Bettor biases and the home-underdog bias in the NFL.
Humphreys, Brad R. ; Paul, Rodney J. ; Weinbach, Andrew P. 等
In a recent article, Dare and Dennis (2011) explore the nature of
the home-underdog bias in NFL betting markets. They conclude that the
home-underdog bias exists due to bettors consistently underestimating
the scoring ability of home underdogs, but properly estimating the
scoring ability of away favorites. Their findings depend critically on
two underlying assumptions: first, prices set in the NFL betting market,
the point spread and the total, are set simultaneously and reflect
bettors forecasting the final score of the game, which informs their
wagering decisions; second, the presence of a balanced book on the part
of the sports book reflecting that prices are set to clear the market by
equalizing betting on either side of the point spread and totals
propositions.
Although a balanced book is not explicitly posited by Dare and
Dennis (2011), descriptions of their findings as reflecting the overall
actions of bettors, their lack of any explicit discussion of sports book
behavior, and their statement that "both the sides and totals
betting lines are determined by market participants, they should reflect
market expectations and forces" (p. 661) suggest that their
findings be interpreted as stemming from the traditional balanced-book
model.
As noted by Dare and Dennis (2011), research on sports betting
markets in North American team sports has identified what Woodland and
Woodland (1994, 2003, 2001) termed a "reverse-favorite
longshot" bias in baseball and hockey, where bets on better teams
tend to produce larger negative returns than bets on weaker teams. (1)
This bias has been attributed to the actions of bookmakers seeking to
balance betting action in order to generate positive returns without (or
with less) risk. If bettors systematically overestimate the favorite
(stronger) team's abilities, or simply prefer to bet on stronger
teams, a bookmaker that sets a line as a forecast will likely experience
imbalanced betting, and adjust the line to reflect the flow of bets.
Sports bettor biases therefore should tend to move prices and make bets
on better teams relatively more expensive, driving down returns to bets
on those teams.
The term favorite-longshot bias was originally used by
psychologists Griffith (1949) and McGlothlin (1956) to describe the
tendency for long-odds horses in parimutuel wagering markets to produce
lower (larger negative) returns than short-odds horses. It should be
noted that in parimutuel betting markets, odds are automatically driven
by betting volume, so biases are a direct consequence of bettor actions.
In North American team sports betting, where it is commonly assumed that
bookmakers similarly try to balance the flow of betting action, research
suggests that fans tend to over-bet the strongest teams in baseball and
hockey (Woodland & Woodland, 1994, 2003, 2001). Dare and Holland
(2004) and Golec and Tamarkin (1991) find that the strongest teams
appear to be overbet in National Football League point spread betting
markets. Dare and McDonald (1996) found that the model used by Golec and
Tamarkin (1991) was biased and resulted in inappropriate findings of
market efficiency in that study and developed an alternative model
specification for testing the joint null hypothesis of informational
efficiency in wagering markets. Dare and McDonald (1996) found little to
no evidence against market efficiency in betting markets for NFL and
college football regular season games.
In this paper, we replicate the Dare and Dennis (2011) results for
the years following the end of their sample, 2005-2011. Although the
mean forecast errors generated in this later sample are positive for
both away favorites and home underdogs, as they are in the original Dare
and Dennis (2011) sample from 1981-2004, testing for statistical
significance of the mean forecast errors reveals the opposite result of
Dare and Dennis (2011). Specifically, under their assumptions, in the
2005-2011 period, it appears that bettors underestimated the scoring
ability of away favorites, but properly estimated the scoring ability of
home underdogs.
These findings cast doubt on the assumptions and conclusions of
Dare and Dennis (2011) about the source of the home-underdog bias. With
this in mind, we offer an alternative theory of the source of the
home-underdog bias that can explain why it appears to have diminished
over time. Using detailed data on betting percentages from
www.sportsinsights.com, we show that the balanced-book hypothesis does
not hold in this context. Sports books appear to allow large imbalances
in betting volume ("take a large position" in this market) in
cases where imbalances are driven by highly predictable bettor
tendencies, such as bettor preferences for betting on the biggest
favorites (best teams) and bets on the over (bets that the total score
will be above the posted total), as opposed to the under (bets that the
combined score will be below the posted total). Bettors tend to place
more wagers on favorites, with that percentage increasing with the point
spread, and also have a tendency to bet more on away favorites than home
favorites, with away favorites routinely attracting 70% or more of the
bets on a game.
In addition, we show that there is a clear relationship between the
percentage of bets on a team and the recent success of that team; that
is, good teams tend to attract more bets than weak teams. The best teams
in the NFL consistently attract the highest proportion of bets game
after game and season after season. Also, over the period 20052011, all
32 teams in the NFL attracted a higher percentage of bets as the away
team than they attracted as the home team. Even with these clear biases,
in the period studied (2005-2011) the point spread appears to be set as
a forecast of game outcomes, as simple wagering strategies of betting
against these biases do not generate profits or reject market
efficiency.
Given these findings, we hypothesize that the home-underdog bias is
actually a function of simple bettor preferences for betting on the best
teams in the point spread market and high scoring in the totals market.
Bettors, behaving as fans rather than savvy and profit-seeking
investors, enjoy placing wagers on the best teams in the NFL as these
are the teams they most enjoy watching. The best teams in the league
become the biggest favorites in games and have enough talent to overcome
the implicit home-field advantage and become away favorites. In the
situation where the best teams are away favorites, bettors appear to
enjoy wagering on these teams at a "discount" as the prices
(point spreads) are lower than when these same teams are at home.
