# THE DETERMINANTS OF SCORING IN NFL GAMES AND BEATING THE SPREAD

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1 THE DETERMINANTS OF SCORING IN NFL GAMES AND BEATING THE SPREAD C. Barry Pfitzner, Department of Economics/Business, Randolph-Macon College, Ashland, VA 23005, Steven D. Lang, Department of Economics/Business, Randolph-Macon College, Ashland, VA 23005, Tracy D. Rishel, Department of Business, Belmont Abbey College, Belmont, NC 28012, ABSTRACT In this paper we attempt to predict the spread for National Football League (NFL) games for the season. Separate regression equations are identified for predicting points for the home and away teams in individual games based on information known prior to the games. The difference in the predictions from the regression equations (updated weekly) serve as a prediction of the spread for NFL games and those results are used in a wagering experiment to determine if a successful betting strategy can be identified. All predictions in this paper are outof-sample. INTRODUCTION Bookmakers set favorite/underdog spread lines for virtually all NFL games. Suppose the Dallas Cowboys are favored by 10 points over the Washington Redskins. Suppose further that a gambler wagers with the bookmaker on Dallas for this game. If Dallas wins by more than 10 points, the gambler wins the wager. If Dallas wins by fewer than 10 points (or loses the game), the gambler loses the bet. If Dallas wins by exactly 10 points, the wager is tied and no money changes hands. The process works symmetrically for bets on the Redskins (the underdogs) Since losing bets pay a premium (often called the vigorish, vig, or juice and typically equal to 10%), the bookmakers will profit as long as the money bet on the favorite is approximately equal to the amount of money bet on the underdog (Bookmakers also sometimes take a position, that is, will welcome unbalanced bets from the public if the bookmaker has strong feelings regarding the outcome of the wager [see also the reference to Levitt s [5] work in the literature review]). It is widely known a gambler must win 52.4% of the wagers to be successful. That particular calculation can be established simply. Let P w = proportion of winning bets and (1 P w ) = the proportion of losing bets. The equation for breaking even on such bets where every winning wager nets \$10 and each losing wager represents a loss of \$11 is: P w (\$10) = (1 P w ) (\$11), and solving for P w P w = =.5238, or approximately 52.4%. This research attempts to identify methods of predicting the points scored by each team in a particular game based on information available prior to that game. The primary research question is whether or not these methods can then be utilized to formulate a successful gambling

3 models to predict the probability that a team will cover the spread. Gray and Gray find several strategies that would beat the 52.4% win percentage in out-of-sample experiments (along with some inconsistencies). They also point out that some of the advantages in wagering strategies tend to dissipate over time. Vergin [7], using data from the seasons, considers 11 different betting strategies based on presumed bettor overreaction to the most recent performance and outstanding positive performance. He finds that bettors do indeed overreact to outstanding positive performance and recent information, but that bettors do not overreact to outstanding negative performance. Vergin suggests that bettors can use such information to their advantage in making wagers, but warns that the market and therefore this pattern may not hold for the future. A paper by Paul and Weinbach [6] is a departure from the analysis of the spread in NFL games. They target the over/under wager, constructing simple betting rules in a search for profitable methods. These authors posit that rooting for high scores is more attractive than rooting for low scores. Ceteris paribus, then, bettors would be more likely to choose over bets. Paul and Weinbach show that from , the under bet won 51% of all games. When the over/under line was high (exceeded the mean), the under bet won with increasing frequency. For example, when the line exceeded 47.5 points, the under bet was successful in 58.7% of the games. This result can be interpreted as a violation of the EMH at least with respect to the over/under line. Levitt [5] (of Freakonomics fame) approaches the efficiency question from a different perspective. It is clear that if NFL bets are balanced, the bookmaker will profit by collecting \$11 for each \$10 paid out. As we suggested earlier, bookmakers at times take a position on unbalanced bets, on the assumption that the bookmaker knows more about a particular wager than the bettors. Levitt presents evidence that the spread on games is not set according to market efficiency. For example, using data from the seasons, he shows that home underdogs beat the spread in 58% of the games, and twice as much was bet on the visiting favorites. Bookmakers did not move the line to balance these bets, thus increasing their profits as the visiting favorite failed to cover in 58% of the cases. Dare and Holland [3] re-specify work by Dare and MacDonald [2] and Gray and Gray [4] and find no evidence of the momentum effect suggested by Gray and Gray, and some, but less, evidence of the home underdog bias that has been consistently pointed out as a violation of the EMH. Dare and Holland ultimately conclude that the bias they find is too small to reject a null hypothesis of efficient markets, and also that the bias may be too small to exploit in a gambling framework. Still more recently, Borghesi [1] analyzes NFL spreads in terms of game day weather conditions. He finds that game day temperatures affect performance, especially for home teams playing in the coldest temperatures. These teams outperform expectations in part because the opponents were adversely acclimatized (for example, a warm weather team visiting a cold weather team). Borghesi shows this bias persists even after controlling for the home underdog advantage.

