1. NFL Underdog Market Efficiency
By: Matthew R. Barbian
Faculty Advisor: Doctor Teshome Abebe
Eastern Illinois University
May, 2015

2. 1. Introduction: Observing the NFL underdog market
2. Literature Review
3. Kelly Criterion
4. A Random Walk Down Wall Street
5. Efficient Market Hypothesis
6. Bookmakers available information
7. Putting the fact together
8. Data
9. Methodology
10. Results
11. Conclusion
12. References
Abstract
This paper intends to analyze NFL underdog market inefficiencies with an intention
to refute the Efficient Market Hypothesis (EMH). Researchers have analyzed many
different angles of finding inefficiencies in the NFL betting market- whether it be
point spreads, money line, over/under. NFL Regular Seasons 2006-2014 results
were collected and put into a modified version of the Kelly Criterion in an attempt to
prove inefficiency. Prior research using the Kelly Criterion observed point spread
bets, which will result in a fixed payout ratio. Due to the money line having different
payouts from the bookmaker balancing the line, the payouts for a line will be
variable. I fail to refute the Efficient Market Hypothesis, and find that in nine
seasons of data, the market remained efficient in the ong run.

3. 1. Introduction
The NFL betting market is not a mirror image of the stock market, but they do
share some common traits. Sports gambling tends to be a zero-sum game, a wager
is lost or won. In the stock market, you may lose some of your investment, but you
are not likely to lose the entire investment. According to the EMH, stock market
efficiency causes existing share prices to always incorporate and reflect all relevant
information. By picking all closing lines, true value should be represented by all
relevant information. Information is offered by bookmakers to attract customers
and balance lines to maximize profits. If we follow the EMH, that information
offered is pointless to predict outcomes of the games. In both markets, there are
“experts” who charge fees to investors to help them profit. A method in which an
investor may obtain higher earnings would be to pick a riskier investments- hence
why underdogs were the topic of study.
2. Literature Review
Kuper (2012) concluded that the domestic NFL betting market for the closing
money lines of the 2011 season are statistically inefficient. The findings suggest that
the inefficiency is such that a true profit rendering strategy can be utilized. The
weak form EMH is observed by using ESPN’s “Week X: Pick ‘Em”, to strengthen the
prediction model. Although the information on the ESPN webpage consists only of
how the analysts’ performed in the previous week and a short write-up, the line will
not change due to demand. One single line will be used for the picks.

4. Dare (2006) found that the eleven-for-ten betting rule for sides and totals
(resulting in a minimum of 52.38 winning percent to profit) is an inadequate level to
deem inefficiency. Dare sets to find a new hurdle rate for inefficiency. He mentions
the fact that betting strategies cannot be diversified and needs much greater
required return than the risk-free rate. Dare also stated that “at a minimum, a
betting strategy should at least make the risk-free rate to be considered and
inefficiency”. Hurdle rates will vary using the money line, depending on the payout.
Different lines have different payout ratios, which will need different hurdle rates to
deem inefficiency.
Aadland and Wever (2010) build on previous research and expose a new
market inefficiency. A differential strategy of betting on home and visitor
underdogs with large closing lines can produce significant profitable returns.
Evidence shown from this study suggest that the recent NFL betting market has
underpriced large underdogs while bettors have failed to recognize the amount of
parity in the NFL. The inefficiency is consistent with a certain amount of herd
behavior toward highly publicized elite teams. Underdogs yield significant returns
from a low-risk, high-reward scenario. For the most part, bottom strength teams
can play with the medium strength teams and medium strength teams can keep up
with the top teams. The closer the spread is, the closer the game should be.
Difilippo (2012) hypothesized that bettors in a gambling market pay too high
a price in order to cater their biases from teams qualifying for the prior season’s
playoffs. It is stated that the structure of the betting marketplace, the
overabundance of naïve participants, and the limits on entry of informed bettors