Assuming that tastes and preferences of bettors have not changed
over time, that bettors have always enjoyed wagering on the best teams
and on the over (perhaps because fans derive greater consumption value
from these bets when watching games), it begs this question: Why are
there are differences in estimates of the mean forecast errors in games
in the Dare and Dennis (2011) sample and the more recent sample used in
this study? In addition, why was wagering on home underdogs apparently
much more profitable in the earlier sample than in the later sample?
One possible explanation lies in the pricing strategy of sports
books, which may have changed over time. We hypothesize that increased
competition in the marketplace and the widespread availability of
information through the use of technology have reduced the incentive for
sports books to shade the line in the direction of the more popular side
of the wagering proposition when the sports book believes the imbalance
is merely fan-bias driven. This can explain why bookmakers appear to
tolerate large and predictable betting imbalances in the market and
still set a price that essentially acts as a forecast of game outcomes.
In this case it is the knowledge of the bookmaker that generates a
forecast of game outcomes, even as the bets made by the general public
are influenced by their preferences and biases. Sports books may have
changed their pricing strategy solely due to increased competition or
because of the increased prevalence and actions of informed bettors.
Wiseguys, as informed bettors are known, also benefit from technology as
decreasing costs of obtaining information about teams, players, and
games work to their benefit. If sports books price as a response to a
small group of informed bettors, better access to information may allow
for greater possible exploitation of biased point spreads or totals on
the part of wiseguys, leading to sports books that more effectively
price as an unbiased forecast of game outcomes.
This paper begins by describing the Dare and Dennis (2011) model
and estimates their model using data from recent NFL games over the
period 2005-2011. The next section uses detailed data on betting
percentages to illustrate behavioral biases of bettors toward favorites
and overs in a variety of settings. The subsequent section tests for
market efficiency and examines profitability in betting against the
clear behavioral biases in this market. The final section discusses the
results in terms of changes in the betting market over time, including
new technology and increased competition, and concludes the paper.
Mean Forecasts Errors and the Dare and Dennis (2011) Model
To begin, we estimate the Dare and Dennis (2011) (2) model using
data from recent NFL seasons. The model used by Dare and Dennis (2011)
assumes that the point spread ("side") and total for each game
are jointly set in the betting market for NFL football. Their assumption
implies that the prices in these betting markets are simultaneously set
and are determined, specifically, by bettors basing their bets on
forecasts of an expected final score of the game. Therefore, the side
and total are linked in this market.
Under the assumptions of Dare and Dennis (2011), bettors form an
expected score of the home team and the away team and then bet
accordingly. Their model is as follows:
E([S.sub.H]) = Expected Score of Home Team
E([S.sub.A]) = Expected Score of Away Team
(CSL) = -(E([S.sub.H]) - E([S.sub.A])) [Closing Line]
(CTL) = E([S.sub.H]) + E([S.sub.A]) [Closing Total]
E([S.sub.A]) = (CTL + CSL)/2
E([S.sub.H]) = E([S.sub.A]) - CSL
[FE.sub.H] = [S.sub.H] - E([S.sub.H]) [Forecast Error Home]
[FE.sub.A] = [S.sub.A] - E([S.sub.A]) [Forecast Error Away]
The closing point spread is formed by taking the negative of the
difference between the expected home score and expected away score (home
favorites are denoted with a negative value). The closing total is the
sum of the expected scores. From here, algebraic manipulation generates
the expected home and away scores, which then allows for the calculation
of the forecast errors for the home and away teams by taking the
difference between actual and expected scores.
Dare and Dennis (2011) used this model to calculate mean forecast
errors for a sample of NFL games from 1981 to 2004. They found that all
characteristics of teams analyzed (favorites, underdogs, home teams,
away teams, home favorites, away underdogs, away favorites, home
underdogs) generate positive mean forecast errors, implying that bettors
systematically underestimate the scoring of all teams in the NFL.
Specifically, for the focus of their study, Dare and Dennis (2011) find
statistically significant evidence that bettors underestimate the
scoring of home underdogs, but also find that bettors properly estimate
the scoring of away favorites (although the mean forecast error is
positive, it is not statistically significant). Dare and Dennis (2011)
conclude that the home-underdog bias is a function of bettors
underestimating the scoring of home underdogs, making findings of
profitable strategies based on betting home underdogs truly a function
of a public bias against home underdogs.
Although statistically correct given their data sample, we dispute
the assumptions underlying the Dare and Dennis (2011) model. First, we
do not believe the vast majority of bettors behave as sophisticated
investors. In other words, we do not believe that most bettors estimate
the final score of the game in question and make their bets accordingly.
Casual observation of bettor behavior suggests that the majority of
bettors do not use statistical models to generate estimates of final
scores and determine bets. Instead, bets appear to be made based on
"feel" or intuition as bettors believe that one team will
blowout the other team, or due to both teams scoring many points in
previous games, the game will be a "shoot-out," leading
bettors to place large number of bets on favorites and overs.
