL games.

Humphreys, Brad R.

Introduction

A growing body of research finds that sports book makers actively participate in betting by taking large positions on the outcomes of sports events. This evidence challenges the validity of the "balanced book" model frequently referred to in the sports betting literature. (1) Levitt (2004) documented the outcome of a season-long prediction contest for National Football League (NFL) games. While this contest did not resemble sports betting markets in many respects, it generated detailed data on bettor behavior and revealed that the volume of bets was not balanced on a majority of the games picked by contestants. Paul and Weinbach (2007) analyzed betting volume data from an on-line sports book, sportsbook.com, and found evidence of unbalanced volume on bets placed on NFL games in the 2006 season. Paul and Weinbach (2008) found evidence of unbalanced betting volumes on National Basketball Association (NBA) games in the 2004-2006 seasons. Humphreys (2010) showed that betting on NBA games was unbalanced and developed theoretical and empirical evidence that the presence of informed and uninformed bettors in the market explained this unbalanced betting volume. Taken together, the evidence in these papers suggests that the "balanced book" model may not describe actual outcomes in sports betting markets, and that a relationship exists between unbalanced bet volume and point spread shading in sports betting markets.

The "balanced book" model predicts that book makers set the point spread to balance betting volume on either side of a game in order to make a certain profit from the commission charged in losing bets in point spread betting markets (Paul & Weinbach, 2008). This model motivates much of the literature testing for point spread betting market efficiency using data on point spreads and game outcomes (Sauer, 1998).

In this paper, I investigate the financial implications of unbalanced betting volume on the returns to sports books. I use a novel data set that includes information on betting volume on all NFL regular season games played in the 2005-2008 seasons. These data contain evidence of significant imbalances in bet volumes in 9 out of 10 NFL games, as well as evidence that sports books systematically set point spreads to reduce the probability that a bet on the favored team wins when the volume of bets on the favored team increases.

To date, most of the empirical research on betting imbalance has focused on documenting the extent of betting imbalances and exploring the relationship between observed imbalances in betting and profitable betting opportunities. Little research has focused on the financial implications of these betting imbalances for sports books. Since bet volumes, point spreads, and game outcomes can be observed in some data sets, this information can be combined to simulate the profits and losses earned by sports book makers on individual games and to assess the total gains and losses accumulating over the course of a season. The results of the financial simulations performed here indicate that the unbalanced betting action accepted by sports books was profitable over the course of four seasons, and in three of the four seasons generated returns in excess of those that would have been generated by a balanced book. The results presented here further call into question the ability of the "balanced book" model to describe basic outcomes in sports betting markets, and suggest that sports books increase their profits by operating an unbalanced book, consistent with the standard risk-return relationship in finance.

Empirical Analysis

The general approach uses data on the volume of bets on each side of NFL games to determine gains and losses for book makers on individual games over four football seasons. Since the data used here have not been analyzed extensively before, I first perform the standard tests of weak form market efficiency to demonstrate that the point spreads set by the sports books are efficient in that they predict the actual difference in points scored in NFL games. After establishing weak form efficiency in this setting, I simulate the profits and losses incurred by sports books based on the actual volume of bets on either side games for all regular season NFL games that had a line over the 2005 through 2008 seasons.

Data Description

Outside of market efficiency tests, little evidence exists that the balanced book model describes actual outcomes in sports betting markets. The primary reason for this lack of evidence has been a general lack of data on the volume of bets made on either side in individual games. While point spreads and game outcomes are readily observable, until now, researchers have not had access to data on betting volume. Because of this lack of data, researchers have proceeded under the assumption that point spreads are set by sports so that an equal amount of money is bet on either side of all games, and tested the efficiency of this market, or tests for inefficiencies in the form of profitable betting strategies.

