Introduction

Since the Associated Press (AP) started its football poll in the 1930s, there has been much interest in ranking the relative strength of major college football programs. The poll has been used in the past to crown the mythical national champion. It helped determine the participants in the national championship game of the Bowl Coalition in the 1990s and was part of the formula to determine participation in the subsequent Bowl Championship Series (BCS). Poll position also provides fans with bragging rights and programs with information they can use in recruiting. The AP panel of pollsters currently consists of 61 sportswriters and broadcasters that are picked for their expertise in college football, as well as geographical diversity. The poll ranks teams from 1 to 25 by aggregating the number of points assigned by each voter (highest ranked team receives 25 points and twenty-fifth ranked program receives 1 point). The final AP Poll is taken after the bowl games and gives the pollsters’ consensus team rankings at the end of the football season.

There can be substantial roster turnover between seasons in college football, with seniors losing their eligibility and others declaring for the National Football League (NFL) draft. This paper investigates the extent to which bettors rely on the prior season’s final poll results as an indication of relative team strength in the first game of the following season. If there is holdover bias, or over-reliance on last season’s poll, bets on those Top 25 teams will lose against the spread significantly more than 50% of the time.

Fodor et al. (2013) found holdover bias or sticky bettor preferences for the NFL. Betting against teams that made the playoffs the previous year in the first game of the following season beat the point spread 64.4% of the time for the period studied. This supported the hypothesis that bettors could place undue emphasis on prior information which might be of little use when the bets were made. They noted that this was consistent with work in the finance literature such as Brown and Cliff (2005) and Haruvy et al. (2007) who found that investor sentiment could be backward-looking and slow to react to new information.

There has been research into biases in football poll voting, the effectiveness of poll ranking on predicting game outcome, and the effect of team performances against the betting line on the next week’s polling, but to date there has been no effort to analyze the effect of the prior season’s poll on betting in the subsequent season. This paper examines whether the betting market is efficiently pricing games that involved last season’s top teams. Is there a simple rule, such as betting against these teams, that wins against the spread significantly more than half the time?

Literature Review

There has been work on voter biases in the college football polls. Campbell et al. (2007) found that increased television exposure increased rankings and the poll reacted positively to running up the score. Coleman et al. (2010) found that AP voters favored teams and conference members in their home state as well as teams with more television exposure. Stone (2013) found that voters underreacted to wins by low ranked teams and overreacted to losses by top ranked teams. He also noted that they tended to underestimate home field advantage. Witte and Mirabile (2010) found that the AP Poll over-ranked teams from some major conferences relative to non-major conferences and also rewarded running up the score. Andrews et al. (2018) found that AP voters exhibited confirmatory bias in that they tended to overreact to small deviations from expectations. They concluded that pollsters substantially altered their estimates of quality when they saw weak signals that had little new information.

Ross et al. (2012) found that the polls did a very good job of predicting game outcomes. They found some evidence of conference bias in the polls, but concluded that eliminating the bias would only slightly improve the predictive power of the polls. Paul et al. (2007) and Sinkey (2015) found that over- or under-performing relative to the spread resulted in significant impact on subsequent poll votes. The former article also found that the effect was greater if the game was televised.

There were a large number of papers that searched for sports betting strategies that violated efficiency (win significantly more than 50% of the time), or allowed for profitability after accounting for the bookmaker’s commission (bet $1.10 to receive $2.10 for a winning bet). Though most of these papers focused on professional sports, there were a number of articles that looked at college football.

Paul et al. (2003) found that the college football betting market was mostly efficient, except for some sub-groups (underdogs of a certain amount) for some time periods. They reported that 28-point or more underdogs won significantly more than 50% of the time against the spread, but profitability was not statistically significant. Also, for the latter years in their sample (1991–2000), betting on home underdogs of more than 7-points won significantly more than half the time against the spread but was not profitable, while underdogs of more than 28-points playing at home did win enough to be profitable.

Paul and Weinbach (2005, 2009) found that betting the under for relatively high college game totals won significantly more than 50% of the time and the latter paper found this strategy profitable. Paul and Weinbach (2009) also reported that home underdogs won significantly more than 50% of the time against the spread.

