Using betting market odds to measure the uncertainty of outcome in Major League Baseball.
Paul, Rodney J. ; Weinbach, Andrew P. ; Borghesi, Richard 等
Using Betting Market Odds to Measure the Uncertainty of Outcome in
Major League Baseball
Major League Baseball offers an interesting dilemma in terms of
competitive balance. Schmidt and Berri (2001) show that the 1990s, using
traditional measures of competitive balance based on win percentages,
were the most competitive decade in the history of Major League
Baseball. As Schmidt and Berri (2001) note, during the same timeframe,
fans and the media believed that baseball became much less competitive.
This apparent dichotomy begs the question of how the field of economic
research on sports could be so different from public perception. If the
1990s were truly the most competitive decade in baseball, why did the
fans and media not recognize this?
One possible explanation is that economists are more acute
observers of sporting events and that fans in general cannot sort out
more competitive play from less competitive play. This explanation may
be appealing to economists, especially when sitting around at the sports
bar, but it does not offer insight into the source of this bias in
judgment by fans and the media. Another possible explanation is that the
term "competitive balance" means something different to the
typical fans and media members who attend and watch countless baseball
games. Their version of "competitive balance" may more closely
resemble the term "uncertainty of outcome," a familiar term to
economists that focuses on the doubt, or lack thereof, in the outcome of
a sporting event. The economic definition of "competitive
balance," on the other hand, uses win percentages of the teams or
other ex-post figures (e.g., championships, division titles) to measure
competitive balance within leagues on an annual basis. There are a wide
range of studies in the economic literature on competitive balance in
baseball and other sports. Excellent discussion on the topic is
available in articles by Sanderson and Siegfried (2003) and Fort (2003)
in a special issue of the Journal of Sports Economics.
Although the economic definition of competitive balance is quite
useful, there are many reasons to consider that uncertainty of outcome
measures may be much more useful and important. First, expectations of
the uncertainty of outcome are formed ex-ante, when consumer (fan)
decisions take place. These decisions include purchasing tickets to the
game and watching the game on television. These choices by consumers are
ultimately the most important factors to the league, teams, television
networks, and advertisers, who are all attempting to maximize profits.
Current measures of competitive balance may capture the desires of fans
to see close games, but it can only do this after the games have
actually been played.
Given the fact that understanding fan preferences would be
advantageous before games are played, the question remains if there is a
way to measure the uncertainty of outcome before games are actually
played. Thankfully, there exists a market that estimates the uncertainty
of outcome. This market is the betting market for Major League Baseball.
Odds that exist on baseball games serve as a proxy for the uncertainty
of outcome of games. The higher the average odds (in absolute value--as
bettors must lay more than a dollar to win a dollar), the more certain
the outcome of the game appears to be. The closer the odds are to even
money propositions, however, the more uncertainty of outcome there is in
baseball games. The use of betting lines to estimate the uncertainty of
outcome in games is not new, as it was used in attendance studies of
baseball (Knowles, Sherong, & Haupert, 1992; Rascher, 1999) and was
directly suggested as a measure of uncertainty of outcome for soccer in
Peel and Thomas (1988, 1992) and Forrest and Simmons (2002). Betting
odds were found to be the superior measure of uncertainty of outcome,
although it had little predictive power in forecasting attendance (nor
did other uncertainty of outcome measures), in Premier League Football
matches in Spain (Buraimo, Forrest, & Simmons, 2006).
Researchers have previously addressed the question of market
efficiency in the baseball betting market. Woodland and Woodland (1994)
found a reverse favorite-long shot bias, where favorites were overbet.
When correcting for the proper specification of a unit bet, however, as
performed in Gandar, Zuber, Johnson, and Dare (2002), the reverse
favorite-longshot bias was no longer found in general in the baseball
market. If the betting market for Major League Baseball cannot reject
the null hypothesis of efficient markets, then the odds give a good
representation of the prediction of the outcome of a game. Therefore,
the average odds would give an excellent measure of the uncertainty of
outcome. If this measure of uncertainty of outcome reveals something
different about market perceptions of baseball games compared to ex-post
measures of competitive balance, it will help to explain the difference
between the findings of Schmidt and Berri (2001) and the thoughts
generally expressed on competitive balance by the baseball-watching
public.
Efficient Markets and the Reverse Favorite-Longshot Bias in
Baseball
Before proceeding to use baseball betting odds as a measure of the
uncertainty of outcome, it is necessary to test whether the betting odds
themselves represent an unbiased and optimal prediction of the outcome
of the game. To do this, we test the betting market for Major League
Baseball from 1990-2006 compared to the results expected under the
efficient markets hypothesis. Data was taken from the Stardust
sportsbook as compiled by www.thelogicalapproach.com.