4 DATA AND METHOD We focus on predicting the spread for NFL games and the corresponding favorite/underdog line for that game. With the objective of estimating regression equations for home and away team scoring, data were gathered for the season for the analysis. The variables include: TP = total points scored for the home and visiting teams for each game played PO = passing offense in yards per game RO = rushing offense in yards per game PD = passing defense in yards per game RD = rushing defense in yards per game D = a dummy variable equal to 1 if the game is played in a dome, 0 otherwise PP = points scored by a given team in their prior game L = the betting point spread (line) on the game Match-ups Matter (we think) The general regression format is based on the assumption that match ups are important in determining points scored in individual games. For example, if the team A with the best passing offense is playing the team B with the worst passing defense, ceteris paribus, team A would be expected to score many points. Similarly, a team with a very good rushing defense would be expected to allow relatively few points to a team with a poor rushing offense. In accord with this rationale, we formed the following variables: PY = PO + PD = passing yards RY = RO + RD = rushing yards For example, suppose team A is averaging 325 yards (that s high) per game in passing offense and is playing team B which is giving up 330 yards (also, of course, high) per game in passing defense. The total of 655 would predict many passing yards will be gained by team A, and likely many points will be scored by team A. The dome variable will be a check to see if teams score more (or fewer) points if the game is played indoors. The variable for points scored in the prior game (PP) is intended to check for streakiness in scoring. That is, if a team scores many (or few) points in a given game, are they likely to have a similar performance in the ensuing game? We also test to ascertain whether or not scoring is contagious. That is, if a given team scores many (or few) points, is the other team likely to score many (or few) points as well? We test for this by two-stage least squares regressions in which the predicted points scored by each team serve as explanatory variables in the companion equation.

5 General Regression Equations The general sets of regressions are of the form: TP hi = β 0 + β 1 (PY hi ) + β 2 (RY hi ) + β 3 (D i ) + β 4 (PP hi ) + ε hi (1) and TP vi = α 0 + α 1 (PY vi ) + α 2 (RY vi ) + α 3 (D i ) + α 4 (PP vi ) + ε vi, (2) where the subscripts h and v refer to the home and visiting teams respectively, and the i subscript indicates a particular game. Betting Strategies Equations such as 1 and 2 are estimated and predictions are made for weeks 7 through 15 of the season. The difference between the each equation s predictions represents our estimated spread which will then be compared to the actual line for each game. For example, suppose TP hi = 24 and TP vi = 16, then the home team is favored by our method to win by 8 points. Thus if the actual line on the game is that the home team is favored by only 1 point (stated as home team -1), we might choose to wager on the home team for that game. We entertain several strategies for wagering based on our predicted spread versus the actual betting line. We choose to make simulated wagers only if our predicted spread differs from the actual spread by 10, 8, or 5 points. Those simulated wagers will then be compared to the outcome of the actual game in a test for profitability. In summary: 1. Bet only games for which our predicted spread differs from the line by more than 10 points. 2. Bet only games for which our predicted spread differs from the line by more than 8 points. 3. Bet only games for which our predicted spread differs from the line by more than 5 points. As stated previously, a betting strategy on such games must predict correctly at least 52.4% of the time to be successful. If a given method cannot beat this 52.4% criterion, as a betting strategy it is deemed to be a failure. Out-of-Sample Method Since it is widely known that betting strategies that yield profitable results in sample are often failures in out-of-sample simulations, we use a rolling regression technique for each week of games. That is, we estimate equations TP hi and TP vi with the data from weeks 4-6 (we wait until week 4 so that the team statistics are more reliable), then feed those equations with the known data for each game through the end of week 6, generating predicted points for the visiting and home team for all individual games in week 7. The predicted points are then totaled and

6 compared to the point spread for each game. Next we add the data from week 7, re-estimate equations TP hi and TP vi, and make predictions for week 8. The same updating procedure is then used to generate predictions for weeks 9 through 15. This method ensures that our results are not tainted with in-sample bias. Descriptive Statistics RESULTS Table I contains some summary statistics for the data set. Teams averaged approximately 212 yards passing per game (offense or defense, of course) for the first fifteen weeks of the season, and they averaged approximately 114 yards rushing over that same period. The statistics reported on the rushing and passing standard deviations without parentheses are for the offenses and the defensive standard deviations are (as you might guess) in parentheses. Interestingly, both passing defense and rushing defense are less variable across teams than are the offensive counterparts. Home teams scored approximately 23 points on average during weeks 1-15 and outscored the visitors by about two points. Total points averaged 43.6 over this period and the over/under line averaged 43.0 (the difference in these means is, of course, not statistically significant). Not surprisingly, the standard deviation was much smaller for the line than for total points. TABLE I: SUMMARY STATISTICS (THROUGH WEEK 15) Variable Mean Standard Deviation Passing Yards (21.8) Rushing Yards (21.4) Visitor Points Home Points Total Points Line Spread* Win Margin* *Spread and win margins are stated in terms of the home team, i.e., home teams were favored by 2.84 points on average and won by an average of 2.04 points. Note that the spread averaged points, that is, the home team was favored by an average of a little less than 3 points Regression Results In the estimations of equations 1 and 2, we find no role played by points scored in the prior week and we also find no support for the hypothesis that scores of the opposing teams are related (estimations on these issues are available from the authors upon request). Typical estimated equations are:

