5. Data from Various Sports 51
The results for the 2003-04 season are qualitatively different than
those found by Camerer. Through the All-Star break (February 15,
2004), teams having a winning streak, playing teams with equal or
shorter streaks, beat the spread in 193 out of 370 games, or 52.2% of
the games. Teams having a losing streak, playing teams with equal or
shorter streaks, beat the spread in 179 out of 375 games, or 47.7% of
the games. Thus, betting on teams with winning streaks, and betting
against teams with losing streaks, would have resulted in a winning
percentage of 52.2%. Note that this is the opposite of what happened
in Camerer’s data. Does the reader think that this change will persist,
and if so, is it because the bettors have gotten smarter (i.e. have they
incorporated the fact that streaks are over-rated into their betting
practices)?
Exercise.
1. Show that if there is a 10% vig, and a bettor makes bets of
a constant size, then the bettor needs to win 52.6% of the
time to break even.
5.3. Horseshoes. The game of horseshoes differs in many ways from
the games of baseball and basketball. In studying streakiness, some
of these differences make it easier to decide whether the results in
horseshoes diverge from those that would be predicted under the as-
sumptions of the Bernoulli trials model.
In the game of horseshoes, two contestants face each other in a
match. A match consists of an indefinite number of innings. In each
inning, one player pitches two shoes, and then the other player pitches
two shoes. The shoes are pitched at a stake that is 37 feet from the
pitching area. If the shoe encircles the stake, it is called a ringer.
A nonringer that is within 6 inches of the stake is called a “shoe in
count.” The former is worth three points and the latter is worth one
point. If one player throws j ringers, and the other player throws k
ringers, where j k and j 1, then the first player gets 3(j k)
points, and in this case, shoes in count do not count. If neither player
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