The Evolution of Prices in the 21stCentury American superbowl wagering Market Abstract We report the intraday characteristics of wagering prices and

The Evolution of Prices in the 21stCentury American superbowl wagering Market Abstract We report the intraday characteristics of wagering prices and odds in the American superbowl wagering market. Using data from an online sports book we find systematic differences in the return distributions and the frequency of changes in prices and commissions over the day and over the week. Volatility is greatest in the minutes leading up to kickoff. Additionally, volatility is greater than normal when prices are initially quoted and in the middle of the day. Consistent with market efficiency, there is little or no evidence of autocorrelation in returns for either a portfolio of games or for individual games. -------------------------------------------------------------------------------- Page 3 1The Evolution of Prices in the 21stCentury American superbowl wagering Market One of the advantages of analyzing wagering markets, unlike equity markets, is that all securities, i.e., bets, reach a known terminal value in a relatively short period of time. Additionally, unlike para-mutuel wagering, once a bet is placed, the impact of subsequent wagering does not affect the odds on the placed bets. Empirical studies on American superbowl wagering markets have, by necessity, used prices observed at daily or weekly intervals.1In this paper we report the intraday characteristics of wagering prices in the American superbowl wagering markets using data observed at 15 minute intervals during the 2003 regular season. Related to our work, Avery and Chevalier (1999) examined the hypothesis that sentimental bettors can affect the average prices and the path of prices in superbowl wagering markets. Using daily NFL data from 1983-1994, they examined whether the changes in the lines from the open to the close reflects either sentiment or new information or both. They found that 79% of the point spreads change over the week and that point spreads move predictably, partiallyin response to variables known prior to the opening of wagering. However, the changes are small, so that a wagering strategy of wagering against the predicted movement in the point spread is only borderline profitable. Like Avery and Chevalier, we find that price changes are quite common. Our observations, made at fifteen minute intervals, enable us to analyze a finer pattern of price movement through the week preceding a game. 1See e.g., Avery and Chevalier (1999), Dare and MacDonald (1996), Even and Noble (1992), Gandar, Zuber,O’Brien, Russo (1988), Golec and Tamarkin (1991), Gray and Gray (1997), Lacey (1990), Pankoff (1968), Paul and Weinbach (2002), Sauer, Brajer, Ferris, Marr (1988), Stern (1991), Tryfos, Casey, Cook, Leger, and Pylypiak(1984), Vergin and Scriabin (1978), Winkler (1971), Woodland and Woodland (2000), Zuber, Gandar, Bowers(1985). -------------------------------------------------------------------------------- Page 4 2We find the following intraday patterns in American superbowl wagering market prices. First, there are systematic differences in the return distributions and the frequency of changes in prices and vigorish (commissions) over the day and over the week. Volatility is greatest in the minutes leading up to kickoff as the standard deviation of returns on odds bets is about ten times larger than normal. Volatility is also observed to be somewhat larger when prices are initially quoted and during the middle of the day. Second, we observe a negative correlation of the time series of transactions costs and the volatility of wagering prices. One explanation for this negative relationship is that there is an increase in liquidity concomitant with volatility. In addition to the analysis of the intraday changes in the point spread, we examine intraday changes in the money line, or odds. In a money line wager the bettor obtains a payoff in the event of an outright win by the chosen team. To encourage bets on the underdog, the sports book will offer increased odds. Because money line wagers on superbowl games have been unavailable until recently (see Bassett (1981) and Woodland and Woodland (1991)), the time series of these Arrow-Debreu securities has never been examined.2We add to the literature by testing for efficiency in the odds market for superbowl games. Consistent with market efficiency, we find little or no evidence of autocorrelation in returns for either a portfolio of games or for individual games. I. Description of the Data wagering data were gathered from the internet using a computer program that downloaded a webpage every 15 minutes. The internet sports book we used is maintained by Sports 2Campbell, Lo, and MacKinlay (1997, p. 507) note that “in practice, since true Arrow-Debreu securities are not yet traded on any organized exchange, Arrow-Debreu prices are not observable.” -------------------------------------------------------------------------------- Page 5 3(http://www.sports.com), which is located on Costa rica. Over the course of the season there were occasions when the website was down, presumably because of network or system maintenance. There were also times when our network was unavailable. Overall, we were able to obtain more than 90% of the observations during the 2003 regular season. There did not appear to be any systematic period when data-processing was