7 TP hi = (PY hi ) (RY hi ) (D) + e hi (1 ) (2.52)* (2.27)** (1.46)*** R 2 =.066 SEE = 9.92 n = 164 F = 4.81 p-value for F = TP vi = (PY vi ) +.074(RY vi ) (D) + e vi (2 ) (2.64)* (3.78)* (0.28) R 2 =.101 SEE = 9.84 n = 164 F = 7.12 p-value for F = (***represents significance at α =.10 or better, ** represents significance at α =.05 or better and * represents significance at α =.01 or better for one-tailed tests) For the home points equation (1 ), with the exception of the dome variable, each explanatory is statistically significant at the α =.05 level or better and the equation explains a modest 6.6% ( R 2 =. 066 ) of the variance in home points scored. (We retain the dome variable for symmetry with our earlier findings.) On the other hand, the F-statistic suggests that the overall equation meets the test of significance at less than α <.01. The estimated coefficients for all of the variables have the anticipated signs (although there is no theoretical reason other than weather including wind which makes indoor venues more conducive to scoring). To interpret those coefficients, an additional 100 yards passing (recall that this is the sum of the home team s passing offense and the visitor s passing defense) implies about four additional points for the home team, whereas an additional 100 yards rushing implies almost 5 additional points. Surprisingly (that is, we don t have an explanation for this), the visiting team estimation yields a somewhat better fitting equation. The explanatory variables are statistically significant at α <.01 (with the exception of the dome variable), the equation explains about 10% ( R 2 =. 101) of the variance in visiting team points, and the F-statistic implies overall significance at far less than α <.01. The coefficients for passing and rushing suggest a slightly greater effect for the visiting team than the home team. If the coefficients are to be believed, an additional 100 yards passing yields approximately 4 points for the visiting team, and an additional 100 yards rushing is worth 7.4 points. The dome effect is weakly significant for the home team, but not significant for the visiting team. We retain the dome variable to be consistent with prior empirical results.

8 Do the regression equations produce reasonable results? On at least one basis, we can conclude that the answer is yes. Our model produces a predicted spread of that is, the home team is expected to score 3.32 more points on average than the visiting team. This is consistent with the mean spread of from Table I. Betting Results We entertain three betting strategies for the predicted points versus the over/under line on the games. These strategies are: 1. Bet only games for which our predicted spread differs from the betting line by more than 10 points. 2. Bet only games for which our predicted spread differs from the betting line by more than 8 points. 3. Bet only games for which our predicted spread differs from the betting line by more than 5 points. It is widely known that a betting strategy on such games must predict correctly 52.4% of the time to be successful. If a given methods cannot beat this 52.4%, as a betting strategy it is deemed to be a failure. TABLE II: RESULTS OF DIFFERENT BETTING STRATEGIES Betting Strategy (Differential) Games Played W-L-T Record Win Percentage > 10 points % > 8 points % > 5 points % Table II contains a summary of the results for the three betting strategies. The first betting strategy yields only four plays over weeks seven through fifteen. That betting strategy would have produced two wins, one loss, and one tie (or push, in betting parlance). For this small sample, this strategy is, of course, profitable. The second strategy (a differential greater than 8 points) yields 10 plays and a record of a winning percentage of 67%. The 5 point strategy yields 41 bets and a 44.7% success rate. It is important to note that we make no adjustment for injuries, weather, and the like that would be considered by those who make other than simulated wagers. We offer these methods only as a guide, not as a final strategy. SUMMARY AND CONCLUSIONS The regression results in this paper identify promising estimating equations for predicting the spread between the scores of NFL opponents. In a rolling regression framework, we apply the method to three simulated betting procedures for NFL games for weeks 7-15 of the 2008 regular

9 season. Betting strategies that require a large differential between the regression method and the betting line are profitable, albeit for a relatively small sample. REFERENCES [1] Borghesi, R. The home team weather advantage and biases in the NFL betting market. Journal of Economics and Business, 2007, 59, [2] Dare, W.H. & MacDonald, S.S. A generalized model for testing home and favourite team advantage in point spread markets. Journal of Financial Economics, 1996, 40, [3] Dare, W.H. & Holland, A.S. Efficiency in the NFL betting market: Modifying and consolidating research methods. Applied Economics, 2004, 36, [4] Gray, P.K. & Gray, S.F. Testing market efficiency: Evidence from the NFL sports betting market. The Journal of Finance, 1997, LII(4), [5] Levitt, S.D. How do markets function? An empirical analysis of gambling on the national football league. National Bureau of Economic Research working paper 9422, [6] Paul, R.J. & Weinbach, A.P. Market efficiency and a profitable betting rule: Evidence from totals on professional football. Journal of Sports Economics, 2002, 3, [7] Vergin, R.C. Overreaction in the NFL point spread market. Applied Financial Economics, 2001, 11,

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