5. allow for the existence of inefficient prices. Results from the 2004-2011 seasons
showed unprecedented profitability based on taking a contrarian strategy of
wagering against prior playoff teams in the following season’s opening week. Fan
bias’s plays a major role in market betting. Just because one team is seen as
superior to its opponent doesn’t mean that they will win the game. Week one tends
to have the most bias’s from fans- this can be explained by no recent trends or
statistics.
Golec and Tamarkin (1992) find that NFL bettors underestimate the home
field advantage and all too often ‘go with the winners’. Results show that the home
field bias is disappearing, but the bias towards favorites is slowly growing. As
biases towards favorite’s increases, market inefficiency in underdogs does as well.
the method adjusts for the appropriate level of risk and return for the strategy under investigation.
3. Kelly Criterion
The Kelly Criterion was originally intended for long distance telephone signal
noise issues while John Kelly worked at AT&T. This “new interpretation of
information rate” has since then rapidly spread into a general money management
system. Due to the level of risk associated with gambling, one must be able to adjust
for risk and return, which is what the Kelly Criterion does. Money line betting will
result in winning, losing the amount wagered, or the slight chances of a game ending
in a tie would result in a push. Before placing a wager, one must realize the risk they
are putting on the line in proportion to how much wealth they have. This is why I
have selected this criterion, as it can be used as a proportional wealth management
gambling system. By using the criterion, optimal proportions of wealth to bet,

6. return, and growth rate of each betting strategy will be calculated. A majority of the
NFL studies using this method use the point spread and have a constant payout ratio
in the formula. For my research, the payout ratio became variable because of
different money lines closing at slightly different values. By switching the ratios,
some winners from previous studies became losers, and winners pay a higher
return.
4. A Random Walk Down Wallstreet
“A random walk is one in which future steps or directions cannot be predicted
on the basis of past actions. Taken to its logical extreme, it means that a blindfolded
monkey throwing darts at a newspaper’s financial pages could select a portfolio that
would do just as well as one carefully selected by the experts”. Every team has
historical trends- from current trends to dating back to back many years before that.
These trends are offered by bookmakers to provide information to bettors. This
information is made available to get more customers. The objective of the
bookmaker is to adjust the line to create balance from demand to get a larger pool of
bets, because “the house always wins”. The bookmaker will make $0.09 on every
dollar bet from an automatic (-110) money line on point spreads and totals.
If future steps or directions cannot be predicted on the basis of past actions,
we can say that the outcome of any NFL game cannot be predicted of how they have
done in the past. Just because a team that has performed well at home is playing a
team that has performed poorly on the road doesn’t mean that the home team will
win. Obviously some teams are superior, but nothing is guaranteed. If all favorites

7. won, there would be no parity in the NFL and it would take a drastic downfall. If
everybody knew that a team was guaranteed to win a game, who would watch it?
There would be absolutely no value in the money line market. Nobody wants to see
a team continuously dominate. A game can change from any random event, or a
series of unexpected events. Lines will follow demand, but I expect some to prove
inefficiency in the short-run underdog market.
5. Efficient Market Hypothesis
The Efficient Market Hypothesis states that no stock is a better buy than any
other, a conclusion that justifies random choices. According to classical theory, a
stock price always equals the present value of expected dividends and that expected
dividends are the best possible forecasts because of rational expectations. The price
of a stock always equals the best estimate of the stock’s value. This equality implies
that undervalued stocks do not exist, thus, it’s futile to look for them.
The closing line represents the best estimate of the line’s value. That is the
balance made from the demand for the lines. Looking for undervalued money lines
are useless. Available information will represent the closing line- the movement in
line impossible to predict. If underdogs at the +3 spread win every week, available
information will show the result. Bettors would all place wagers on the +3 line,
which would make the line sell for a higher price. Even if the strategy yields a
positive results for a few games, seasons, how do you know when to stop?

