# A Comment on Paul and Weinbach's (2005) "Bettor Preferences and Efficient Markets in Totals Markets"

By Francisco, James; Moore, Evan | Journal of Economics and Finance, October 2018 | Go to article overview

# A Comment on Paul and Weinbach's (2005) "Bettor Preferences and Efficient Markets in Totals Markets"

Francisco, James, Moore, Evan, Journal of Economics and Finance

(ProQuest: ... denotes formulae omitted.)

1Introduction

Various sports wagering markets have served as fertile ground for testing the Efficient Market Hypothesis (EMH). Paul and Weinbach (2005) did just that, testing whether the totals markets in football wagering yielded any profitable strategies. "Totals" wagering in football refers to bets placed on the combined score of both teams. According to SportsInsights.com, the total indicates "...the total amounts of points that will be scored in the game." Bettors can wager on the over (under), which is that the teams' combined score will be greater than (less than) the given total. A winning wager is referred to as a "cover."

Most American bets are offered at odds of -110, which means that the bettor must risk \$110 in order to win \$100. Because of this, in order to break even, a bettor must win approximately 52.4% of his or bets in order to break even. Paul and Weinbach (2005), using data from 1999 to 2003 and 2000-2004, found that a naive strategy of betting "under" was profitable for certain totals (i.e. that this strategy would yield a winning percentage significantly greater than 52.4%) in college and arena football. By establishing that such a strategy was profitable, the authors concluded that the totals markets in these sports were not, in fact, efficient. However, they also suggested the possibility that, "a simple explanation of the rejection of efficient markets in totals markets in college football and arena football is that these markets are relatively new and, given time, the inefficiencies will disappear." (Paul and Weinbach 2005, at 413). In this paper, we find that this statement was prescient, at least with respect to the college football totals market.

2Model and data

We utilize the same model as Paul and Weinbach (2005), who cite Gandar et al. (1988) and Sauer et al. (1988), laid out as follows.

...

where "Score" is the actual game score, and "Total" is the closing total offered at gametime. The joint null hypothesis of efficiency is that a0 = 0 and ß1 = 1.

To address the possibility of skewed forecast errors, Paul and Weinbach (2005) also employed the test developed by Even and Noble (1992), which tests the null hypothesis that a given bet is "fair" (i.e. that the probability of both losing the bet = 0.5). These authors utilized the test as follows:

...

where n is number of covers, N is number of matchups, and q is ratio of covers to matchups. To "cover" means to win a bet.

Because this method assumes that an efficient market means that q = 0.5, we substitute 0.5 for q which yields the following likelihood ratio for the null hypothesis:

...

Paul and Weinbach (2005), then adapted that approach to test for the null hypothesis that a bet is not profitable (i.e. that it does not generate a "cover" more than 52. …

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