Football betting and the efficient market hypothesis.

Badarinathi, Ravija ; Kochman, Ladd

The efficient market hypothesis asserts that investors cannot consistently "beat the market" because stocks reside in perpetual equilibrium. Supporters point to the 100,000+ analysts and traders whose collective actions ensure that the prices of the 3000 or so major stocks do not stray too far from their respective values. Pankoff (1968) reasoned that the football-betting market attracts participants no less numerous, knowledgeable or competitive than its Wall Street counterpart and therefore functions as a convenient proxy for testing the fallibility of market consensus.

Pankoff concluded that Las Vegas pointspreads on National Football League games contained no exploitable biases after regressing actual winning margins (WM) on betting lines (BL) for the 1956-65 seasons and finding intercept (a) and slope (b) coefficients insignificantly different from the values - 0 and 1, respectively - expected in an efficient market. The first

WM = A + bBL + e (1)

analysis of pointspreads in the context of betting rules(1) was performed by Vergin and Scriabin (1978) who applied 70 strategies to NFL games during the 1969-74 seasons. Their claim that 23 of those rules were profitable attracted the attention of Tryfos et al. (1984) who investigated how Vergin and Scriabin measured profitability and whether their findings were sample-specific. After demonstrating that the Z-value used by V&S ([Z.sub.1]) tested only for nonrandomness and that profitability required a separate Z-value ([Z.sub.2]), Tryfos et al. still found that 20 of the 23

[Z.sub.1] = [W - 0.5 (B)] X [[B(p)(1 - p)].sup.-1/2] (2)

[Z.sub.2] = W/B - (1.1)L/B / [{1/B[(W/B + (1.21)L/B) - [(W/B - (1.1)L/B).sup.2]]}.sup.1/2] (3)

where: W = winning bets B = total bets p = probability of wining (= 0.5) L = losing bets

strategies that V&S had incorrectly characterized as profitable were, in fact, just that. However, when Tryfos et al. applied those same 23 rules to the 1975-81 NFL seasons, only three emerged as profitable.

Methodology

The purpose of this study is to apply the three betting strategies touted as profitable during both the 1969-74 and 1975-81 periods to the 1984-93 seasons. All three rules called for betting on the underdog when the pointspread was greater than five points. Vergin and Scriabin then suggested that by taking advantage of the variation in spreads among bookmakers in different cities, it was possible to improve the underdog's spread by one or more points. The vehicle for finding such an advantage is a syndicate, which V&S defined as a collection of gamblers located around the country each having betting arrangements with several local bookmakers. The specific strategies dictated the following:

RULE #2: Bet on the underdog when the spread is greater than 5 points and an advantage of 1.0 point can be obtained in favor of the underdog.

RULE #3: Bet on the underdog when the spread is greater than 5 points and an advantage of 1.5 points can be obtained in favor of the underdog.

RULE #4: Bet on the underdog when the spread is greater than 5 points and an advantage of 2.0 points can be obtained in favor of the underdog.

An additional rule was taken from V&S to measure the success of betting on underdogs when the spread is greater than five points but no point advantage is obtained. While the strategy did beat the 52.38-percent breakeven [rate.sup.2] for V&S, its use in this study has less to do with testing market efficiency than with isolating the value of a syndicate.

RULE #1: Bet on the underdog when the spread is greater than 5 points.

To illustrate how the foregoing rules were applied to the 1984-93 NFL games, imagine that you bet on a team that enters a contest as a 6 1/2-point underdog and exits as an 8-point loser. Denied any point advantage, Rule #1 results in an obvious loss. Rule #2 also leads to a losing wager since 7 1/2 points-that is, the 6 1/2-point handicap plus the extra point from a syndicate - fail to cover the eight-point deficit. Rule #3 produces a point-wise tie - i.e., no bet - since the 6 1/2-point spread plus the 1 1/2-point advantage equal the eight-point losing margin. Rule #4 provides a winning bet inasmuch as 6 1/2 points plus the two-point advantage exceed the eight-point gap. The source for all pointspreads and final scores for the 1984-93 period was Feist (1994).

Results

A total of 2272 regular- and post-season NFL games were played during the 1984-93 seasons. Games in which the pointspread was less than 5 1/2 points numbered 1191 and were dropped from further consideration. When Rule #1 was applied to the remaining 1081, 543 wins and eight ties resulted. After eliminating the tied games, we calculated a wins-to-bets ratio of 50.61 percent - or 543/1073. The failure of the strategy to beat the 52.38-percent breakeven mark precluded the need to test its nonrandomness per Eq. (2) or its profitability per Eq. (3). The same rule produced a 54.60-percent W/B ratio for V&S over the 1969-74 years and a 53.47-percent rate for Tryfos et al. for 1975-81. Table 1 displays the 1984-93 results for Rule #1 in the aggregate as well as by team.

Predictably, Rule #2 achieved a higher W/B ratio with 570 wins and 16 ties out of the 1081 games with spreads greater than five points. That ratio (53.53 percent - or 570/1065) proved to be nonrandom in the Eq. (2) sense but failed the Eq. (3) test of profitability. See Table 2. V&S and Tryfos et al. reported ratios of 57.54 percent and 56.40 percent, respectively, when they bet on underdogs given at least 5 1/2 points by Las Vegas and an additional point by a syndicate.

