Using Past Performance to Predict superbowl Outcomes
Using Past Performance to Predict superbowl Outcomes:A Chartist ApproachMarch 1997This Revision: April 1997
Abstract
A simple approach to predicting outcomes of National Football League games is demonstrated inapplications to the 1995-96 and 1996-97 seasons. The approach amounts to a chartist strategy: it involvesestimating team-specific probit models for predicting success or failure versus point spreads, using asexplanatory variables own and opponent performance versus the spread in the previous week. Variousstrategies which trigger bets as functions of predicted probabilities of success are found to be profitable.Intraweek movements in betting lines are also found to be useful explanatory variables. The findingsreflect negatively on the efficient markets hypothesis
Page 2 1Using Past Performance to Predict superbowl Outcomes:A Chartist ApproachDavid N. DeJongI. IntroductionIn setting point spreads on sporting events, gambling houses attempt to equate the flow of bets onboth sides of the spread. Because bettors must risk $11 to win $10 (i.e., they must pay a ten-percentvigorish on losing bets), this point-setting rule ensures a profitable outcome for the house regardless of theoutcome of the contest (with the exception of ties). Initial spreads issued by the house can thus beinterpreted as “forecasts of the forecasts of bettors”. Early movements in the spreads typically reflectinaccuracies in houses’forecasts; subsequent movements typically reflect the arrival of new information(e.g., injury updates); and differences between closing lines and final scores reflect forecast errors on thepart of bettors.The efficient markets hypothesis, applied to the gambling market for National Football Leaguegames, holds that point spreads are the best unbiased forecasts of actual outcomes. Under this hypothesis,it should not be possible to use past performance against the spread to predict future success or failure: tothe extent that it is relevant, information regarding past performance should be embodied in current pointspreads. The hypothesis does not seem to hold in this setting: using what amounts to a simple chartisttechnique, I demonstrate profitable strategies for predicting outcomes of superbowl games.The technique I employ involves estimating team-specific probit models for predicting success orfailure versus point spreads. The models use as explanatory variables own and opponent performanceversus the spread in the previous week, and movements in betting lines observed during the course of theweek. Various strategies which trigger bets as functions of predicted probabilities of success are found tobe profitable when applied to data from the 1995-96 and 1996-97 seasons. Due to the ten-percent vigorishcharged by the house on losing bets, a success rate of 52.38 percent is required to break even. Thestrategies I consider have success rates ranging from 58 to 63 percent; these rates significantly exceed thebreak-even rate, both in an economic and statistical sense.Several previous studies have examined the efficiency of superbowl point spreads issued by Las Vegas betting houses. This work generally reflects positively on the efficiency of these spreads. Pankoff (1968)regressed winning margins on point spreads and a constant and found no exploitable biases using data fromthe 1956 - 1965 seasons, and Stern (1991) showed that differences between winning margins and pointspreads measured from 1981 - 1986 are approximately normally distributed with zero mean and variance
Page 3 2of 14.1Vergin and Scriabin (1978) reported finding 23 strategies among 70 competitors that generatedwinning percentages significantly greater (statistically) than 50 percent over the 1969 - 1974 seasons.However, Tryfos et al. (1984) showed that only three of these strategies were profitable after takingvigorish into account: i.e., only three strategies had success rates significantly greater than the break-evenrate.2Finally, Zuber et al. (1985) reported a 59-percent success rate using a strategy based on predictionsgenerated by a regression equation which models point spreads as a function of “fundamentals” such asnumber of wins per team, yards rushed, etc. The model was estimated using data from the first eight weeksof the 1983 season, and was then used to predict point spreads over the remaining eight weeks of theregular season. Discrepancies between actual and predicted point spreads were used to trigger bets; usinga discrepancy of 0.5 points or more as a trigger, 60 of 102 bets turned out to be winners. But while theauthors noted that this success rate is significantly greater than 50 percent, it is not significantly differentfrom the 52.38 percent break-even rate (the p value