Although we do not believe that many bettors actually form specific
estimates of the exact final score before placing wagers, if the
assumptions of Dare and Dennis (2011) are correct, bettors should place
a similar number of wagers in both the sides and totals market. Under
the assumption that bettors estimate expected scores for both teams,
bettors should be willing to place wagers on both the side and total
propositions suggested by their expected scores. This is simply not
observed in NFL betting markets (or in other sports) as the amount of
money bet in the point spread market consistently far exceeds that in
the totals market. Point spread wagers are extremely popular with
bettors, while totals bets are not nearly as popular. Also, mean
forecast errors generated for all groupings of teams (favorites,
underdogs, home teams, away teams, etc.) are uniformly positive,
implying that bettors underestimate the scoring of every team in the
NFL. This is inconsistent with findings that simple strategies of
betting the under in the totals market for games with the highest totals
has been found to reject the null hypothesis of market efficiency and
also reject the null of no profitability (Paul & Weinbach, 2002). In
addition, casual observation suggests that overs are much more popular
bets than unders; this has been borne out in studies of betting
percentages (Paul & Weinbach, 2008, 2011), where bets on the over
have been shown to be clearly preferred to bets on the under.
The primary assumption underlying the Dare and Dennis (2011) model
that we question, however, is the implicit assumption that sports books
strictly adhere to the balanced-book model. Dare and Dennis (2011)
assume that point spreads and totals are set by the actions of bettors.
Sports books are assumed to set prices in an attempt to attract even
betting action on each side of the proposition. If bettors prefer one
side of the proposition to the other, prices are assumed to move in the
direction of the betting action as sports books attempt to minimize risk
by attempting to balance the overall betting dollars by inducing later
bettors to take the other side of the proposition. For example, if team
A is a 7-point favorite and the betting volume is heavily skewed toward
bets on team A, the balance-book model predicts that bookmakers would
increase the line, making team A an even heavier favorite, in an attempt
to induce bettors to bet on team B to cover.
The balanced-book model was challenged by Levitt (2005). Levitt
used data from a betting tournament based on NFL games to demonstrate
that bettors prefer favorites to underdogs, particularly road favorites
compared to home underdogs. Levitt reported that sports books shade the
line toward road favorites, resulting in higher returns to wagering on
home underdogs. Although Levitt used data from a betting tournament,
which may not reflect the incentives and decisions in actual betting
markets, the fact that bets on favorites (particularly road favorites)
are more popular than bets on underdogs has been shown to exist in
actual betting markets (Paul & Weinbach, 2008, 2011) where betting
percentages from actual sports books show a clear preference for
favorites and overs; the predictions of the balanced-book model appear
to be inconsistent with betting volume in on NFL games and in other
sports.
If sports books are not pricing according to the balanced-book
model and are willing to take positions on individual games, the
conclusions of Dare and Dennis (2011) can be questioned as closing
prices in the betting market reflect decisions made by bookmakers (in
addition to any informed bettors in the market to whom sports book
managers may respond) and not the preferences of the majority of
bettors. If the sports books price as a forecast of game outcomes, as
suggested by Paul and Weinbach (2008), the market prices may leave no
profit opportunities, despite the presence of clear behavioral biases on
the part of bettors. The closing lines and totals may therefore reflect
the actions of bookmakers (and/or the actions of a small group of
informed bettors), and not necessarily be driven by the actions of
overall bettors in the market.
To illustrate the potential problems with the assumptions
underlying the Dare and Dennis (2011) model, we first estimate their
model using data from the most recent seasons in the NFL. Their sample
of data was taken from the sports book at the Stardust Casino in Las
Vegas from the 1981-82 to 2004-05 NFL seasons. We begin our initial
sample in 2005-06 and include each NFL season through 2011-12 with data
gathered from www.covers.com.
Using the exact model from Dare and Dennis (2011), shown in the
previous section, we calculate mean forecast errors (the difference
between the expected and actual game outcomes) using data from the
2005-06 to 2011-12 seasons for a number of identifiable game
characteristics. The results are shown in Table 1.
Like the results in Dare and Dennis (2011), all mean forecast
errors from this sample are positive. In terms of the home-underdog
bias, the results from 2005-06 to 201112 reveal the opposite outcome
compared to the earlier sample period. The null hypothesis that the mean
forecast error is zero can be rejected for away favorites, but cannot be
rejected for home underdogs. Therefore, the results from the later
sample, under the assumptions of Dare and Dennis (2011), show that
bettors now underestimate the scoring ability of away favorites, but
correctly estimate the scoring ability of home underdogs. Therefore, the
home-underdog bias would be more properly called the away-favorite bias.
Our data goes back to the 1985-86 season. Breaking this sample into
5-year intervals (6 years for the most recent period), we examine how
the model of Dare and Dennis performed over these subsamples, focusing
on the groupings of away favorites and home underdogs with t-stats in
parentheses and are presented in Table 2 below.
As can be seen from Table 2, there are considerable differences
across the five-year periods, especially for away favorites. During the
first 5-year subsample (1985-1989), the mean forecast error was
negative, meaning that bettors overestimated the scoring ability of away
favorites. In all of the other subsamples, the mean forecast error was
positive, implying that bettors underestimated the scoring ability of
away favorites to some degree, including by a statistically significant
margin in the most recent subsample. The results for home underdogs show
more consistency across the subsamples as the mean forecast error was
positive in all periods shown, but the factor likely driving the overall
results reported in Dare and Dennis (2011) was during the late 1990s
(1995-1999). Based on the Dare and Dennis (2011) assumptions, breaking
the sample into subperiods reveals that there could have been a change
in the preferences of bettors for away favorites over the years, in
addition to varying degrees of underestimation of scoring of both away
favorites and home underdogs.