Recently, data on betting volumes have become available to researchers, primarily from on-line sports books. Sports Insights, an online sports betting information service, recently began making betting data, including information on betting volume, available. The data analyzed here were purchased from Sports Insights. Sports Insights has agreements to obtain betting volume data from four large on-line sports books: BetUS, Carib Sports, Sportbet, and Sportsbook.com. There are a large number of online sports books operating in the point spread betting market, as well as a large number of sports books operated by casinos in Nevada. The on-line point spread betting market is highly competitive, as is the point spread betting market in Nevada. The data files that Sports Insights makes available include the opening and closing point spreads, the actual score of the game, and the percentage of bets reported on each side of a proposition for all regular season games played in the National Football League (NFL) in the 2005-2008 seasons. The data collected by Sports Insights represents an average across the four participating sports books. The betting volume is not available for all sports books and is not available for each game played over the course of the season. In addition, the total dollars bet on each game is not known. Table 1 shows summary statistics for key variables in this data set.

The NFL regular season runs from September until early January each year. A number of pre-season games are played in August and early September, but these games do not count toward the league championship. I exclude both pre-season and post-season games and analyze only regular season games NFL games. Most NFL regular season games are played on Sunday afternoon and evening. In addition to Sunday games, one (and occasionally two) games are played on Monday night, and some other games are played on Thursdays and Saturdays later in the season. Each team plays 16 regular season games spread over 17 weeks. A small number of teams with the best records during the regular season advance to the postseason knock-out tournament that culminates in the Super Bowl. Betting on NFL games takes place on a rigorous schedule. Sports books issue an opening point spread on each game early in the week for the entire slate of games scheduled to take place over the next week. The opening line is made public on Sunday evening or Monday morning. Throughout the week, information about the status of injured players and expected weather conditions at each venue are made public, and the sports books observe the order flow in the market. Point spreads are changed on some games, either in response to new information about players or weather conditions, or in response to observed betting volumes on the games. The final point spread is the point spread that is posted immediately prior to the start of each game, when betting ends. In NFL point spread betting, each bet is evaluated at the point spread that was in place at the time the bet was made.

The first row on Table 1 is the average actual score difference, expressed as home team score minus visiting team score, for all NFL games in the data set in each season. The second two rows are the average opening and closing point spread set by the four on-line sports books on each game in each of the three seasons. Note that the actual score difference exhibits considerably more variation than either of the point spreads. Sauer (1998) reported a similar pattern in data on betting on National Basketball Association (NBA) games in the 1980s, and many others have reported that actual outcomes are much more variable than point spreads. On average, the point spread changed by roughly one point from the opening line to the closing line an all three seasons. However, in a significant number of games, 28% of them, the point spread did not change over the course of the week. The next two rows show the win percentage of bets placed on the home team and the favored team in each game. The overall average winning percentage for bets on the home team (0.48) and bets on the favored team (0.49) are less than 0.50, suggesting that sports books may shade the point spread against these bets. However, these winning percentages show considerable variation across seasons, indicating the presence of an important random component in these outcomes.

The last row contains some interesting information about betting volumes. The data set contains information on the volume of bets placed on either side of the propositions for each game. This fraction will not be equal to the fraction of money bet on each side when the average value of the bets on the two sides are different. However, anecdotal evidence suggests that the proportion of bets on each side is equal to the volume of money bet on each side. Clearly, the volume of bets on either side are not balanced very often in these data. The average fraction of bets are not equal to 50% in any season, and the standard deviations are relatively large, indicating substantial variation in the volume of bets. Bettors like to bet on favorites in the NFL. In each season, more than 60% of the bets placed were on the favored team. Again, the fact that a majority of the bets were placed on the favorite, and the win percentage of bets on the favorite was less than 50% suggests shading of the point spread by bookmakers, potentially to take advantage of uninformed bettors.

Distribution of Betting Volume

The disparity in the volume of bets placed on either side of games revealed on Table 1 does not fit with the typical "balanced book" model described in the literature. The volume of bets made is skewed toward favorites, the team that is expected to win the game, in all four NFL seasons. A closer look at the data on the fraction of bets made on either side of propositions shows a large number of games with unbalanced betting. The large standard deviations on the bet volume data shown on Table 1 suggest that the betting volume on individual games might be quite different from a balanced book.