In previous research on baseball betting markets, a reverse of the
favorite-longshot bias was found in odds-based wagering markets. The
bias was first noted by Woodland and Woodland for Major League Baseball
(1994) and the National Hockey League (2001). In both of these leagues,
Woodland and Woodland found that favorites were overbet and underdogs
were underbet, the opposite result of what was seen in the horse racing
studies (for review of the literature, see Sauer, 1998).
Gandar et al. (2002) and Gandar, Zuber, and Johnson (2004)
corrected the studies of Woodland and Woodland in baseball and hockey,
respectively, for the proper definition of a unit bet on the favorite
and the underdog. In baseball (Gandar et al. 2002), the reverse
favorite-longshot bias was no longer found to be significant, although
in hockey (Gandar et al. 2004) the bias was still found to be
significant, although less pronounced. Gandar et al. (2002) and Gandar
et al. (2004) also noted that the bias is not strictly along the lines
of favorite/longshot but also a bias in terms of whether the favorite is
playing at home or on the road. In general, it appears that road
favorites are significantly overbet in these markets.
Using the betting simulations test outlined in Woodland and
Woodland (1994) and updated for the proper use of a unit bet by Gandar
et al. (2002), we test the returns to simple strategies of betting the
underdog (for the sample as a whole and for subsets of road underdogs
and home underdogs) compared to the results expected under the efficient
markets hypothesis. In addition, we use the distinction of slight
(underdog odds of less than 1.60) and heavy (underdog odds of greater
than or equal to 1.60) underdogs. Each grouping displays the number of
observations, returns (assuming a one dollar bet), expected returns
(assuming efficient markets), and z-statistics associated with the test
that actual returns are equal to expected returns. Results are shown in
Table 1.
In the overall results for the Major League Baseball gambling
market from 19902006, results are similar to those found in previous
seasons by Gandar et al. (2002), as the null hypothesis of efficient
markets cannot be rejected for the sample as a whole. Groupings of
slight and heavy underdogs in the overall sample also do not reveal
rejections of the efficient markets hypothesis. Losses on underdogs are
slightly lower than expected, although still negative for each grouping
in the sample of all games. (1)
In relation to the home/road distinction noted by Gandar et al.
(2002), road underdogs were not found to reject the null of efficient
markets. For home underdogs, only heavy home underdogs were found to
earn positive profits during this time frame, with a z-statistic that
rejects the null hypothesis of efficient markets at the 10% level.
Overall, the odds appear to represent a good forecast of the
outcome of baseball games. The efficient markets hypothesis could not be
rejected for any of the overall samples from 1990-2006, with only the
small subset of games with home underdogs managing to reject the null at
a 10% level. Therefore, we will use the odds on baseball games as a
measure of the uncertainty of outcome and an ex-ante measure of
competitive balance.
The Baseball Betting Market and Uncertainty of Outcome
Given the results of the efficient markets tests in the previous
section, where the null of efficient markets could not be rejected for
the Major League Baseball gambling market, we will now proceed to use
these odds as a measure of the uncertainty of outcome of baseball games.
Betting odds are formed in a market, where bettors wager on either team
against posted odds by sportsbooks. These bettors are likely to be part
of the multitude of fans that follow this sport in North America and the
world. Odds on baseball games are publicly available to all sports fans,
not only gamblers, through publications such as the USA Today, local
newspapers, and various websites on the internet.
Observing the betting odds for baseball games may shed some insight
into the findings of Schmidt and Berri (2001) and the related comments
of the media and fans. Although Schmidt and Berri found Major League
Baseball to be quite competitive during the 1990s, fans and the media
thought otherwise. Fans in general perceived baseball as becoming much
less competitive during this time frame. What they actually could have
been implying, however, is that the level of uncertainty of outcome has
lessened during this time frame.
If the uncertainty of outcome of baseball games has changed during
the 1990s (and beyond), this will likely be captured in the betting
market odds. Games where there are big underdogs have a low level of
uncertainty of outcome. Games where the odds are closer to even money
imply a greater level of uncertainty of outcome. The use of odds as a
measure of uncertainty of outcome has been used before in English Soccer
(Peel & Thomas, 1988, 1992; Forrest & Simmons, 2002).
It is important to note that betting odds as a measure of
uncertainty of outcome has distinct advantages over measures of
competitive balance above and beyond the obvious advantages of being
known before the game is played. Although win-loss percentages,
championships, and division or conference titles are all formed in a
binary manner (a team either wins or loses, wins a title or does not),
betting odds offers a measure of the strength of a favorite along a
continuous spectrum. A team that is a--400 favorite is much more likely
to win a game than a -200 favorite. With competitive balance figures, a
win is simply a win. With betting market odds as a measure of
uncertainty of outcome, the relative magnitude of the favorite offers
insight into the game not available in the typical measures of
competitive balance.