associated with this test is 0.17 -- see Section IV fordetails on this test).In sum, the literature on superbowl point-spread behavior has generally supported the efficient marketshypothesis; here, the hypothesis is cast in a less favorable light.II. The dataThe data I consider are superbowl point spreads and winning margins for the 1995-96 and 1996-97seasons. Point spreads are Las Vegas betting lines as reported by the Associated Press; they were gleanedfrom the Pittsburgh Post-Gazette (P-G). Opening spreads are defined as the first available publication ofspreads for upcoming contests. Closing spreads are defined as those published on game day. Differencesin closing and opening spreads are defined as line movements.In the 1996-97 season, on which I concentrated initially, the P-G published opening lines onMonday.3A histogram of line movements observed over the course of this season is illustrated in Figure1a. Line movements were observed for 61 percent of all games played; 52 percent of these movementswere by a mere 0.5 points. Such movements, though subtle, seem important. For example, consider the1The means and standard deviations observed for the 1995-96 and 1996-97 seasons are (-0.9, 12.5) and (-0.43, 13).2The profitable strategies amount to the location of cross-country arbitrage opportunities; they involve findingdiscrepancies in point spreads offered by bookmakers around the country on underdogs of five points or more.Badarinathi and Kochman (1996) found only one of these strategies to be profitable over the 1984 - 1993 seasons:bet on an underdog of five points or more if a two-point discrepancy can be found in favor of the underdog. Theyreport a 56-percent success rate using this strategy.3Over the course of the season, 18 games were listed on Monday as NL (no line). This typically occurred forgames in which there was sufficient initial uncertainty about the status of one or more key players that bookmakers
Page 4 3spread on the Super Bowl, which opened at 13.5 in favor of Green Bay the day after the championshipgames, moved to 14 the following day, and did not move from that point forward. Bookmakers werewilling to risk the possibility of a tie versus the spread in making this adjustment, a risk they did not facegiven the opening spread. So the value of this minor adjustment must have outweighed the risk of a tie,which was in fact realized: Green Bay won by exactly 14 points, an outcome that, according the toAssociated Press, resulted in a decrease in winnings for Nevada bookmakers of approximately $5 millionfrom the previous year. (Source: P-G, February 1, 1997.)In the 1995-96 season, the P-G did not publish point spreads on Monday, so “opening” spreadswere not available from this source until Tuesday at the earliest.4This delay matters: the histogram of linemovements observed for the 1995-96 season illustrated in Figure 1b clearly contrasts with that illustratedin 1a. In the 1995-96 data, line movements were observed for only 51 percent of the total games played,and a χ2test of the null hypothesis that the two histograms were generated by the same underlyingdistribution rejects the null at the six-percent significance level. Initially, I found this difference in data setsdisappointing, because it prevents a clean comparison of the forecasting performance of my procedureacross data sets. However, this difference does enable a rough breakdown of line movements into errors inhouses’forecasts of the forecasts of bettors, and movements in response to new information. Assumingthat the former error is embodied only in the 1996-97 data, it follows that the ten-percentage-pointdifference in line movements observed across data sets is attributable to houses’forecast errors. Thisattribution is of course only an approximation, but it does suggest that houses are quite adept in forecastingbettors’forecasts.Distributions of differences between winning margins and closing spreads observed over the twoseasons are illustrated in Figure 2. These distributions are quite similar. As noted above, the means andvariances computed over the 1996-97 season are -0.43 and 13; corresponding figures for the 1995-96season are -0.9 and 12.5. Moreover, a χ2test of the null hypothesis that the two histograms weregenerated from the same underlying distribution fails to reject the null at virtually any significance level.While these histograms do not indicate obvious profit opportunities, the next section presents a simpleapproach for their discovery.were unwilling to issue a spread. I included data on these games in my sample, but their exclusion yields similarresults.4I considered these data only after completing my analysis of the 1996-97 data; I did this to check the robustnessof my findings for the 1996-97 data.