Table 2 takes a closer look at the distribution of betting volume data across individual games. From the standard break even condition, easily derived from the "risk 11 to win 10" betting rule in point spread betting markets, if the fraction of bets on the favored team falls between 47.6% and 52.4%, then the sports book makes a profit on the betting no matter which team wins the game. If the fraction of bets on the favored team falls outside this range, the then the sports book takes a position on the game, and can either earn larger profits or larger losses, depending on the outcome of the game. From Table 2, the distribution of the bets placed on the favored team is quite skewed. Sports books consistently take positions on games, and these positions are mostly on the underdog. The fifth row on Table 2 shows the percent of games in which the observed fraction of bets on the favorite fell inside the certain profit range in the 2005-2007 NFL seasons. In more than 90% of the games in these three NFL seasons, the observed fraction of bets on the favorite fell outside the certain profit range. In other words, the four on-line sports books represented in this data set took a position, on average, on 9 out of 10 NFL games that they took bets on. Either these books were exceptionally bad at setting point spreads to equalize betting on either side of the game, or achieving a balanced book was not the goal of sports books taking bets on NFL games.

[FIGURE 1 OMITTED]

Figure 1 shows the distribution of the fraction of bets on the favored team in each game in each season. The red vertical lines on Figure 1 show the boundaries of the certain profit region. Figure 1 shows a large amount of variation in the fraction of bets on the favorite. Again, Figure 1 indicates that sports books took large positions on games, and that a majority of bettors prefer to bet on the favored team. This tendency for sports bettors to over bet favored teams has been documented by Woodland and Woodland (1994) in Major League Baseball, by Paul and Weinbach (2005) in the National Basketball Association, and by Levitt (2004) in the NFL. Note that this tendency to over bet favored teams occurs in (weak-form) efficient markets.

The distribution of the bets on the favored team in point spread betting on the NFL falls well outside the certain profit range for almost all games, indicating that sports books take positions on games frequently. Most previous research has assumed that sports books attempt to set point spreads to balance the volume of bets on either side of the game. If this were the case, we would expect to see many more instances of the betting volume falling in the certain profit range. Previous research also indicates that point spreads are unbiased and minimum variance estimators of actual game outcomes. One reason for the unbalanced book outcomes observed above could be that point spreads were not efficient during these three seasons for some reason.

Market Efficiency Tests

One important characteristic used to evaluate sports betting markets is the efficiency of the market. Efficiency in sports betting markets is typically defined as the absence of profit making opportunities; that is, in efficient sports betting markets bettors are unable to make positive profits in the long run. Given the unbalanced betting volume described above, testing for efficiency in this setting seems to be warranted, in order to exclude the possibility that the unbalanced bet volumes reflect the presence of inefficiencies in this market. Sauer (1998) showed that efficiency in sports betting markets implies that, given symmetry of the distribution of point score differences, the point spread set by sports books on a game is an unbiased, minimum variance estimator of the difference in points scored in the game. In practical terms, tests of efficiency in sports betting markets are based on a regression model

[DP.sub.i] = [alpha] + [beta][PS.sub.i] + [e.sub.i] (1)

where [DP.sub.i] is the difference in points scored by the two teams involved in game i, [PS.sub.i] is the point spread set by sports books on game i, and [e.sub.i] is an unobservable random variable assumed to be distributed with mean zero and constant variance that captures all other factors that affect the difference in points scored. In this regression model, tests of efficiency are based on the joint hypothesis test based on the null

[H.sub.o]: [alpha] = 0 and [beta] = 1.

By convention, the points scored variable is expressed as visitor's points scored minus home team's points scored, and the point spread is expressed as negative numbers when the home team is favored and positive numbers when the home team is the underdog. The distribution of the points scored variable is relatively symmetric, the mean is -2.42 and the median is 3, so regression based efficiency tests appear to be appropriate in this case. The opening and closing lines are observed in this data set, and bets can be placed at either, so efficiency tests can be performed for both the opening line and the closing line.

