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Information Incorporation in Online In-Game Sports …
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Information Incorporation in Online In-Game Sports
Betting Markets
Sandip Debnath,1,4 David M. Pennock,2,4 C. Lee Giles,1,3,4 and Steve Lawrence4
1 2 4
Computer Science and Engineering Overture Services, Inc. NEC Laboratories America, Inc.
3
Information Sciences and Technology 74 N. Pasadena Ave., 3rd floor 4 Independence Way
Pennsylvania State University Pasadena, CA 91101 USA Princeton, NJ 08540 USA
University Park, PA 16801 USA david.pennock@overture.com lawrence@necmail.com
debnath@cse.psu.edu,giles@ist.psu.edu
ABSTRACT
We analyze data from 52 online in-game sports betting mar-
kets (where betting is allowed continuously throughout a
game), including 34 markets based on soccer (European
football) games from the 2002 World Cup, and 18 basket-
ball games from the 2002 USA National Basketball Associa-
tion (NBA) championship. We show that prices on average
approach the correct outcome over time, and the price dy-
namics in the markets are closely coupled with game events, Figure 1: (a) ALS and (b) AE of 34 soccer markets.
agreeing with efficient market assumptions. We also exam-
ine qualitative distinctions between the two types of games.
2. DATA AND METRICS USED
Categories and Subject Descriptors We analyze information incorporation in markets on the
World Sports Exchange where traders can bet on sporting
J.4 [Computer Applications]: Social and Behavioral Sci- events continuously throughout a game. The markets are
ences--Economics; G.3 [Mathematics of Computing]: double auctions in contracts that pay off $100 if and only
Probability and Statistics if the favored team wins the game by more than l points,
where l is a nonnegative opening line or spread.
General Terms To measure the accuracy of implied market forecasts over
Economics, Measurement time, we use the logarithmic score, a standard measure of
the accuracy of probabilistic forecasts [5]. We took the mar-
Keywords ket price to be the midpoint between the bid and ask prices,
and normalized prices between 0 and 1. Let the price of
Information incorporation, economic efficiency, efficient mar- the ultimate winner at time t be pwin (t). Then the Aver-
kets hypothesis, in-game sports betting, market reaction, age Logarithmic Score (ALS) for the market at time t is
soccer, logarithmic score, entropy. 1/N · N log pwin (t) where N is the number of markets.
i=1
Similarly, the Average Entropy (AE) at time t is
1. RELATED WORK
N
A market can serve as a tool for aggregating buyers' knowl- 1 ¡
· -p(t) log p(t) - (1 - p(t)) log(1 - p(t)).
edge about items of uncertain value. One of the stronger N i=1
forms of the so-called efficient markets hypothesis states
that information is incorporated into market prices virtu- Note that ALS can only be computed after the game ends,
ally instantaneously. Gambling markets epitomize trading as it depends on the identity of the winning team, while AE
contracts of uncertain value. Analyses of horse racing mar- does not depend on who wins.
kets [4], NBA point spread markets [1], and a market in the
Euro 2000 soccer tournament [3], to name a few, are largely
consistent with strong efficiency assumptions.
3. SOCCER MARKETS
We analyze markets corresponding to 34 soccer games
played during the 2002 World Cup. Every 10 seconds during
every game, we recorded prices from the Sports Exchange
as well as score changes and game clock information from
CBS Sportsline. 1 ALS and AE for all 34 games appear in
Figure 1. ALS increases roughly monotonically, indicating
that prices approach the correct outcome over time. In-
Copyright is held by the author/owner. creases in ALS reflect incorporation of evidence pertinent to
EC'03, June 912, 2003, San Diego, California, USA. 1
ACM 1-58113-679-X/03/0006. http://www.sportsline.com/
the outcome of the game [2]. The graph seems to display
two qualitatively different regions: a roughly linear increase
(indicating a constant influx of information) until just after
halftime, and a superlinear increase approaching the end of
the game. The final few minutes (near the 104th minute
on the graph, which is the 89th minute of the game after
subtracting the 15 minute halftime) show the largest price
movements, as any uncertainty about the outcome rapidly
dissolves. AE is roughly monotonically decreasing during Figure 2: (a) ALS and (b) AE of 18 basketball mar-
game play (remaining roughly constant during halftime), re- kets.
flecting decreasing uncertainty. AE drops to 0 (certainty) as
the game ends. The superlinear decay indicates a more rapid
resolution of uncertainty near the end of the game.
4. MARKET REACTION
In previous work [2], we examined the reaction of politi-
cal stock markets to newsworthy events. For in-game sports
betting markets, the clear dominant factors are the game
score and the time remaining. Second-order factors include
penalties, ball possession, perceived momentum, and fan en- Figure 3: (a) Soccer reaction curve; (b) Correlation
thusiasm, though some are hard to quantify. between logarithmic score and score difference for
Speed of reaction.We evaluate how promptly the mar- San Antonio vs. LA Lakers, May 7, 2002.
ket reacts to score changes in the games. We denote the time
of a goal or score as s and the time of the corresponding
the correlation in one of the 18 games. The top curve is the
price swing as p . Communication delays (including net-
normalized score difference between the two teams and the
work and updating delays) from Sportsline and the Sports
bottom curve is the logarithm of the price of the winner.
Exchange are represented as s and p , respectively. We as-
The correlation between these two is 0.93. The average of
sume that any negative time difference between p + p and
all the correlations for all games is 0.61
s + s is due to delays rather than market foresight. We
factor out delays by using the most negative difference as a
threshold. This results in a conservative (over-) estimate of 6. COMPARING THE GAMES
delay. We define the measured delay as Basketball games are more uncertain for a larger propor-
tion of the game, and so in one sense more exciting. On
m = (p + p ) - (s + s ). the other hand a comeback in soccer, being unlikely, is more
Now for all the goals scored we recalculate the thresholded dramatic than in basketball. In both cases, price is highly
delay as = m + where the threshold is defined as correlated with scoring. In soccer, where scoring is infre-
quent, price changes are infrequent but dramatic. In bas-
= |min({i , i})|,
m ketball, where scoring is frequent, price changes are frequent
where the superscript i ranges over all goals scored in a but less drastic. Meaningful goals late in a game affect price
game. We found that the average thresholded delay for the much more than early goals.
74 goals scored in the 34 games is 31.633 seconds. Note
that this difference reflects a conservative estimate, due to 7. REFERENCES
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5. BASKETBALL MARKETS predict the outcome of an event? The euro 2000 soccer
We analyze markets from 18 games during the 2002 NBA champioships experiment. Max planck Institute for
Championship. Figure 2 plots ALS and AE for these games. Research into Economic Systems working paper, 2002.
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with score changes. The right side of Figure 3(b) displays