One explanation for this pattern of results is that bettors are
fickle and their tastes and preferences change over time. If we assume
that tastes and preferences do not change over time (Stigler &
Becker, 1977), however, there could be another explanation for this
pattern of results. If bookmakers have changed the nature of their
pricing decisions over time, similar results could be found without the
tastes, preferences, and expectations of bettors changing. We find the
conclusion that bettors underestimate the scoring of both away favorites
and home underdogs (or any category of teams shown in Table 1) to be
dubious given results that unders have outperformed overs in the totals
betting market in the NFL (Paul & Weinbach, 2002) and many other
sports. If bettors truly underestimated scoring by both teams, the under
should be a much more popular bet than the over, which previous research
has shown not to be the case (Paul & Weinbach, 2008, 2011).
Therefore, we believe there are other explanations for the home-underdog
bias that are consistent with constant preferences. The next section
explores these possibilities by analyzing more detailed betting market
data.
Betting Percentages and the Home-Underdog Bias
Data from www.sportsinsights.com show detailed information on
betting percentages on the favorite and underdog (in addition to the
over and under) for each NFL game from 2005 to 2011. These betting
percentages are based on the number of bets placed on each side in the
wagering proposition, not on dollars wagered. Although the actual amount
of money bet is not known, the betting percentages in the Sports
Insights data has been demonstrated to be very similar to the data
available on www.sportsbook.com, which reports the percentage of dollars
bet (see Paul & Weinbach, 2011, for details). Other anecdotal
evidence of imbalances in dollars bet on either side of propositions
exists. During the 2012 NFL season, comments by sports book operators
and industry experts in the media remarked on the lopsided betting on
the Monday Night Football game between the Green Bay Packers and Seattle
Seahawks early in the season, where a poor call at the end of the game
not only changed who won the game, but also changed which team covered
the point spread. Accounts of the wagering action on the game noted a
heavy betting imbalance toward Green Bay, who ultimately lost the game
and whose bettors lost their bets, with the reported percentages
(generally around 70%) in line with forecasts of betting percentages for
similar games in Paul and Weinbach (2008, 2011). We assume that the
percentage of bets placed on either side is highly correlated with the
percentage of dollars bet and treat them as equivalent. Humphreys, Paul,
and Weinbach (2010) discuss the relationship between bets placed and
dollars bet.
Under the balanced-book model, the amount bet on either side of a
proposition should tend to be even on average, without systematic and
predictable patterns. The model predicts that the betting volume should
be equal on average because bookmakers set prices and adjust them
periodically to achieve balanced betting on each side of wagering
propositions. This balanced betting eliminates their risk and allows the
sports book to earn a certain return equal to the vigorish (commission)
on losing bets. Previous tests of the balanced-book model in the NFL
soundly reject the null hypothesis of a balanced book (Levitt, 2005;
Paul & Weinbach, 2008; 2011). Table 3 summarizes the betting
percentages for all NFL games, games with home favorites, and games with
away favorites in terms of the percentage of bets on the home team, away
team, the over, and the under for the Sports Insights data over the
period 2005-2011.
Table 3 reveals rather straightforward patterns in betting volume.
Bettors slightly prefer to bet the away team to the home team. Depending
on whether the home team or away team is favored changes the side
bettors prefer. Bettors slightly prefer home favorites by a 57%-43%
margin, but have an extreme preference for away favorites by a 71%-29%
margin. We hypothesize that this actually has very little to do with
preferences for betting on teams on the road or at home, but has
everything to do with the relative quality of teams in the league. The
teams that are performing the best and have a history of success are
much more likely to be home favorites and the best-of-the-best teams
have enough of a talent advantage on their opponent to overcome the
implicit home field advantage and become away favorites. The patterns in
the betting percentages on Table 3 simply reflect that bettors prefer to
wager on the best teams, just like they prefer to attend games when
teams are performing well and to watch games on TV between the best
teams. The over/under bets reveal (across all specifications) that
bettors prefer the over to the under by a 65%-35% margin. This shows
that bettors prefer to wager on high scoring games, not defensive
struggles. The behavioral explanation that bettors behave like fans and
enjoy wagering on the best teams and like to watch (and place bets on)
scoring is simple, straightforward, and, we believe, intuitively
appealing.
To further illustrate this point, we present simple regression
results with the percentage bet on the favorite (in the sides market)
and the over (in the totals market) as the dependent variables in two
regression equations. The independent variables are an intercept, the
absolute value of the point spread, and a dummy for a team being an away
favorite in the sides regression and an intercept and the total in the
totals market regression. Under the balanced-book model, the intercept
should equal 0.5 and the other variables should not be statistically
significant. We estimate these regression models using OLS. Results are
presented on Table 4 below. Statistical significance is noted with *
-notation (*** -significance at the 1% level) and t-statistics are shown
in parentheses below the parameter estimates.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
The regression results reveal that bettors appear to prefer away
favorites by a large margin, with the simple designation of a team as an
away favorite leading to a 16%+ increase in the percentage bet on that
team. In addition, the bigger the favorite, the greater the percentage
of bets on the team, with each additional point of the point spread
leading to a 1.3% increase in the percentage bet on that team. Given
that the best teams are the teams who earn the designation of away
favorites and are likely to be biggest favorites on the board (both in
home games and away games), it is clear that bettors prefer the best
teams when they place wagers. Also, they clearly prefer to bet the over
in games with higher totals, as the percentage bet on the over rises
with each point of the total (by nearly one percentage point). The
preferences of bettors are easily identified, and there is no strong
evidence or logical justification that would suggest that the sports
books should be expected to be balanced when these preferences are so
easily identifiable.