Kuester and Sanders (2011) found that when schools from humid regions played at schools from non-humid regions, they lost against the spread 56.64% of the time during the period 1999–2006. This was both significantly different from 50% and significantly different from the 52.4% necessary for profitability after commission.

Fodor (2013) and Paul et al. (2013) found that betting against non-major conference National Collegiate Athletic Association (NCAA) football schools when these schools played major conference schools won against the spread significantly more than 50% of the time. Coleman (2017) found that betting on a home team that was a favorite during the last half of the season, when the visitor traveled one time zone east, won significantly more than both 50% and 52.4% of the time.

Sinkey and Logan (2014) reported that betting lines were not independent from game to game, but that a sizable number of bettors believed in the so-called hot-hand. They concluded that favorites were overpriced and home teams were underpriced relative to the betting line. They also found that betting on home underdogs and betting against favorites with a strong tradition could be profitable.

This paper adds to the literature by determining whether a simple betting rule can shed light on the efficiency of the college football betting market when there is a possible holdover bias. As Fodor et al. (2013) noted, there were a substantial number of naïve or low-information bettors, and limits to maximum bets constrained the better informed. The literature cited above provided evidence that betting lines could be inefficient. This paper seeks to discover whether bettors over-rely on information from the previous season.

Data and Methodology

The data set consist of all subsequent season first games for the period 2008–2016, where a member of the previous season’s final AP Top 25 played a team not making that poll. The data are from the 2013–2017 issues of Phil Steele’s College Football Preview.

Following Even and Noble (1992), a likelihood ratio test is performed to test for efficiency and profitability. The unrestricted function is

$$ \mathrm{L}\left(\mathrm{un}\right)=n\left[\ln (p)\right]+\left(N-n\right)\ln \left(1-p\right), $$
(1)

where N is the number of observations, n is the number of observations where a bet on the AP Top 25 team wins, and p is the percent of the time that the AP Top 25 team wins the bet. The two restricted log likelihood functions (L(res)) replace p with 0.5 for efficiency, and 0.524 for profitability. This makes the likelihood ratio statistic for efficiency equal to

$$ 2\left(\mathrm{L}\left(\mathrm{un}\right)-\mathrm{L}\left(\mathrm{res}\right)\right)=2\left[n\left[\ln (p)-\ln (0.5)\right]+\left(N-n\right)\left[\ln \left(1-p\right)-\ln (0.5)\right]\right]. $$
(2)

The likelihood ratio statistic for profitability is equal to

$$ 2\left(\mathrm{L}\left(\mathrm{un}\right)-\mathrm{L}\left(\mathrm{res}\right)\right)=2\left[n\left[\ln (p)-\ln (0.524)\right]+\left(N-n\right)\left[\ln \left(1-p\right)-\ln (0.476)\right]\right] $$
(3)

if p is greater than 0.524. If p is less than 0.476, p is redefined to be the percent of the time that the non-AP Top 25 team wins the bet, and n is redefined to be the number of times a bet on that team wins.

Analysis

There were 174 games where the AP Top 25 team played a next season first game against a team outside of that poll which resulted in one team or the other covering the spread.Footnote 1 The Top 25 team was on average a 24.67-point favorite in these games, and won a large majority of the games outright (151 games or 86.8%). Of interest here is how they did against the spread.

The first section of Table 1 indicates that teams in the previous season’s final AP Top 25 covers the spread in only 42.53% of the next season first games. This is significantly different from 50%, indicating that there is holdover bias in college football as there is for NFL playoff teams. This is not statistically significant for profitability, but an $11 bet against the Top 25 team over the period would net $186 ($2100 - $1914), or a 9.7% return.

Table 1 Betting winning percentage and log likelihood tests for previous season’s final AP Top 25 teams in first game of following season (2008-2016)
Full size table

Table 1 also shows results for the teams ranked in the top 10 of the previous season’s final AP poll in first next season games against teams outside the top 10.Footnote 2 The top 10 schools only covered the spread 37.35% of the time. This is significantly different from 50%. Bets against these teams win against the spread significantly more than the 52.4% necessary for profitability. An $11 bet against the top 10 team over the period would net $179 ($1092- $913), or a 19.6% return.