Table 3 shows the results of estimating Equation (1) using data from the 2005, 2006, 2007, and 2008 seasons separately. The key statistics on this table are the F-statistics on the test of the joint hypothesis that the intercept is equal to zero and the slope parameter is equal to one. This is the conventional test of betting market efficiency; if the null is not rejected, then the point spread is an unbiased minimum variance estimate of the difference in points scored. Not rejecting the null implies the absence of profit opportunities for bettors in this market. This null hypothesis is not rejected at conventional significance levels for all seasons for both the opening point spread and the closing point spread on Table 3. Only tests based on the closing line in the 2006 season show weak evidence that point spreads may not be a good predictor of game outcomes. Pooling data across seasons also did not lead to a rejection of the null hypothesis. Both the opening line and closing line are good predictors of the actual point score in NFL games in these four seasons, despite the imbalanced bet volumes. This result is consistent with other tests of efficiency in NFL point spread betting markets found in the literature (Dare & Holland, 2004; Stern, 2008).

Financial Simulations

Based on the bet volume data described above, sports books take positions on many games, rather than setting point spreads to balance the volume of bets on either side of games. One way to investigate the implications of this behavior is to analyze the actual returns earned by sports books, given the observed point spreads, game outcomes, and distribution of bets on either side in this market. This data set contains enough information to conduct financial simulations of the profitability of sports books. Note that I lack access to the data required to calculate the exact profits earned by sports books for three reasons. First, I do not have data from specific sports books. The betting volume data are averages across four different on-line sports books. If there is a significant amount of heterogeneity in point spreads, bets taken, and the volume of bets on each side of a game across these sports books, then the average data will not reflect this heterogeneity. Second, I do not have access to data on the timing of individual bets. All I observe is the opening line and the closing line on each game, the difference in points scored in each game, and the final volume of bets on each side. Because the point spread changes over the course of the week, by an average of about 1 point, in about 75% of the games, I do not know the exact amount of money wagered on each side at each point spread that was available during the week that bets could be placed on games. This is important because point spread bets pay off based on the point spread that was posted at the time the bet was made, not based on the last point spread posted. Third, I do not know how much money was wagered on each game; I only have access to information on the fraction of bets placed on either team in each game. Because of these limitations, I use simulations to estimate the gains, losses, and profits earned by sports books on point spread bets in NFL games taken over these four seasons.

The simulations are straightforward. For each game, I compare the opening and final point spread to the actual game outcome to determine which side of the bet won, and which side lost. The winning bets enter the simulations as losses, since bookmakers must pay the bettors who made these bets. The losing bets enter the simulations as gains, plus the 10% commission charged by sports books to bettors on losing bets. That means for each $100 wagered on a losing bet, the sports book collects $110 from the bettor. In addition, I assume the average size of bets on the favorite is equal to the average size of bets on the underdog. Under this assumption, the fraction of bets made on each side is equal to the fraction of dollars bet on each side. Using the fraction of bets placed on each side on each game, I calculate the gains and losses on each game, and sum these losses and gains over the entire season. Strumpf (2003) carried out similar simulations using data from several illegal bookmakers in the New York City area in the 1990s.

Again, the simulations assume an equal volume of betting took place on each game in the season. For simplicity, I assume that 100 total "units" were bet on each game. While this assumption probably does not match reality--the total amount bet on games may vary depending on the teams involved--it is a convenient baseline for comparing the simulation results. This assumption must be made because I observe only the fraction of bets placed on each side of a game, and not the total number of bets placed on the game.

Table 4 shows selected summary statistics for the financial simulations. The top panel assumes that all bets are made at the opening point spread; the bottom panel assumes that all bets are made at the final point spread. The actual distribution of the timing of bets lies somewhere between these two points, unless the line does not change over the course of the week. So these two assumptions represent the upper and lower bounds of the actual financial outcomes for each game. The row labeled "Loss" shows the average amount lost by the sports books when the book took a position on a game and was on the losing side of the bet. For example, in the 2005 season, when sports books took a position on a game and the largest volume of bets was on the side that won, sports books lost on average 50.1 units based on 100 units bet on the game, with a standard deviation of losses of 17.7. In the 2005 season, when sports books took a position on a game and the largest volume of bets was on the side that lost the game, the sports book won on average 54.8 units based on 100 units bet on the game, with a standard deviation of gains of 19.4.

