Baseball attendance and outcome uncertainty: a note.

Kochman, Ladd ; Badarinathi, Ravija

Recent claims that spiralling players' salaries doom the demand for Major League Baseball (MLB) make studies like Knowles et al. (1992) especially timely and useful. By following the lead of past writers--most notably Quirk and El Hodiri (1974)--Knowles et al. proxied the demand for MLB with game attendance and (like Quirk and El Hodiri) reported that attendance is maximized when the home team is slightly favored.

The home team's role and degree as favorite or underdog were quantified by transforming the Las Vegas odds into a probability. Different transformation techniques were proposed, but the one chosen made the favorite's probability of wining equal to

(1) [P.sub.F] = (F + U / 2) / (F + U / 2) + 5

where: F = $ bet to win $5 on favorite

U = $ won from $5 bet on

underdog

Thus, if Team X were rated 6-7 to win, its probability of winning would be

(2) [P.sub.F] = (7 + 6 / 2) / (7 + 6 / 2) + 5 = 0.6562

The shortcoming of the Knowles et al. study lies not in its analysis--which found that attendance is maximized when the home team's winning probability is 0.60--but rather in its interpretation of the results. Despite underlying odds of 7-8, Knowles et al. (1992:77) inferred that attendance is greatest "when the home team is slightly favored." Knowles et al. attribute the same conclusion to Quirk and El Hodiri.

It is apparent that neither set of writers has engaged in any actual wagering on MLB games. Odds of 7-8 (or sometimes quoted 8-5) are reserved for games where the favorite is a heavy choice to win. The slight characterization used by the writers above must be based on their improper focus on the corresponding probability.

Typical of 8-5 games was the June 1,1993 contest pitting San Diego against Atlanta. The visiting Padres had a record of 20-30 while the Braves were 29-23. Further, a rookie was pitching for the visitors while the home team was throwing one of its ace pitchers. Other examples of games where the host team was rated 8-5 include Chicago (28-28) at San Francisco (38-22) on June 11 and Cleveland (25-36) at Detroit (38-23) on June 14.(1)

To the extent that MLB attendance is maximized when the home team's odds of winning are 8-5 (or p = 0.60), it seems fair to criticize the larger conclusion of Knowles et al.--namely, that uncertainty contributes positively to baseball's demand. In truth, fans may have a strong preference for certainty as represented by a decided home favorite.

Note

(1.) Odds were taken from various issues of USA Today.

References

Knowles, Glenn, Keith Sherony, and Mike Haupert. "The Demand for Major League Baseball: A Test of the Uncertainty of Outcome Hypothesis." The American Economist, Vol. 36 (Fall 1992), 72-80.

Quirk, J., and M. El Hodiri. "The Economic Theory of a Professional Sports League." Government and the Sports Business. Brookings Institution (1974), 33-80

Ladd Kochman, School of Business, Kennesaw State College, Marietta, GA 30061

Ravija Badarinathi, School of Business, Univ. of North Carolina, Wilmington, NC 28403