[FIGURE 3 OMITTED]
Another way to present the results is to simply plot the
relationship between the percentage bet on a team and the team winning
percentage. Obviously, this unconditional approach does not capture all
of the information that a point spread on a game would, but it clearly
illustrates how team quality affects the percentage bet on the team.
Each of the three following figures show the percentage bet on the team
on the vertical axis and the straight-up win percentage of the team on
the horizontal axis. The first figure is for all games, the second
figure is for home teams, and the third figure is the away team.
In all three figures, it is quite clear that the percentage bet on
a team increases with the winning percentage of the team. Under the
balanced-book hypothesis, this simply cannot be the case because the
point spread is assumed to be set to attract equal amounts of money on
each side of the proposition. In each figure, the most successful teams
on the field attract the highest percentage of bets in the wagering
market.
One last simple example to demonstrate that bettors prefer to wager
on the best teams can be illustrated by calculating average betting
percentages by team. Again, under the balanced-book hypothesis, the
point spread will be set and changed based on bet volume to balance the
betting action. Any individual team should not accumulate a majority of
bets. A simple calculation of the average percentage bet by team shows a
clear hierarchy, where the best teams in recent years are also the ones
who are the most popular to bet. Table 5 shows the betting percentage by
team in the NFL for the sample period. Listed are the average percentage
bet on the team as an away team, the average percentage bet on the team
as a home team, the difference (in percentages) of home compared to
away, the average point spread as an away team, the average point spread
as a home team, and the difference between the average home point spread
and average away point spread.
Table 5 shows that the best teams over the past six years have also
received the most bets. Perennial playoff teams, conference champions,
and Super Bowl winners populate the top teams who receive the backing of
the betting public. Teams with the most well-known quarterbacks, a key
position both for the game and for the fans, the New England Patriots
(Tom Brady) and the Indianapolis Colts (Peyton Manning until his injury
in 2011), top the list. (3) Other successful teams like the Pittsburgh
Steelers and New York Giants also rank near the top of the list. The
teams at the bottom of the distribution in terms of fan interest in
betting include teams that have not had much success through most of the
seven-year sample period. The Oakland Raiders, Houston Texans, and
Detroit Lions, who were rather poor teams until recently, attracted the
fewest bets.
Another point that can easily be seen in Table 5 is that teams
attract a higher percentage of the bets in games when they are the away
team, rather than the home team. Each of the 32 teams attracted a higher
average percentage of the bets when they were the visiting team. Teams
are bigger underdogs or smaller favorites on the road due to the home
field advantage (see the last three columns of Table 5), which is
commonly estimated as three points. Bettors appear to be more willing to
wager on a team when they are the away team, perhaps due to the fact
that the point spread appears more favorable when a team is on the road.
This result is consistent with the idea that bettors do not believe the
home field advantage is worth as much as the point spreads imply, or
somehow fail to recognize the full potential advantage of being the home
team.
Bettor Biases, Sports Book Pricing, and Market Efficiency
The previous section suggests the presence of behavioral biases in
betting on NFL games. The betting percentage data reveal that this bias
is not an underestimation of the scoring ability of home underdogs, as
suggested by Dare and Dennis (2011), but a more straightforward
behavioral bias: fans prefer to wager on the best teams in the league.
The bigger the favorite, particularly when the favorite is the away
team, the higher the percentage of bets that accumulates on that team.
The best teams in the league are the teams who are favorites on the road
and are the biggest home favorites. In addition, fans prefer to wager on
games with a possibility of more scoring in the totals market and bet
more on away teams in general, who may view these as opportunities to
bet on a team at a discount, if fans do not fully appreciate the value
of the home field advantage included in to the point spread.
A key question in this analysis: Do any of these biases result in
profitable betting strategies for those willing to wager against public
opinion? If bettors can earn profits by taking positions against the
betting public, specifically by wagering on home underdogs and/or
underdogs in general, this would imply that the behavioral bias is
affecting the pricing of games and market inefficiencies may exist.
Table 6 below illustrates that this is not the case. Table 6 shows the
win-loss-push records and win percentages resulting from simple
strategies of betting favorites and underdogs for games with home
favorites, games with road favorites, and all games. In addition, the
results for the totals market are shown in terms of over and under
wagers.
None of the win percentages from these simple strategies win enough
to overcome the bookmaker's commission. Sports books use a wager
$11 to win $10 rule, implying that bettors must win more than 52.38% of
wagers to earn profits. (4) Although bettors have a clear bias toward
road favorites, favorites in general, and the over, these biases do not
appear to be priced into the market, as favorites and underdogs (overs
and unders) each win about 50% of the time, with contrarian strategies
earning negative returns.
It does not appear that sports books set prices based on the
expected actions of biased bettors. While sports books may adjust prices
in response to betting imbalances, bettors are shown to exhibit obvious
and predictable tendencies and sports books appear to set a price as a
forecast of game outcomes, despite predictable imbalanced betting
activity from the betting public. This was observed in previous studies
of NFL betting percentages in the wagering market (Paul & Weinbach,
2008, 2011) and is seen in this setting as well. In the time period
analyzed, the assumption that the prices set by sports books are a
simple reaction to the decisions made by bettors does not appear to be
valid, nor does a strategy of shading the point spread in the direction
of the more popular team (e.g., Levitt, 2004). Rather, it appears that
the sports book sets point spreads and totals as forecasts of game
outcomes (perhaps as a response to the actions of a small group of
informed bettors), allowing the betting imbalances to persist over time.