Several interesting features emerge from the financial simulations. First, despite the lack of a balanced book for nearly all the games, the sports books make a positive return on average over the course of each season, no matter which point spread is used. Because of the assumption that 100 units are bet on each game, averages reported on the "Return" row can be interpreted as the percent return on all bets taken by the sports books. So, for example, in the 2005 season the average return on all bets taken, assuming that they were made at the opening point spread, was 4.7, or a 4.7% return on 100 units of betting action.

Second, note that the variability of losses is smaller than the variability of gains in the simulations, and that the variability of profits is largest of all. Operating a sports book is a risky business, because profits are highly variable. The minimum and maximum values on Table 4 underscore just how risky operating a sports book can be. Assuming that all bets are made at the latest point spread, the largest loss in each of the four seasons was between 64% and 73% of the average bet on each game.

How do these returns compare to what would have been earned if the book was balanced on all games? In point spread betting, each bettor must risk $11 to win $10. Consider the simple case where only two bettors wager on a game, and each bettor wagers $110 to win $100 on each team. The sports book collects $220 from the two bettors and the betting is balanced. The losing bettor loses $110, and the winning bettor gets her $110 wager back, plus $100. The sports book keeps $10. The book's return is 10/220=4.55%.

From Table 4, the simulated rate of return exceeds 4.55% in three of the four seasons examined, and it exceeds this value in all four seasons when the simulations are based on the opening point spread. By setting point spreads in a way to produce an unbalanced book on 9 of 10 games played, the sports books earned a return higher than the certain return in the 2006, 2007, and 2008 seasons, and a lower return in the 2005 season for the simulation based on the closing point spread. In the 2005 season, the return at the opening point spread, 4.7%, exceeds the certain rate of return from operating a balanced book.

Note that returns are always lower for the simulations at the final point spread than at the opening point spread. Again, the data contains no information on the timing of bets, and can only conclude that the actual return to sports books lies between these two estimates. A number of papers have analyzed changes in point spreads in sports betting markets, including Gandar, Zuber, O'Brien, and Russo (1988), and Avery and Chevalier (1999). The focus of this line of research has been to explain why point spreads change over the course of the week in the NFL, and the extent to which informed traders or bettor sentiment, as captured by observable variables associated with past team performance, explains observed changes in point spreads. This analysis cannot address the question of why point spreads change, but the simulation results indicate that changes in point spreads affect the returns earned by sports books. Future research should address the factors that explain observed changes in point spreads.

Also note that the average return was lowest in the 2005 season. Recall, from Table 4, on average, more than 60% of the bet volume was on favored teams, and that 55% of the bets on favored teams paid off in the 2005 season. In the other three seasons bets on favored teams paid off much less frequently. The lower simulated returns earned by sports books in the 2005 season are consistent with this observed higher winning percentage on the bet favored by sports bettors.

I do not have access to enough data to estimate the variance of returns, so it is unclear how likely a sports book is to earn a return in excess of the certain return of 4.55% by taking positions on games in the long run. I can conclude from the simulations that it is possible, and likely, for sports books to earn returns larger than the certain return generated by a balanced book by operating an unbalanced book. Levitt (2004) raised the possibility that unbalanced bet volumes arise because of the presence of uninformed bettors in the betting market, and that sports books systematically "shade" point spreads to take advantage of these uninformed bettors. The simulation results indicate that sports books earn larger returns by operating an unbalanced book.

Discussion and Conclusions

The results above indicate that sports books regularly take large positions on NFL games, and they earn a larger, although more variable, profit from taking positions than they would have if they operated a balanced book. These results stand in contrast to the "balanced book" model that predicts an equal amount of betting on each side of a game, a risk minimizing strategy. The emerging evidence from research on betting volumes indicates that sports books are willing to take positions on games, even when the point spreads set on these games are unbiased minimum variance predictors of the game outcomes in many different settings. The results here extend this research by showing that unbalanced betting on games generates profits for the sports books, and that these profits can exceed what would have been earned if the betting volume was perfectly balanced on all games. Since the "balanced book" model of sports book behavior cannot explain observed outcomes in sports betting markets, researchers should focus on developing models that can explain actual outcomes in these markets. Clearly, an improved model should take into account the presence of informed and uninformed bettors in the market and strategic interaction between sports books and informed bettors.