Page 5 4III. Charting successMy goal in evaluating the efficiency of superbowl betting lines was to determine whether a simplebackward-looking model was capable of outperforming Las Vegas spreads. In my view, the harder I had tosearch for an effective model, and the more complicated was the resulting model, the weaker would be theevidence (if any) I uncovered against efficiency. My search was a short one: the first set of team-specificmodels I considered yielded strong evidence against efficiency. The following subsection providesbackground for my choice of models; the subsequent subsection provides technical details.BackgroundAs an avid participant in recreational office pools (for entertainment only, of course), I have longrelied on past performance to guide my weekly selections.5This has yielded mixed results: every year, itseems that some teams treat me well, while others wipe me out. Looking back at the 1996-97 superbowl seasonsuggested an explanation for this: many teams experienced extended streaks over the course of the season,thus rewarding my tendency to bet for last week’s winners, and against last week’s losers; at the sametime, many others whipsawed over extended periods (e.g., won-lost-won-lost...), thus punishing mytendency.6(Explaining why such patterns coexist is difficult. Extended streaks could reflect adaptiveexpectations on the part of bettors; and whipsawing may be a manifestation of overshooting driven by anaggregate tendency to favor last-week’s winners; but the compatibility of these explanations seemstenuous.) It occurred to me that different backward-looking models seemed appropriate for different teams.It also occurred to me that a formal statistical model had the potential to outperform my eyeball approach.Besides past performance, I have also paid attention to line movements in making my weeklyselections. The pool I participate in revolves around opening spreads, so I have interpreted line movementsas signals of bargains generated by the market. I have found these signals valuable in competing againstopening spreads; in specifying my team-specific models, I decided to investigate whether the signals wereuseful in competing against closing spreads as well.The modelsSince the outcome of a bet against the house can be thought of as a dichotomous random variable(equaling 1 if the bet wins and 0 if it loses), logit or probit models seemed well suited for fitting and5I blame genetics: my father was a dyed-in-the-wool chartist.6Notable teams in the former category were Indianapolis (eight-game losing streak); Green Bay (seven-gamewinning streak, five-game losing streak); and Carolina and Pittsburgh (six-game winning streaks). Notable teams
Page 6 5forecasting in this application. Given Stern’s (1991) results on normality, I chose probit specifications, butlogit specifications yield similar results. For the reasons given above, I estimated separate models for eachteam; the models consisted of a constant and three explanatory variables: own and opponent differences inwinning margins and closing spreads from the previous game, and intraweek line movements. (I includedonly one lagged difference to keep the models simple, and to maximize the length of the forecasting windowafforded by their use.)I employed a dynamic forecasting algorithm in using these models to generate predictedprobabilities of winning. The first set of probabilities I generated were for week eleven of the regularseason; the models used to generate these probabilities were estimated using data observed over theprevious ten weeks.7I then reestimated each model by updating the explanatory variables to include week-eleven observations, and generated a second set of probabilities. I repeated this process for the remainderof the season, including the playoffs and Super Bowl.Before describing the algorithms used to process the resulting set of probabilities, two notes are inorder. The first concerns the choice of the initial ten-week estimation window. Other choices are certainlypossible, and one faces a clear tradeoff in choosing this width: shortening the window yields forecasts forearlier weeks, at the cost of a loss of observations available for estimating the models used to generate theearlier forecasts. The Washington Redskins are responsible for my choice of a ten-week window: I had towait ten weeks before I could estimate their model, because their first eight dependent observationsconsisted of seven wins (speaking of streaks) and one bye week. I could have started forecasting in weekten by ignoring Washington and focusing on the remaining teams (doing so would have resulted in a fiveand two record for my leading algorithm in week ten), but I decided to begin in week eleven so that allteams could be treated symmetrically. The second note concerns the use of the dynamic updating algorithmused for reestimating the forecasting models. Use of this algorithm turned out to provide little value addedover the use of the original models (estimated over the first ten weeks) over the entire forecasting horizon:it generated only one additional win, a result which speaks well for the stability of the models.Use of these team-specific models yielded two predicted probabilities of success for each game:one for each contestant. I considered two strategies for triggering bets as functions of these probabilities.The first I will refer to as conservative: bet on a team if the predicted probability generated by its model isgreater than 0.5, and the probability generated by its opponent is less than 0.5. The second I will refer toin the latter category were New England and San Francisco (nine-week whipsaw streaks); and Denver and Seattle(six-week whipsaw streaks).
Page 7 6as aggressive: bet on a team if the predicted probability generated by its model is greater than theprobability generated by its opponent’s model.In order to assess the marginal value of the information embodied in intraweek line movements, Igenerated a second set of predicted probabilities by dropping line movements as explanatory variables inthe probit models, and repeating the process described above. So I considered a total of four bettingstrategies: conservative and aggressive, with and without incorporating line movements. The performanceof these strategies is discussed below.IV. Beating the houseAs mentioned above, I initially applied my betting strategies to the 1996-97 season, and thenapplied them to the 1995-96 season to examine the robustness of my original findings. Table 1, fashionedafter Zuber et al.’s (1995) Table 2, illustrates the payoffs generated by the four strategies I considered bypresenting the results of a gambling simulation conducted for each strategy over the 1996-97 season. (Tosave space, simulation results obtained for the 1995-96 season are not tabled, but are summarized in thetext.) The simulations involve betting $11 each time a bet is triggered. For each strategy, weekly wins andlosses are reported, along with weekly and cumulative amounts bet, net winnings, and net returns. (Betsplaced on games that resulted in ties are treated as nonbets.)Consider first results obtained by including line movements as explanatory variables. Over the1996-97 season, the conservative strategy had a 65.4-percent success rate, triggering 52 bets which netted$142 in net winnings (a 24.8-percent net rate of return). The aggressive strategy had a 58.4-percentsuccess rate, triggering 113 bets and netting $143 in winnings (an 11.5-percent net rate of return). Similarresults were obtained over the 1995-96 season: the conservative strategy had a 60.1-percent success rate(31 wins, 20 losses) and generated a 16-percent net rate of return, while the aggressive strategy had a 58-percent success rate (62 wins, 45 losses) and generated a 10.6-percent net rate of return. Weekly netreturns exhibited high volatility over the course of the season, but cumulative net returns settled down quitequickly (approaching their ultimate levels within four to five weeks).Consider now the results obtained by excluding line movements as explanatory variables. Thesuccess rate of the conservative strategy fell by five percentage points in the 1996-97 season, and the netrate of return it generated fell to 15.4 percent. The success rate of the aggressive strategy fell by threepercentage points, and its net rate of return fell to 5.5 percent. The exclusion of line movements in the7Typically, this estimation window yielded eight dependent observations by week ten: one observation was lostdue to the use of lagged results as explanatory variables, and another was often lost because most teams enjoyed abye week during this period.