problematic, although ’s planned site maintenance tended to be in the late evening or early morning hours. Size and Scope of Internet superbowl wagering Markets It is logical to question the value of using the online markets to characterize wagering markets, in general. However, we know of no other way to obtain intraday data. One obvious question that arises is: what is the size of the online markets relative to casino sports books?Strumpf (2002) reports, that in 2000, there were 204 online wagering sites with winnings of $1 billion, compared to 156 wagering locations in Nevada with winnings of $113 million. In a recent 60 Minutes piece, CBS (2001) reports that one online site, World Sports, has millions of dollars in revenues. World Sports is the largest of the nearly 1,000 internet gambling sites. Further, CBS indicates that online sports books presently collect more money from the Super Bowl than fromall of the sports bookies in Las Vegas combined. Thus, it appears that the online market dominates the casinos in the area of sports wagering. In fact, it is also fair to say that internet gambling is growing at a much faster rate. Sinclair (2001) reports that internet gambling -------------------------------------------------------------------------------- Page 6 4increased by 89% in 2000 and brought in an estimated $2.2 billion in worldwide revenues (Bedell 2001).3wagering on superbowl Games We collected the following information from the website: point spreads, money lines, and totals (over-unders), along with the vigorish pertaining to each price. A representative quote appears below. superbowl superbowl Mon 12/29 GameSpread Money Line Total PointsMon 12/29 417 Michigan State +3.5 -109 +144 OVER 48.5 -104 06:00 PM 418 Nebraska -3.5 -101 -159 UNDER 48.5 -112 The point spread, also referred to as the “line,” refers to the number of points that are added to a team’s score to determine the winner of the bet. Often point spreads are quoted using half points. In the example above Nebraska is favored to beat Michigan State by 3.5 points. A point spread bet on Nebraska would require Nebraska to win by more than 3.5 points for the bettor to win. A bet on Michigan State would require Michigan State to win outright, or for Michigan State to lose by less than 3.5 points. In the event that Nebraska beats Michigan State by exactly 3.5 points (an impossibility when the line includes a 1/2 point) the bet is a push and all money is returned. In our sample of NFL and superbowl games, the modal point spread is −3 points for home teams in the NFL, indicating that the home team was typically favored by 3 points. Other peaks in the distribution of point spreads are found at −7, −4 and +3 points. The distribution of the 3Spain (2004) reports that one of the world’s largest online-gambling enterprises expected to handle 150,000 calls with an average bet of $111 during the 2004 Super Bowl. Additionally, the Super Bowl alone is expected to generate $375 - $400 million in bets online, about three times the total race and sports wagering in Nevada in 2002. -------------------------------------------------------------------------------- Page 7 5superbowl point spreads indicate a bit more variation and a larger range of spreads, as more than 106 games had a spread less than −15 and 45 games had a spread greater than 15.4The difference in the distribution of closing lines from NFL and superbowl games implies the differences in skill levels between the two opponents is perceived to be, on average, greater for the marginal superbowl game than the marginal NFL game. In these markets, which are dealer markets, a bet is made between an individual and the house, i.e., dealer. In point spread markets the dealer is guaranteed revenue if an equal amount of money is bet on each team. In most Las Vegas casinos, the vigorish, or commission, is 10% for any losing bet. Continuing the example above, suppose Nebraska wins the game by fourteen points and there was $10 bet on each team. Each bettor would initially pay $11 ($10 bet, plus $1 commission), and the bettor choosing Nebraska would have $21 returned. The bettor choosing Michigan State would not win anything. Using this 11-for-10 rule, one must win 52.4% of their point spread bets to break even. Unlike casinos, the sports book typically charges a vigorish of 5%. Therefore the bettors using the sports book must win 51.2% of their point spread bets to break even. ’s margins are smaller probably because their overhead is lower than that of a casino, as the cost of casino construction and maintenance is significantly higher than developing a website to perform similar functions. While the superbowl wagering market has largely consisted of point spread wagering since the 1940s (see Woodland and Woodland (1991)), money line or odds wagering has recently becomeavailable as a wagering option. The money line quotation above has Michigan State +144 and Nebraska −159. The outright winner of the game determines the winner of the bet. If the favorite wins, in this case Nebraska, a bet of $159 would win $100. If the underdog wins, in this case 4Again, we consider the home team as the reference team. -------------------------------------------------------------------------------- Page 8 6Michigan State, a bet of $100 would win $144. To ensure positive revenues the dealer must receive more money bet on the favorite. More specifically, for this particular game, if the dealerdesired equal