With a 1 1/2-point advantage, Rule #3 won 585 bets out of 1081 with 13 pointwise ties for a W/B ratio of 54.78 percent - or 585/1068. The strategy's success rate was decidedly nonrandom but profitable only at the 10-percent probability level. V&S and Tryfos et al. found ratios of 58.79 percent and 57.68 percent, respectively, when they bet on underdogs receiving more than five points from Las Vegas and 1 1/2 points from a syndicate.

Finally, Rule #4 produced a 56.03-percent W/B ratio on the strength of 599 wins and 12 ties out of 1081 bets - or 599/1069. At the one-percent probability level, the result was both nonrandom and profitable. V&S and Tryfos et al. claimed ratios of 60.59 percent and 59.26 percent, respectively, when they applied the spread-plus-two rule.

Conclusions and Recommendations

It is tempting to conclude that since exploitable opportunities can be found among only 14 weekly NFL pointspreads, the capital market with its thousands of chances to speculate could hardly be invulnerable to diligent and opportunistic analysts. A less sweeping, yet more defensible, conclusion is that regular profits are possible by betting on NFL underdogs who receive 5 1/2 points or more from bookmakers and no fewer than two points from syndicates. An additional insight is that legislators in states contemplating legalized football betting can act to reduce the probability of systematic losses by minimizing the variation of pointspreads within their boundaries and, in turn, neutralizing the effect of syndicates.

TABLE 1

Wins-to-bets results from four betting rules (1984-93)

TEAM RULE #1 RULE #2 RULE #3 RULE #4

Arizona 31/66 35/66 36/66 37/67
Atlanta 37/74 39/74 40/74 41/73
Buffalo 15/32 16/31 17/32 17/31
Chicago 8/16 8/16 8/16 8/15
Cincinnati 19/41 20/40 21/40 22/40
Cleveland 15/26 15/26 15/24 17/26
Dallas 20/38 21/38 21/38 21/37
Denver 8/17 8/17 8/16 9/17
Detroit 30/59 31/60 31/60 31/60
Green Bay 31/57 31/57 31/56 34/58
Houston 20/38 21/38 21/38 21/37
Indianapolis 37/84 41/83 43/85 43/83
Kansas City 17/32 17/31 18/32 18/32
LARaiders 10/18 10/18 10/18 10/18
LARams 15/34 15/34 15/34 15/34
Miami 7/13 7/12 8/13 8/13
Minnesota 11/28 12/27 13/27 14/27
New England 32/59 35/59 36/60 36/60
New Orleans 16/33 17/32 18/32 19/32
NYGiants 10/22 10/22 10/22 10/22
NYJets 25/46 25/47 25/47 25/47
Philadelphia 20/32 21/31 22/32 22/32
Pittsburgh 24/46 25/45 26/46 26/46
San Diego 25/39 27/39 27/38 28/39
San Francisco 0/ 2 0/ 2 0/ 2 0/ 2
Seattle 15/34 17/32 19/32 21/33
Tampa Bay 41/81 41/82 42/82 42/82
Washington 4/ 6 4/ 6 4/ 6 4/ 6
Totals 543/1073 570/1065 585/1068 599/1069
 (50.1%) (53.52%) (54.78%) (56.03%)
TABLE 2

Tests of nonrandomness ([Z.sub.1]) and profitability ([Z.sub.2]) for
four betting rules (1984-93)

RULE [Z.sub.1] [Z.sub.2]

#1 0.40 -1.16
#2 2.30(a) 0.74
#3 3.12(a) 1.58(b)
#4 3.95(a) 2.40(a)

a significant at prob. [less than] 0.01
b significant at prob. [less than] 0.10

Notes

1. Some sports-betting researchers distinguish between the Pankoff and Vergin and Scriabin methodologies by referring to statistical tests and economic tests of market efficiency, respectively.

2. If each of 10,000 bets were $1.10 to win $1, only a total of 5238 wins (or 52.38 percent) could produce profits ($5238) equal to losses ($5238 or 4762 losses "times" $1.10). The difference between the $1.10 wage and the $1 payoff ($.10) represents the bookmaker's standard 10-percent transaction fee.

References

Feist, Jim. Pro Football 1994 Annual. Las Vegas: National Sports Services, Inc.

Pankoff, Lyn. "Market Efficiency and Football Betting." Journal of Business, April 1968, pp. 204-214.

Tryfos, P., S. Casey, S. Cook, G. Leger, and B. Pylypiak. "The Profitability of Wagering on NFL games." Management Science, January 1984, pp. 123-132.

Vergin, R. C., and M. Scriabin. "Winning Strategies or Wagering on National Football League Games." Management Science, April 1978, pp. 809-818.

Ravija Badarinathi and Ladd Kochman

Cameron School of Business, University of North Carolina, Wilmington, NC 28403

Coles School of Business, Kennesaw State College, Marietta, GA 30061