For instance, it is possible that two seasons may have similar
levels in standard deviation of win percentage and GINI coefficients but
could have very different levels of average betting odds. As an extreme
hypothetical example, a league where the home team always wins by a
large margin may appear to be quite competitive through traditional
measures of competitive balance, but the betting market odds as a
measure of uncertainty of outcome will show the games are not expected
to be close, as average odds on the favorite will be much higher.
[FIGURE 1 OMITTED]
To illustrate how the uncertainty of outcome, as measured by the
betting market odds, has changed over the course of our sample, consider
Figure 1. This figure plots the average favorite odds (in absolute value
terms) for each season from 1990-2006. The figure shows the odds in the
American League (AL) and in the National League (NL).
As can be seen in Figure 1, the odds on both AL and NL games
steadily increased during the 1990s. Both AL and NL odds rose from the
low 130s (for odds on the favorite) to slightly above 150, representing
an increase of more than 10% during the decade. These odds spiked even
higher in the early 2000s, with AL odds reaching an average of nearly
170 and NL odds reaching a peak of around 150. In the mid-2000s,
however, these odds have settled back into the low 150s for the AL and
low 140s/high 130s for the NL.
Assuming these odds represent the expectations of bettors and fans
concerning the outcome of baseball games, it can be seen that they
became increasingly confident in the certainty of outcome of baseball
games in terms of the favorite. Competitive balance measures do not bear
out these findings, as noted in Schmidt and Berri (2001). For comparison
purposes to the previous figure, the standard deviation of win
percentage and the GINI coefficient on win percentage are shown for both
the AL and the NL in Figure 2.
Although stable early in the 1990s, spikes occurred in the standard
deviation of win percentage and the GINI coefficient in the NL and AL at
slightly different times in the mid-1990s before immediately settling
back into the levels seen in the early 1990s. By the end of the 1990s,
however, a major increase in the standard deviation of win percentage
and GINI coefficients occurred and continued into the early 2000s. The
AL, with the Red Sox and Yankees rivalry as the driving force, saw the
biggest increases (meaning less competitive balance), but the NL
increased as well. By the mid-2000s, however, the levels of the standard
deviation of win percentage and GINI coefficients dropped to the level
of the late-1990s in the AL and below the lows of the early 1990s in the
NL.
[FIGURE 2 OMITTED]
Although the ex-post measures of competitive balance were
reasonably stable in the 1990s and were shown as historic lows in these
averages by Schmidt and Berri (2001), the average odds on baseball games
steadily increased. As an example, comparing 1997 (before the decrease
in competitive balance at the end of the decade noted in Schmidt and
Berri (2001)) to 1991 (the within-decade lows in the odds) reveals that
the standard deviation of win percentage in the AL (increase of 1.9%)
and NL (decrease of 4.6%) changed very little. The change in the average
odds, however, increased by a much greater margin in both the AL
(increase of 8.2%) and the NL (increase of 12.0%). How could this have
happened? Given the findings of market efficiency, odds are unbiased
forecasts of outcomes of games; therefore, it shows that baseball games
on an individual game level became more certain in terms of the outcome
during this time frame, while the actual win-loss percentages at the end
of the season revealed little change. If the individual games are
expected to have more certain outcomes (stronger favorites), it is not
surprising that the public and the media express their concerns that
baseball is less competitive than it used to be, even though the
aggregated actual win-loss percentages may not have changed by any
substantial margin.
The odds, therefore, give a useful measure of how uncertainty of
outcome has differed from the ex-post measures of competitive balance in
Major League Baseball. The betting market-based odds provide a measure
of the uncertainty of outcome, which has increased during this time
frame. The uncertainty of outcome measure affects the ex-ante level of
competitive balance in the minds of fans and the media, explaining why
these entities may not believe that baseball is as competitive as it
appeared through traditional measures of competitive balance. Although
ex-post measures of competitive balance showed that baseball was
extremely competitive during the 1990s, the uncertainty of outcome
steadily increased, leading casual observers (e.g., media, fans) to
state, with good reason, that baseball had become less competitive.
Conclusions
In an attempt to explain the difference between public and
economist perceptions about competitive balance in Major League
Baseball, the difference between the ex-ante formed uncertainty of
outcome and competitive balance, as measured ex-post by win percentages,
was explored. A way to measure the uncertainty of outcome was suggested
to be the average favorite odds formed in the betting market for Major
League Baseball. The average odds represent the ex-ante expectations of
bettors and fans of the outcome of upcoming games. The higher the odds,
the more certain fans are of the outcome of the game. The closer the
odds to even money propositions, the more uncertainty of outcome there
is in games.