profit regardless of the outcome of the game, the amount wagered on the favorite would need to be about 50% more than that wagered on the underdog.5The last type of wager we consider is the over-under, or total. A bet on the total is a wager on the combined number of points scored in a game, see, e.g., Gandar, Zuber, and Dare (2000) or Paul and Weinbach (2002). The bettor can choose either over or under. If the total points scored is greater than the over-under, then the bettor choosing over would win. Data In most cases, a superbowl team will play one game per week. Most of the superbowl/NFL games are played on Saturdays/Sundays, although some games are played on other days. Las Vegas Sports Consultants provides the opening line for many casinos. Historically the Stardust sports book would produce the first line available, usually providing their lines on Sunday nights. With the success of internet sports books, many internet sites will be the first to post prices. In our dataset we find that the point spreads and over-unders are posted first. In general, point spreads and over-unders are available on the website Sunday evening for the following weekend’s games. The money lines tend to be posted a day or two after the point spreads. In most cases, the first money lines were posted on Tuesday for the next weekend’s games. 5The payoff to the dealer in the event the favorite won would be XDOG– XFAV(100/159) and the payoff to the dealerin the event the underdog won would be XFAV– XDOG(144/100), where XDOG& XFAVare the amount wagered on theunderdog and the favorite. Equating the payoffs results in XDOG/XFAV≅ 0.668 or XFAV/XDOG≅ 1.5. -------------------------------------------------------------------------------- Page 9 7As mentioned above, the use of online sports book data may be of questionable value, possibly because of the size and scope of the sports book used in this study. To further address these concerns we collected historical daily wagering data from the website (. The archives include data from casinos () as well as other online markets (e.g., ,). We computed the correlation of the data with that of the casino and other online market data. In all cases, we found that the correlations of point spreads, money lines, and totals to be greater than 0.98. These high correlations are assuring, and give us confidence in making inferences with regard to wagering markets in general. Another issue needs to be addressed regarding wagering on the website. That issue is market depth, a term familiar to market microstructure researchers. Depth in this market refers to the largest amount of money that can be wagered at a published price. Presumably, restricts the amount of any bet because they would like to reduce the adverse selection problemcaused by giving the market a free option to trade (Glosten and Milgrom 1985). ’s advertised depth for superbowl/NFL games is $20,000/$10,000 per bet for point spread wagering, $10,000/$5,000 per bet for money line wagering, and $5,000/$3,000 per bet for totals wagering. Consecutive bets may be placed, but the bets must be at least one minute apart. This delay allows to adjust prices in response to order flow. II. Summary StatisticsTable 1 reports the summary statistics for our dataset with the upper panel corresponding to all NFL observations and the lower panel corresponding to all superbowl observations. In all, we process over 130,000 NFL observations, with the average observation occurring 4,550 minutes -------------------------------------------------------------------------------- Page 10 8(75.8 hours or 3.2 days) prior to kickoff. The median line using the home team as reference is −3 points, indicating the market considers the home field advantage to be about 3 points. This line is consistent with the observed outcome, as the median difference in the home team’s score and the visiting team’s score is 3 points. The superbowl sample consists of 267,092 observations with a median line of −4 points. Interestingly, the median observed outcome is 5 points. To illustrate ’s quoting convention of the commissions, consider the MichiganState vs. Nebraska example above. In this game, a $101 point spread bet on Nebraska would win $100 if Nebraska scored 3.5 more points than Michigan State. A $109 point spread bet on Michigan State would win $100 if Michigan State beat the spread. If the quotation included a positive number instead of a negative one, the point spread payoff would be computed in a way that is similar to how payoffs are determined for money line wagers. That is, if the game were quoted Nebraska −3.5 +105, then a $100 point spread bet on Nebraska would pay $105 conditional on a Nebraska win against the spread. Table 1 reports the vigorish as follows: if the observed quotation is negative, the value is set to the observed value + 100. If the observed quotation is positive, the value is set to the observed value – 100. For both the NFL and superbowl samples, the mean and median vigorish are about –5, meaning that the typical bettor must wager $105 to win $100. For a bettor to profit they must win, on average, 51.2% of their wagers to overcome this 5% commission. Note that the typical bet in a casino has a 10% vigorish requiring the average bettor to win 52.4% of their bets to obtain a profit. As the standard deviation of the vigorish is 6.2, the NFL vigorish varies considerably. The standard deviation of the superbowl vigorish is a notably smaller 