The last section of Table 1 reports the results for teams ranked 11 through 25 in the previous year’s final AP Poll. There were 104 games between schools ranked 11 through 25 and schools not ranked in the previous year’s final AP Top 25.Footnote 3 Betting against these lower ranked AP Poll members covered the spread 52.88% of the time, which was not statistically significant.

The results above indicated that the inefficiency found was primarily due to the previous year’s top 10 schools being substantially overvalued in the betting market at the start of the next season. Betting market efficiency could not be rejected for the rest of the previous year’s Top 25 in their first games the following season. This was consistent with the holdover bias that Fodor et al. (2013) found for NFL playoff teams in their first games the next season. The strength of the top 10 teams at the end of the season should be better known, since they would for the most part have played in the more popular and lucrative bowl games. In addition, both Nutting (2011) and Stone (2013) found that the precision of the polls declined as the team ranking became lower. Bettors should have more confidence in the relative strength of these more highly ranked teams as of the conclusion of the previous season, which was carried into the next season’s first game if they exhibited holdover bias. There appeared to be no significant holdover effect for the teams that were not at the very top of the poll.

Table 2 divides the information from Table 1 according to whether the opponent is a so-called Power 5 school or not. The Football Bowl Subdivision (previously called Division I-A) of National Collegiate Athletic Association (NCAA) college football is characterized by a dichotomy between the 65 schools that belong to the Power 5 conferences (Atlantic Coast, Big Ten, Big 12, Pac-12, and Southeastern Conferences, along with Notre Dame), the relative haves, and the 65 schools outside the Power 5, the relative have-nots.

Table 2 Betting winning percentage and log likelihood tests for previous season’s final AP Top 25 teams in first game of following season: versus power 5 or non-power 5 (2008-2016)
Full size table

The results in Table 2 for all 174 games involving Top 25 teams show that the significance in Table 1 is primarily due to games against the non-Power 5 schools. Table 2 indicates that the significant difference from both 50% and 52.4% in Table 1 for top 10 teams is entirely due to games against non-Power 5 schools. Bets against the top 10 teams in games with non-Power-5 teams won 69.09% of the time. The differences from 50% and 52.4% were highly significant. $11 bets in each of these games would return $193 ($798 - $605) for a 31.9% return. The holdover effect when the previous year’s top teams played these lesser known schools was driving the results found earlier.

Table 2 shows that the efficiency of the betting market could not be rejected for teams ranked 11 through 25 in the prior season’s final AP Poll for either group of opponents. The significant results found in Tables 1 and 2 were due to top 10 teams playing non-Power 5 schools in the first game the following season. This was contrary to the results of Fodor (2013) and Paul et al. (2013), who found for all games, bets on the major schools won significantly more than half the time when playing non-major schools. The holdover effect for top 10 teams was very pronounced and dominated the effect that they reported.Footnote 4

Conclusion

This study contributed to the literature on inefficiency in sports betting markets. The betting market was shown to be inefficient when prior year AP Top 25 schools played non-Top 25 schools in the next season’s first game. This supported the existence of holdover bias where the betting market overvalued prior season information. A breakdown of the results by schools ranked in the top 10 and those ranked 11 through 25, indicated that the inefficiency was due to the first games involving the top 10, especially when they played non-Power 5 schools. Efficiency could not be rejected for first games involving those ranked 11 through 25. The simple rule of betting against prior season top 10 programs not only rejected efficiency, but won significantly more than the 52.4% necessary for profitability.

Research has shown that poll accuracy declined for lower-ranked teams (Nutting 2011; Stone 2013). The top 10 teams made up the poll’s consensus best programs from the previous season, and this information stayed with the betting public into the following season. The holdover bias exhibited for college football was consistent with that found for NFL playoff teams and added to the literature reporting that market participants could over-rely on outdated information.