The baseball betting market was originally thought to have a
reverse favorite-long-shot bias (Woodland & Woodland, 1994). This
bias implies that favorites are overbet, which, for the case of
uncertainty of outcomes, means that fans believe the league is less
competitive than actual game results reveal. This bias was shown to be a
byproduct of an improper measuring of a unit bet by Gandar et al.
(2002), and a general reverse favorite-longshot bias was shown not to
exist, implying more faith in the efficiency of this market. When the
efficient markets hypothesis cannot be rejected, the odds can be taken
as an optimal and unbiased predictor of the outcome of the game.
For the sample studied in this paper, 1990-2006, which includes
seasons immediately after the data set used in the studies of Woodland
and Woodland (1994) and Gandar et al. (2002), the reverse
favorite-longshot bias was not shown to exist for the sample as a whole,
even with the proper accounting of a unit bet. The only subset where the
null of efficient markets could be rejected at the 10% level was for the
small group of heavy home underdogs. Therefore, because the efficient
markets hypothesis could not be rejected, we use the gambling market
odds for baseball as a measure of the expected uncertainty of outcome in
baseball games.
These findings help to explain the difference between public
thoughts of competitive balance (likely "uncertainty of
outcome" in their minds) and actual competitive balance as noted by
Schmidt and Berri (2001). Schmidt and Berri (2001) showed the 1990s to
be the most competitive decade in baseball history but pointed out that
media and the fans did not believe this to be the case. In observing the
betting market odds in relation to this timeframe, it can be seen that
betting market participants believed the league to be less competitive.
Odds on the favorite increased in both the American League and the
National League during these years.
By measuring the uncertainty of outcome through betting market
odds, the remarks of the fans and the media can be reconciled to the
findings of competitive balance as found by the ex-post measures using
win percentages. Non-economists felt baseball was becoming less
competitive, and their beliefs are borne out by the betting market odds,
as odds on the favorite steadily increased during the 1990s. Therefore,
within the realm of recent history (which is likely most important in
the minds of most observers), baseball was becoming "less
competitive" as the individual game odds were rising in the
direction of the favorites. Even though the competitive balance measures
of economists did show that the 1990s were the most competitive in
history through ex-post measures, these ex-post measures do not capture
all of the information that betting market odds reveal. With
expectations of individual game outcomes becoming more certain, as
evidenced by the uncertainty of outcome, it is not surprising the media
and fans believed competitive balance was a problem in Major League
Baseball in the 1990s and beyond.
The betting market odds as a measure of uncertainty of outcome may
ultimately be useful to Major League Baseball and to economists who
study the league because financial decisions of fans are ex-ante in
nature, rather than ex-post. These financial decisions (e.g., including
the purchasing of tickets, viewing of televised games, buying of
licensed merchandise) are more likely to be based on pre-game fan
perception concerning the uncertainty of outcome, rather than ex-post
measures of competitive balance.
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Endnotes
(1) The results for 1990-2006 are similar to those found in the
1978-1989 sample used by Gandar, Zuber, Johnson, and Dare (2002) in that
the win percentages of underdogs are slightly higher (although not
statistically significant) than the returns implied by efficiency. Given
the z-tests are dependent upon sample size, larger samples may still
reveal significant results if future baseball results are similar to
current and past results.
Rodney J. Paul [1], Andrew P. Weinbach [2], Richard Borghesi [3],
and Mark Wilson [1]
[1] St. Bonaventure University
[2] Coastal Carolina University
[3] University of South Florida--Sarasota
Rodney J. Paul is a professor of economics. His research interests
include the economics and finance of sports, market efficiency, and
time-series macroeconomics.
Andrew P. Weinbach is an assistant professor of economics in the
Wall College of Business Administration. His research interests include
the determinants of consumer demand for sports and entertainment
products and financial markets.
Richard Borghesi is a professor of finance. His research interests
include corporate finance, corruption, market efficiency, and prediction
markets.
Mark Wilson is an assistant professor of economics. His research
interests include sports economics and the economics of crime.
Table 1: Betting Simulations Testing Efficient Markets in the Baseball
Gambling Market 1990-2006
N Returns Expected Z-Statistic
Returns
All Underdogs 1990-2006
All 35974 -0.0096 -0.0187 1.4772
Slight 28611 -0.0102 -0.0189 1.3433
Heavy 7363 -0.0074 -0.0175 0.6322
Road Underdogs 1990-2006
All 25284 -0.0010 -0.0184 1.1303
Slight 19228 -0.0069 -0.0187 1.4566
Heavy 6056 -0.0197 -0.0175 -0.1226
Home Underdogs 1990-2006
All 10690 -0.0087 -0.0194 1.5076
Slight 9383 -0.0168 -0.0196 0.2492
Heavy 1307 0.0496 -0.0173 1.7831 *
Note: * denotes rejection of the null hypothesis of efficient markets
at the 10% level.