3.5. As we show below, point spreads change more frequently in the superbowl market than in the NFL market where the vigorish changes more frequently. -------------------------------------------------------------------------------- Page 11 9Home and visitor money lines on NFL games range from –1,300 to +1,015. These money lines can be used to compute the Arrow-Debreu price for a favorite (Money line < 0) as follows: 100Money linePriceMoney line=−(1) The Arrow-Debreu price for an underdog (Money line > 0) can be calculated as: 100100PriceMoney line=+(2) Therefore, the median price of the wager on the home team with a payoff of $1 is 62.1¢ (= −164 / −264), and the median price of the wager on the visiting team with a payoff of $1 is 40.2¢ (= 100 / 244). As we have seen above, superbowl point spreads are more dispersed than NFL point spreads. This variation also occurs in the money line market. The minimum superbowl moneyline is –9,000 corresponding to a price of 98.9¢ (= − 9000 / −9100). The maximum superbowl money line is +7,000 corresponding to a price of 1.4¢ (= 100 / 7100). We define the money line (no-arbitrage) spread as the sum of the Arrow-Debreu prices of the home and visiting teams minus $1. This spread represents ’s revenue, assuming an equal number of bets on each team. Under this assumption, Table 1 shows that derives revenue between 2% and 3% on these money line wagers.6Lastly, we observe that the average and median over-under, or total is about 41 points for NFL games and 52 points for superbowl games. The range on the NFL totals is 32.5 to 55.5 and the range on the superbowl totals is 37 to 85.5 points. The vigorish on totals is reported in a way similar 6The spread of −57.1¢ was found in one observation in which an obvious data error occurred. In this case the hometeam money line was +400 and the visiting team money line was +350. The home team money line should havebeen entered as −400. In further analysis this observation is excluded with no difference in results. -------------------------------------------------------------------------------- Page 12 10to that of point spreads. The vigorish on superbowl games is approximately 8%, as opposed to 5% for NFL games. III. Time Series Analysis We next examine the changes in the wagering variables over fifteen minute intervals. As noted in Gandar, et al. (1988) "reportedly, no more than five percent of all line movements are due to public information about injuries and weather. The rest are in response to order flow."7Therefore, we expect the intraday patterns in prices to vary most when bettors are placing wagers, not necessarily when information regarding the game is released. Changes in the Time Series Figure 1 charts the probability of a change over 15 minute intervals in event time for the time series variables corresponding to the home team in the superbowl market. To conserve space we do not display the visiting team series or the NFL series, which are very similar. We make the following observations. First, the number of changes in the first few minutes of wagering is greater than the average, this is especially so for the superbowl games. The probability of a change during the first few observations is on the order of 8% to 20%. Second, there is a dramatic increase in the probability of a change in the minutes leading up to kickoff. Third, the vigorish is far more likely to change than the point spread, as the vigorish in the point spread changes more than 80% of the time in the 15 minutes prior to kickoff.8The changes in the series were also 7CBS (2001) quotes an official from one internet sports book “the majority of our gamblers like to wait till rightbefore kickoff. They like to listen to, like, the pre-game show. And then the last half-hour before the game, we’ll get, you know, 100, 150 bets a minute.” 8Note this observation may be unique to as other sports books tend to charge a constant vigorish. -------------------------------------------------------------------------------- Page 13 11examined by time of day, as opposed to event time, and not surprisingly, there are more changes during the middle of the day. In Figure 2 we focus in on the twenty four hours prior to kickoff when most of the wagering activity allegedly occurs. The figure shows that the increase in the probability of changes in all of the series begins approximately 6 hours (24 15-minute-periods) prior to kickoff. Interestingly, point spreads in the superbowl market change nearly 40% of the time in the last 15 minutes prior to game time. Finally, Figure 1 and Figure 2 show that the money line odds are more likely to change than the point spread. In the superbowl/NFL market, the money line odds change almost 45%/70% of the time just prior to kickoff, but the point spread changes less than 40%/15% of the time. Money Line Returns Next, we compute the money line returns over adjacent observations. Returns are calculated as the natural log of the current Arrow-Debreu price divided by the previous Arrow-Debreu price. In Table 2 we provide the summary statistics for the money line returns based on event time. We categorize the data into four distinct time periods: (1) all observations with more than 1 day prior to kickoff, (2) data observed within 24 hours of kickoff, but not within the last hour prior to kickoff, (3) data observed within one hour of kickoff, but not within the last 15 minutes, and (4) observations in the 15 minutes prior to kickoff. For