Discussion and Conclusions
The results above suggest the presence of significant bettor biases
in the NFL betting market that are both persistent and predictable.
Bettors behave much like fans; they tend to place wagers on the best
teams and on the outcome of a high total score (the over). A preference
for betting on the best teams manifests itself as a preference for
favorites overall (with bigger favorites attracting even a higher
percentage of the betting action) and for road favorites in particular.
The best teams in the league are typically the only teams able to
overcome an opponent's home field advantage and become listed as
favorites when they are the away team. In addition, it appears that
bettors underestimate the impact of the home field advantage, as every
team in the league received a higher percentage of bets as an away team
than they did as a home team. The home-underdog bias is a
straightforward combination of fans preferring the best teams (and
higher scoring) and a systematic undervaluation of the impact of home
field.
Although the home-underdog bias was shown to be profitable in the
past, recent studies (including this one) do not find profitability from
wagering on home underdogs. In our analysis of data from the 2005-2011
NFL seasons, home underdogs actually underperformed, winning only 48.35%
of their games against the point spread, despite the huge betting bias
toward road favorites. This is likely due to the balanced-book model not
describing bookmaker's decisions. If sports books allow betting
imbalances, but price as a forecast of game outcomes, the null
hypothesis of efficient markets will not be rejected, despite clear
behavioral biases in the market, as shown in this study.
Given past successes of wagering strategies based on betting home
underdogs and the overall findings of Dare and Dennis (2011), it is
possible that a key element in this market has changed over time.
Assuming constant tastes and preferences (Stigler & Becker, 1977),
meaning that, in general, bettors (like fans) have always preferred to
bet on the best teams and high-scoring games, we consider the
possibility that the pricing strategies of sports books have changed
over time. Due to relative price changes in the market, it is possible
that sports books priced differently in the past (especially 1970s
through part of the 1990s) than they do today. If this is the case,
profitable strategies may have existed in the past but have changed due
to the nature of sports book pricing.
There may be good reason to believe that sports books have changed
how they set and move point spreads over time, due largely to advances
in technology, increased access to information, and increased
competition in the betting market. The dramatic decline in the cost of
historical and current information, driven by the adoption of the
internet and the reduction in costs of data storage and retrieval, as
well as hardware and software, make it easier for bettors and sports
books to access and analyze information. It is now quick and easy for an
individual to back-test betting strategies, learn information about
teams and players, and know the opinions of a number of expert
prognosticators each weekend. Some of the imbalances in betting flows
may actually be fueled or accelerated by disproportionate coverage from
online, radio, and television sources that may drive the actions of
uninformed bettors.
While technology has improved the information available to sports
book managers, it has also improved the information available to
informed bettors. If informed bettors have either become more numerous
or their forecasting accuracy has increased, this also naturally drives
sports books to price as an optimal forecast of game outcomes due to the
actions of this small group of bettors. Under this scenario, the
preferences of a large group of uninformed bettors in a betting market
could generate clear behavioral biases toward the best teams and the
over, and closing point spreads and totals that are still unbiased
forecasts of game outcomes.
An additional important factor driving this change in sports book
behavior is increased competition in the betting market. In the 1990s,
online sports books became a major competitor for both legal sports
betting in Nevada (and around the world) and local illegal sports books
in the U.S. Increased competition, as theory would predict, would lead
prices (point spreads and totals) to converge. In addition, increased
competition likely made it less attractive for an individual sports book
to systematically exploit known bettor biases, such as those for away
favorites and overs.
To illustrate this point, suppose in a hypothetical market all
sports books shade point spreads toward away favorites. In the absence
of competition or through strong collusion between a small number of
sports books, this could be possible. As competition increases, however,
the incentive to set a lower point spread on the away favorite (more in
line with game outcome expectations) becomes quite tempting and perhaps
a profit-maximizing strategy. If betting the away favorites (best teams)
is popular with bettors, offering a slightly lower price than other
bookmakers would increase betting volume for an individual sports book.
This competition could be expected to pressure other sports books to
follow suit. The resulting prices would then converge across sports
books and would also gravitate toward becoming an unbiased forecast of
game outcomes. Behavioral biases may persist but be hidden by sports
books whose lines tended to gravitate toward unbiased forecasts of game
outcomes.
Similarly, suppose that all sports books set point spreads as
forecasts of game outcomes. A single sports book may attempt to shade
the point spread by raising the price on away favorites. Even if this
sports book has some market power with bettors who may not stray from
their regular bookmaker, it is possible that the new inflated line
causes some regular customers to frequent other sports books or attracts
enough attention to become lopsided on the underdog at an inflated line.
If the line move is large enough so that a bet on the contrarian
position has a greater than 52.38% chance of winning, it could attract
bets from informed bettors (or even other sports book managers) to take
advantage of the inflated line. Deterring bettors who place wagers with
a negative expected value and attracting bettors who wish to make a
wager that may offer a smaller negative expected value or even positive
expected value is likely not a good bookmaker strategy for the long run.