8. 6. Bookmakers available information
The gambling market is an enormous market in which bookmakers have
made fortunes, bettors have won a pretty penny, or even blown there bankroll.
There are numerous bookmakers out there who must compete amongst each other
to keep up with such a profitable industry. Extensive trend reports are offered by
these bookmakers to offer information on a team’s historical performance given
certain game circumstances. As bettors interpret the information and make picks,
lines will change as demand changes. As a team becomes more favorable, a higher
price will be charged to purchase that pick. As stated before, a random walk is one
in which future steps or directions cannot be predicted on the basis of past actions.
There is no guarantee that a team will win a game, regardless of how they have
performed previously under certain conditions. Previous trends and performance
can lead to the belief that a team will win, but that is not a guarantee. Some people
claim to be experts, or purchase expert picks, but how can somebody claim to be an
expert at something that has an uncertain outcome? If an “expert” is so good at
making these picks, why are the services available to the public? An expert would
be able to find the inefficiencies in the market and make their own profit. If there is
more profit made from the fees than the picks, a high fee must be charged in
exchange for the picks offered.

9. 7. Putting the facts together
All available information of previous performance from teams has been put
aside to observe betting on all underdog lines. I took Malkiel’s statement, “Taken to
its logical extreme, it means that a blindfolded monkey throwing darts at a
newspaper's financial pages could select a portfolio that would do just as well as
one”, and tested it on the NFL underdog market. If results show that certain closing
lines have consistently beaten the market, available information would be
irrelevant. The market provides information of what should happen in a game, but
inefficiencies can be found at certain lines. Historical odds of closing money lines
are not something offered to many bettors- and even so, why would they choose to
place a wager based on previous closing line trends instead of how a team
performs? Past trends provided by bookmakers, media, and word of mouth can’t
promise a winning wager. These variables will cause demand to change in a money
line, which will alter the risk and reward for both sides.
8. Data
Data was collected from footballlocks.com. Las Vegas historical closing lines
from 2006-2014 are offered, along with services to members. Kuper (2012) found
that “Docsports is an aggregate odds webpage that lists the closing lines from 6
other major NFL betting sources: bodog, BM Bookmaker,BetOnline, Dimes,
Intertops, and Legends. The correlation between footballines and docsports was
0.97”- so we can assume that football locks has similar correlation.

10. 9. Methodology
Money lines of winning under dogs from 2006-2014 NFL regular seasons
were gathered, allocated by point spread, and averaged out. A sample size of 2,304
games was observed to find if certain lines have proved inefficiency in the underdog
market. A ten dollar base rate was used to represent each wager. To determine
inefficiency, the Kelly criterion was chosen. Any line that produced a positive
optimal proportion of wealth to bet was considered efficient and proves market
inefficiency. This series of formulas is a proportional strategy for the optimum
money management strategy for betting. In previous studies using this system, the
point spread was observed. There is a fixed payout ratio in the point spread
criterion, which occurs from the (-110) that the bookmaker receives regardless of
the spread. By using the money line to analyze underdog efficiency, the payout ratio
has been changed to the average closing money line of each spread.
 Optimal proportion of wealth to bet: What percentage of your wealth to place
on a bet in a specific strategy.
 W = Win percentage of the betting strategy. In the data, each line different line
bet is considered a different strategy. For example, all games at +3 would be in
the same strategy,
 F = Payout ratio (average money line for each strategy, which will be variable
among all strategies)
o (W-(1-W)))/F
Growth factor of wealth to bet: The average expected increase in wealth per bet.