While the results above are interesting, they lack a complete explanation. The finding that changes in point spreads affect profits is intriguing, and deserves additional attention. Several possible mechanisms could explain this result. Both line shading, where the sports book strategically moves the point spread to take advantage of known bettor preferences (for example, the tendency of bettors to bet on favored teams at any odds, or the tendency for bettors to bet on the home team), and incomplete information could explain the increase in profits associated with changes in the point spread found here. While I show that unbalanced betting volume and point spread changes are profitable for sports books, I have not fully explained why they are profitable.

Several clear extensions to this research exist. First, the financial simulations need to be expanded to include unequal betting volume on games. Paul and Weinbach (2010) develop evidence that betting volume differs across games in the NHL and NBA. The simplest extension would assume that the volume bet on games is proportional to the size of the markets that teams play in, or proportional to past success by the teams involved. It is possible that variation in betting volume could change the returns to the sports book significantly, given the large variability of returns in the equal volume simulations performed here. A second extension is to perform a similar analysis in different settings. New data are becoming available on betting volume in other point spread betting markets like college football, and professional and college basketball. These sports have the advantage of many more games in each season than the NFL. However, betting on these sports probably exhibits much more variation in total dollars bet on games, which will place a premium on correcting for variation in the amount bet on each game when assessing the total returns to the sports book.

References

Avery, C., & Chevalier, J. (1999). Identifying investor sentiment from price paths: The case of football betting. Journal of Business, 72(4), 493-521.

Dare, W. H., & Holland, A. S. (2004). Efficiency in the NFL betting market: Modifying and consolidating research methods. Applied Economics, 36(1), 9-15.

Levitt, S. D. (2004). Why are gambling markets organized so differently from financial markets? The Economic Journal, 114, 223-246.

Gandar, J., Zuber, R., O'Brien, T., & Russo, B. (1988). Testing rationality in the point spread betting market. Journal of Finance, 43(4), 995-1008.

Humphreys, B. R. (2010). Point spread shading and behavioral biases in NBA betting markets. Rivista di Diritto ed Economia dello Sport, 6(1), 13-26.

Paul, R. J., & Weinbach, A. P. (2005). Bettor misperceptions in the NBA. Journal of Sports Economics, 6(4), 390-400.

Paul, R. J., & Weinbach, A. P. (2007). Does Sportsbook.com set pointspreads to maximize profits? Tests of the Levitt model of sportsbook behavior. Journal of Prediction Markets, 1(3), 209-218.

Paul, R. J., & Weinbach, A. P. (2008). Price setting in the NBA gambling market: Tests of the Levitt model of sportsbook behavior. International Journal of Sport Finance, 3(3), 2-18.

Paul, R. J., & Weinbach, A. P. (2010). The determinants of betting volume for sports in North America: Evidence of sports betting as consumption in the NBA and NHL. International Journal of Sport Finance, 5(2), 128-140.

Sauer, R. D. (1998). The economics of wagering markets. Journal of Economic Literature, 36(4), 2021-2064.

Stern, H. S. (2008). Point spread and odds betting: Baseball, basketball, and American football. In D. B. Hausch & W. T. Ziemba (Eds.), Handbook of sports and lottery markets (pp. 223-237). Burlington, MA: North-Holland.

Strumpf, K. (2003). Illegal sports bookmakers. (Working paper). Chapel Hill, NC: University of North Carolina, Department of Economics.

Woodland, B. M., & Woodland, L. M. (1991). The effects of risk aversion on wagering: Point spread versus odds. Journal of Political Economy, 99(3), 638-653.

Woodland, B. M., & Woodland, L. M. (1994). Market efficiency and the favorite-longshot bias: The baseball betting market. Journal of Finance, 49(1), 269-279.