Page 8 71995-96 data set resulted in decreases in success rates of five and four percentage points for theconservative and aggressive strategies, and decreases in net rates of return to 7.2 and 2.3 percent. So inboth data sets, the information content of line movements seems valuable: exclusion of these movements asexplanatory variables is costly.Information concerning the statistical significance of these findings is provided in Table 2.Classical and Bayesian measures of significance are reported. The Classical measures involve tests of thenull hypothesis that the success rates reported above are significantly greater than 50 and 52.38 percent(i.e., the pure-chance and the break-even rates). These tests are conducted using Z statistics (differencesbetween realized wins and wins expected under the null, measured in standard-deviation units computedunder the null); critical values of the Z statistics are obtained using the normal approximation to thebinomial distribution. In the table, Z1 denotes the test statistic computed for the pure-chance rate, and Z2denotes the statistic computed for the break-even rate; the statistics were used to assess the season-specificand overall performance of each betting strategy. The Bayesian measures of significance are posteriorodds ratios in favor of the null hypothesis that the winning percentages generated by each betting strategyare 55 percent, versus alternative hypotheses of 50- and 52.38-percent. The odds ratios were generatedusing the binomial distribution, and were computed using even prior odds.Two features of Table 2 are particularly noteworthy. First, the two-year performances of both theconservative and aggressive strategies, applied to the predicted probabilities generated by the models whichtake intraweek line movements into account, provide sufficient evidence to reject both the pure-chance andbreak-even hypotheses. The conservative strategy generated 65 wins in 103 bets over this period -- a 63.1-percent success rate -- which leads to a rejection of the break-even hypothesis at the 3-percent significancelevel. Moreover, the posterior odds against the break-even rate are 2.8 to 1 in this case. Identical odds areobtained for the aggressive strategy, which generated 128 wins in 220 bets over this period, a 58.2-percentsuccess rate (the break-even null is rejected in this case at the nine-percent significance level). Second, thevalue of considering intraweek line movements is again in evidence in Table 2. Exclusion of thesemovements leads to reductions in success rates over the two-season period of 5 and 4 percentage points forthe conservative and aggressive strategies. As a result, posterior odds against the break-even rate areapproximately cut in half for each strategy, and the null hypotheses that the success rates of these strategiesare equal to the break-even and pure-chance rates cannot be rejected at the ten-percent significance level.
Page 9 8V. If you’re so smart...Wait until next year. Publicizing the performance of this simple, easily adoptable procedure nowaffords a truly challenging future test of market efficiency: if the procedure becomes well known andcontinues to succeed, the efficiency of the superbowl gambling market will be cast further in doubt. In addition,I will have a satisfying answer to the question: If you’re so smart, why aren’t you rich?
Page 10 9ReferencesBadarinathi, R. and L. Kochman (1996), “Football Betting and the Efficient Market Hypothesis,” TheAmerican Economist 40: 52-55.Pankoff, L. (1968), “Market Efficiency and Football Betting,” Journal of Business 41:203-214.Stern, H. (1991), “On the Probability of Winning a Football Game,” The American Statistician 45: 179-183.Tryfos, P., S. Casey, S. Cook, G. Leger, and B. Pylypiak (1984), “The Profitability of Wagering on superbowlGames,” Management Science 30: 123-132.Vergin, R.C. and M. Scriabin (1978), “Winning Strategies for Wagering on National Football LeagueGames,” Management Science 24: 809-818.Zuber, R.A., J.M. Gandar, and B.D. Bowers (1985), “Beating the Spread: Testing the Efficiency of theGambling Market for National Football League Games,” Journal of Political Economy 93: 800-806.
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