Overall, the reduced cost of information and communication applies
greater pressure toward equilibrium in this market where sports books
have a strong tendency to offer prices that are essentially forecasts of
game outcomes, though behavioral biases are widespread and persistent,
and tests of market efficiency cannot be rejected. In the past, due to
the higher costs of technology and information, and a lack of
competition, sports books could more easily shade lines in obviously
biased situations and restrict the actions of informed bettors by
enforcing betting limits ("booking to face"), so that these
strategies could be profit maximizing. Some basic strategies, such as
wagering on a subset of home underdogs or unders, could have been
profitable for a disciplined and diligent bettor, though such a bettor
would likely be constrained to posted house betting limits on these
wagers. Since sports books reserve the right to reject any wager from
any person for any reason, these strategies would constantly be at risk
of being shut out of the market if their actions upset the sports book
manager. The ability to limit the influence of individuals in the
marketplace allowed point spreads to move in the direction of the
underlying biases of bettors. This would explain the findings of earlier
studies that identified contrarian strategies that yielded positive
returns.
Given increased competition (spurred by innovations in technology),
however, where contrarian strategies may once have been possible, it has
apparently become increasingly difficult to produce a strategy that
could produce a rejection of the null hypothesis of market efficiency.
While the common assumption in financial markets is that this
"market correction" must be a result of market participants
(investors or bettors) learning and changing their behavior, the driving
force behind this change is likely the evolution of pricing strategies
of sports books within the market due to increased competition and
possible response to a small group of informed bettors. While this
distinction may not matter to some, for they are observationally
equivalent, we believe that it is noteworthy that there appears to be
and likely always has been a strong component of consumption and
behavioral biases behind sports betting markets. Although sports books
risk losing money on any individual game or day, as opposed to the
assumptions of the balanced-book hypothesis where they earn their
commission without risk on each game, the sports book still earns its
commission on losing bets in the long-run by offering prices that evenly
distribute wins between favorites and underdogs (or overs and unders).
This is likely a long-run profit maximizing strategy as well, as the
recreational bettors do not lose their money as quickly (under the
balanced-book model, if betting lines become inflated on popular teams,
the sports book would collect a commission, but the recreational bettors
would be generating net transfers to "informed traders" on the
other side). This may keep more bettors placing wagers week after week
and season after season, instead of having their bankrolls depleted
early, decreasing the likelihood of placing wagers in future weeks,
months, and seasons. In the end, betting is a zero-sum game, with real
transactions costs that must be recovered by the sports book. The
average return earned by bettors must therefore be negative in the long
run.
This explanation is consistent with earlier findings of market
inefficiency and current findings supporting market efficiency without
the need for bettors' tastes and preferences to change, or
requiring new market participants to enter to exploit sports book prices
and bring the market back to efficient prices. Most bettors can wager as
a form of consumption rather than investment, with clear and predictable
preferences for betting on the best teams and scoring, yet prices in
these markets still remain unbiased forecasts of game outcomes. In this
simple financial market, strong behavioral biases exist, yet prices are
such that they provide unbiased forecasts of game outcomes due to the
incentives of the market makers (sports books), increased competition
for their services, and the actions of a small number of informed
bettors.
Brad R. Humphreys is on the faculty of the Department of Economics,
in the College of Business and Economics at West Virginia University.
His research interests include the economic impact of professional
sports teams and facilities, the effect of social regulations on
intercollegiate athletics, the economic determinants of participation in
physical activity, and the financing of professional sports facility
construction.
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Brad R. Humphreys [1], Rodney J. Paul [2], and Andrew P. Weinbach
[3]
[1] West Virginia University
[2] Syracuse University
[3] Coastal Carolina University
Endnotes
(1) Gandar, et al. (2002), issued a correction to the methods used
for calculating a unit bet.
(2) Dare and Dennis (2011) are not the first to use this sort of
model. A similar model was also used by Cain, et al. (2000), and
Ioannidis and Peel (2005).
(3) For the period 2005-2010, the Indianapolis Colts received 72%
of the bets on average as the away team, the highest percentage of bets
for any NFL team. In 2011, however, without Peyton Manning, the Colts
received only 43.75% as the away team and 31.85% as the home team.
(4) The percentage of winning bets (WP) necessary to break even
under the 11-for-10 rule is obtained by setting the expected value of
the random variable, a gamble WP(10) + (1 - WP)(11), equal to zero
(Zuber, Gandar, & Bowers, 1985).
Rodney J. Paul is a professor in the Department of Sport Management
at Syracuse University where he specializes in the economics and finance
of sport, macroeconomics, and international economics. He has presented
at conferences nationally and internationally, and his work has appeared
in a number of journals and book chapters on sport economics and
business.
Andrew P. Weinbach is a professor in the E. Craig Wall Sr. College
of Business Administration at Coastal Carolina University. His research
interests include applied microeconomics, sports economics (patterns of
consumer interest in live sporting events, including fan attendance,
television ratings, and betting participation), industrial organization,
and financial economics.