Endnote

(1) Woodland and Woodland (1991, p. 638) claim that a book maker "... establishes an odds or spread line to balance the wagers so that his commission is independent of the final outcome of the contest"

Author's Note

The Alberta Gaming Research Institute provided for financial support for this research. Thanks to seminar participants at the University of Kentucky, Andy Weinbach, and Dennis Coates for useful comments.

Brad R. Humphreys

University of Alberta

Brad R. Humphreys is a professor in the Department of Economics and chair in the Economics of Gaming. His current research focuses on the economic impact of professional sports and the economics of sports gambling.

Table 1: Summary Statistics, NFL Betting 2005-2008

 2005 2006

Variable Mean SD Mean SD

Score Difference 3.78 14 0.85 14.4
Opening Point Spread 2.51 5.6 2.77 5.6
Closing Point Spread 2.7 6.1 2.8 5.9
Home team bet win % 0.49 0.47
Favored team bet win % 0.55 0.42
Fraction of bets on favorite 61.6 13.2 60.33 14.4
Games 256 256

 2007 2008

Variable Mean SD Mean SD

Score Difference 2.86 15.4 2.56 15.3
Opening Point Spread 2.46 6.8 2.7 6.1
Closing Point Spread 2.42 6.7 2.67 6.13
Home team bet win % 0.5 0.44
Favored team bet win % 0.51 0.49
Fraction of bets on favorite 62.34 12.3 61.5 12.8
Games 256 256

Table 2: Distribution of Bet Volume and Dollars Bet

Variable 2005 2006 2007 2008

Average % of bets on favorite 61.6 60.3 62.3 61.5
Median % of bets on favorite 63 62.5 64 63.5
Skewness -0.36 -0.52 -0.54 -0.51
Kurtosis 2.31 2.48 3.24 2.82
% of games where 47.6 [less 7.8 10.5 6.6 7.8
 than or equal to] % of bets
 on favorite [less than or
 equal to] 52.4
% of games where % of bets 59 60 64.1 62.9
 on favorite > 60.0
% of games where % of bets on 21.4 19.4 14.1 13.3
 favorite > 75.0

Table 3: Market Efficiency Tests

Variable 2005 2006 2007 2008

Intercept 0.636 -1.58 0.186 -0.155
P-Value 0.472 0.096 0.837 0.871
Opening Point 1.254 0.879 1.09 1.003
 Spread
P-Value 0.001 0.001 0.001 0.001
[R.sup.2] 0.231 0.116 0.228 0.162
Observations 256 256 256 256
F-stat, 2.81 2.78 0.37 0.01
 [alpha]=0,
 [beta]=1
P-value 0.062 0.058 0.689 0.986

Intercept 0.531 -1.5 0.137 -0.219
P-Value 0.545 0.112 0.878 0.818
Latest Point 1.202 0.838 1.126 1.039
 Spread
P-Value 0.001 0.001 0.001 0.001
[R.sup.2] 0.243 0.118 0.242 0.173
Observations 256 256 256 256
F-stat, 2.06 3.28 0.65 0.05
 [alpha]=0,
 [beta]=1
P-value 0.129 0.039 0.524 0.954

Table 4: Financial Simulations 2005-2008
Seasons

 2005 Season 2006 Season

 Mean SD Mean SD

 100 units bet, all bets
 at opening spread

Loss -50.1 17.7 -48.4 17.6
Gain 54.8 19.4 56.6 19.4
Return 4.7 37.2 8.4 37

 100 units bet, all bets
 at closing spread

Loss -50.6 17.7 -48.7 17.6
Gain 54.3 19.4 56.4 19.4
Return 3.7 37.2 7.7 37.1

 2007 Season 2008 Season

 Mean SD Mean SD

 100 units bet, all bets
 at opening spread

Loss -50.3 17.5 -49.4 17.1
Gain 54.6 19.3 55.6 18.8
Return 4.2 36.8 6.2 36

 100 units bet, all bets
 at closing spread

Loss -50 17.5 -49.7 17.1
Gain 55 19.3 55.3 18.8
Return 5 36.8 5.5 36