both the NFL and the superbowl markets, the average money line returns are essentially zero over the week preceding the game. Consistent with Figures 1 and 2, the magnitude of the standard deviation of the return increases as the time to kickoff decreases. The standard deviation of returns is almost 10 times larger in the 15 minutes prior to kickoff compared to the observations taken more than 24 hours -------------------------------------------------------------------------------- Page 14 12prior to kickoff. The standard deviation and the range of money line returns are greater for superbowl games than the NFL games. We also examine the average and standard deviation of the money line returns by time ofday. Unlike the series shown in Figure 2 of Wood, McInish, and Ord (1985), we find that the wagering return volatility is fairly uniform over the daytime hours. However, the volatility over the nighttime hours is close to zero. Autocorrelation of Money Line Returns Market efficiency, in combination with the assumption that equilibrium expected returns are constant through time, implies that the autocorrelations of the returns are zero for all lags (Fama 1976). In testing for autocorrelation we form an equal-weighted portfolio of returns in event time. Each series is limited to the 24 hours prior to kickoff as that period corresponds to time when prices move the most. Figure 3 displays the coefficient estimates along with the 95% confidence levels for the superbowl home team returns. In general, the plots indicate very little, ifany, autocorrelation in returns. Because there is very little systematic risk in the time series of money line returns, our construction of an equally-weighted portfolio could disguise any potential autocorrelation that may otherwise be evident in a test of game-by-game autocorrelation. Therefore, we estimate the autocorrelation function for each game. Table 3 reports the summary statistics for the coefficients at lags 1-4 along with the percent of coefficients that are significant at the 5% level. The evidence indicates a slight amount of autocorrelation for a minority of games. As a robustness check we included only those games in the highest quartile of volatility over the week and found similar results. These autocorrelation results are consistent with market efficiency. -------------------------------------------------------------------------------- Page 15 13Our results are similar to those reported in Wood, McInish, and Ord (1985) who find negligible autocorrelation for the trading day market return series which excludes overnight returns. Money Line No-arbitrage Spread In computing the money line no-arbitrage spread series we calculate, for each game, the Arrow-Debreu prices for the home team and the visiting team and then subtract $1. Next, we compute the equally weighted average of the spread over the last 200 observations (roughly 2 days). Figure 4 displays the time series of the money line spread. To avoid selection biases we require that for a game to be included in the series at least 80% of the observations need to be present. While the range of the equally weighted money line spread is fairly narrow (approximately 10 basis points), there appears to be a downward trend as the time to kickoff nears. This narrowing of spreads may result from the dealer attempting to attract order flow to balance the book. That is, a discount might be applied to the price of the team with fewer bets. Over the same event-time interval, the cross-sectional standard deviation of money line returns was calculated. The standard deviation of the home team volatility is plotted along with the spread series in Figure 4. As shown previously, the volatility increases as the time to kickoffdecreases. The correlation of money line returns with the spread is reported in Table 4. Consistent with the visual evidence in Figure 4, there is a negative correlation between the spread and volatility. This observation differs with what is found in equity markets because bid-ask spreads have been found to increase with volatility. One explanation for this counterintuitive result is that volatility is a proxy for liquidity. When liquidity increases, the sports book offers a narrower spread. -------------------------------------------------------------------------------- Page 16 14IV. Conclusion We detail the intraday characteristics of prices in the NFL and superbowl wagering markets using an online sports book. We find systematic differences in the return distributions and the frequency of changes in prices and commissions over the day and over the week. Volatility is greater when prices are initially quoted and during the middle of the day, but volatility is the greatest in the minutes leading up to kickoff. The time series results show that intraday returns in the wagering market varysystematically across the trading day and over the week prior to kickoff. Unlike the stock market, prices tend to move more during the middle of the day than at the beginning or end of the day. Not surprisingly, the volatility of prices is highest in the minutes leading up to kickoff. Tests for autocorrelation cannot reject market efficiency. Finally, there is a negative relation between money line spreads and volatility. However, the volatility might result in greater liquidity in the market during times when a significant amount of wagering is taking place.

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