Table 1: Mean Forecast Errors--NFL Betting Market--2005-2011 Seasons
Characteristic Number of Mean forecast t-statistic
observations error
Favorites 1791 0.7549 3.2456 **
Underdogs 1791 0.3881 1.7601
Home team 1793 0.5290 2.3102 *
Away team 1793 0.5982 2.6695 *
Home favorites 1196 0.5355 1.8821
Away underdogs 1196 0.3037 1.1427
Away favorites 595 1.1958 2.9613 **
Home underdogs 595 0.5504 1.4276
Table 2: Mean Forecast Errors--NFL Betting Market--5-Year
Intervals
Years Away Home underdogs
favorites
MFE 1985-1989 -0.7964 0.7254
(-1.4972) (1.3146)
MFE 1990-1994 0.1561 0.6445
(0.3216) (1.4000)
MFE 1995-1999 0.1485 1.4550
(0.2881) (2.9201 **)
MFE 2000-2004 0.2906 0.1819
(0.8093) (0.5321)
MFE 2005-2011 1.1958 0.5504
(2.9613 **) (1.4276)
Table 3: Average Betting Percentages 2005-2011
Situation % bet on % bet on % bet on % bet on
home away over under
All games 47.55% 52.45% 64.94% 35.06%
Home favorites 56.94% 43.06% 64.88% 35.12%
Away favorites 28.72% 71.28% 65.06% 34.94%
Table 4: Sides and Totals Regression Results--NFL 2005-2011
Dependent Dependent
variable: variable:
Percentage bet Totals Percentage bet
Sides regression on favorite regression on over
Intercept 48.98 *** Intercept 23.63 ***
(92.32) (10.99)
Absolute value of 1.30 *** Total 0.98 ***
point spread (18.64) (19.32)
Away favorite 16.25 ***
dummy (29.43)
Table 5: NFL Team Betting Percentages and Average Point
Spreads Home and Away 2005-2011
Difference
% bet % bet (home
Team as away as home -away)
New England Patriots 69.43 59.96 -9.46
Indianapolis Colts 67.93 57.79 -10.14
Pittsburgh Steelers 64.32 55.61 -8.71
San Diego Chargers 62.34 56.30 -6.04
Green Bay Packers 61.96 55.68 -6.29
New Orleans Saints 61.86 56.15 -5.71
Philadelphia Eagles 60.36 50.43 -9.93
New York Giants 60.11 56.88 -3.23
Cincinnati Bengals 58.88 48.18 -10.70
Dallas Cowboys 58.77 51.30 -7.46
Baltimore Ravens 56.27 50.50 -5.77
Atlanta Falcons 56.07 49.95 -6.13
Tennessee Titans 52.88 46.29 -6.59
Chicago Bears 52.63 49.73 -2.89
Denver Broncos 52.07 47.46 -4.61
New York Jets 50.27 46.95 -3.32
Carolina Panthers 49.57 48.54 -1.04
Minnesota Vikings 48.52 46.91 -1.61
Jacksonville Jaguars 48.38 44.70 -3.68
Seattle Seahawks 47.66 45.84 -1.82
Kansas City Chiefs 47.14 46.38 -0.77
Arizona Cardinals 47.07 43.66 -3.41
Houston Texans 46.96 45.39 -1.57
San Francisco 49ers 46.16 41.79 -4.38
St. Louis Rams 45.93 39.43 -6.50
Detroit Lions 45.23 39.70 -5.54
Tampa Bay Buccaneers 44.79 42.46 -2.32
Washington Redskins 44.77 40.32 -4.45
Miami Dolphins 43.95 39.27 -4.68
Buffalo Bills 43.79 42.09 -1.70
Cleveland Browns 41.39 36.84 -4.55
Oakland Raiders 41.16 38.91 -2.25
Difference
(home
Average Average point
point point spread
spread spread -away
as away as home point
Team team team spread)
New England Patriots -3.438 -9.116 -5.68
Indianapolis Colts -1.375 -5.893 -4.52
Pittsburgh Steelers -2.259 -6.955 -4.70
San Diego Chargers -2.036 -7.500 -5.46
Green Bay Packers 0.223 -4.616 -4.84
New Orleans Saints -0.518 -4.682 -4.16
Philadelphia Eagles -0.205 -5.027 -4.82
New York Giants 0.218 -4.868 -5.09
Cincinnati Bengals 2.777 -1.830 -4.61
Dallas Cowboys -0.759 -6.402 -5.64
Baltimore Ravens 0.429 -5.089 -5.52
Atlanta Falcons 2.080 -3.045 -5.13
Tennessee Titans 2.955 -2.098 -5.05
Chicago Bears 1.848 -3.250 -5.10
Denver Broncos 2.241 -3.045 -5.29
New York Jets 3.170 -2.545 -5.71
Carolina Panthers 3.089 -2.036 -5.13
Minnesota Vikings 2.429 -3.188 -5.62
Jacksonville Jaguars 3.063 -2.491 -5.55
Seattle Seahawks 3.107 -2.688 -5.79
Kansas City Chiefs 5.714 0.277 -5.44
Arizona Cardinals 3.652 -1.643 -5.29
Houston Texans 4.116 -1.214 -5.33
San Francisco 49ers 5.750 -0.063 -5.81
St. Louis Rams 6.196 3.027 -3.17
Detroit Lions 6.866 1.911 -4.96
Tampa Bay Buccaneers 4.429 -0.625 -5.05
Washington Redskins 3.571 -0.804 -4.38
Miami Dolphins 4.464 -0.696 -5.16
Buffalo Bills 5.732 0.563 -5.17
Cleveland Browns 6.768 1.580 -5.19
Oakland Raiders 7.804 1.911 -5.89
Table 6: Betting Simulations--NFL 2005-2011
Favorites Underdogs Pushes
Home favorites 570 594 32
Away favorites 298 279 18
All games 868 873 50
Overs Unders Pushes
All games 894 852 45
Favorite Underdog
win win
percentage percentage
Home favorites 48.97% 51.03%
Away favorites 51.65% 48.35%
All games 49.84% 50.14%
Over win Under win
percentage percentage
All games 51.20% 48.80%