11. o (1+Payout ratio*Optimal proportion of wealth to bet)^Win %*(1-
Optimal proportion of wealth to bet)^(1-Win %).
o (1+FP)^W(1-P)^(1-W)
Optimum return to a betting strategy: The overall return for a strategy.
o (Growth factor of wealth to bet^Number of games bet in a strategy)-1
o R=G^N-1
10. Results
No underdog line proved inefficiency in the long run for nine seasons
observed for any of the lines. The largest run was at the +1 spread for three
seasons- which had the smallest average payout ratio. Even though the +1 proved
short-term inefficiency in consecutive seasons, it failed to beat the market in the
long run. Picking the +1 money line for those three seasons is very unlikely. To beat
the market, you would need to have perfect market timing and departure. Eighteen
lines proved efficiency over at least one season, but not in the overall model.
Significant lines were difficult to locate due to the uncommon large spread of
underdog wins. Only eleven lines had more than 20 observations. The eleven lines
are shown in graphs below. Optimal proportion of wealth to bet must break out of
the negatives to be considered an efficient betting strategy. In the second graph,
notice that the same trend lines are significantly above the trend line. The first two
graphs contradict the third graph. Larger underdog strategies will require less to
bet and have lower expected growth, but offer a higher payout. We can observe

12. from the final graph that +3 spread occurred most frequently. This spread beats the
trend line in every aspect of the Kelly Criterion.
-0.0025
-0.002
-0.0015
-0.001
-0.0005
0
1 1.5 2 2.5 3 3.5 4 4.5 5.5 7 7.5
Point Spread
% Of Wealth to Bet
% Of Wealth to Bet
Linear (% Of Wealth to Bet)
0.75
0.8
0.85
0.9
0.95
1
1 1.5 2 2.5 3 3.5 4 4.5 5.5 7 7.5
Point Spread
Growth Factor of Wealth to Bet
Growth Factor of Wealth to
Bet
Linear (Growth Factor of
Wealth to Bet)

13. -1.2
-1
-0.8
-0.6
-0.4
-0.2
0
1 1.5 2 2.5 3 3.5 4 4.5 5.5 7 7.5
Point Spread
Optimum Return to a Betting Strategy
Optimum Return to a
Betting Strategy
Linear (Optimum Return to
a Betting Strategy)
0
50
100
150
200
250
300
350
400
450
1 1.5 2 2.5 3 3.5 4 4.5 5.5 7 7.5
Point Spread
Line Frequency
Line Frequency
Linear (Line Frequency)

14. 11. Conclusion
The adjusted Kelly criterion does not show long-term inefficiencies. Betting
a particular market price will not profit or break even unless market timing and
departure are known. Being able to choose one of these lines during a profitable
period is not likely. Sports betting can be very risky and must be managed properly
to avoid large loss of wealth. The closest line of breaking inefficiency was +3. After
viewing the data above, we can assume that lines occurring more frequently will
bring more upsets. Further study may show that the +3 line will, over time, beat the
market as it occurs more frequently. When adjusting the results to see when long-
term profitability would be met for +3, 13 more wins with the same number of
games bet would become a profitable line. The winning percentage would end up at
50.761421, optimum percent of wealth to bet would then be a positive number. If
this study was taken back a few more seasons, perhaps the +3 closing line would
beat the market in the long run. The most frequently occurring line with a close
spread will result in more upsets, and by adding more seasons to this study results
may deem the +3 closing money line as inefficient.

15. References:
Dare, William.H. 2006. Risk, Return, and Gambling Market Efficiency. Oklahoma State
University, Stillwater.
Filippo, M. D. 2012. Early Season Inefficiencies in the NFL Sports Betting Market, Ohio
University, Athens.
Footballlocks.com (2006-2014 historical closing lines)
Golec, J., & Tamarkin, M. 1991. The degree of inefficiency in the football betting
market. Journal of Financial Economics, 30, 311—323.
Kuper, A. 2012. Market efficiency: is the NFL betting market efficient? University of
California Berkeley,
Malkiel, B. G. 1999. “A random walk down wallstreet” New York, London: W.W.
:Norton & Company.
Wever, S., & Aadland, D. 2012. Herd Behaviour and underdogs in the NFL. Applied
Economics Letters, 19 (1), 93-97.