Jason P. Berkowitz

The Conversion of Money Lines into Win Probabilities: Reconciliations and Simplifications

We contribute to the literature on money line betting markets by investigating the relationships between the various methods used to derive subjective win probabilities from money lines. We show that, although the seven methods described appear to be unique, they actually share many common assumptions and that, surprisingly, they reduce to three distinct estimates of bookmaker commission and subjective win probabilities. We also show that among the three distinct estimates, one is biased when money lines suggest a very heavy favorite in a particular sporting event. Thus, it is important to consider the assumptions for each method when deciding which to use in a particular context. Two empirical examples demonstrate how a market inefficiency, such as a favorite-longshot bias, should influence the choice of methodology.

When Going in Circles is Going Backwards: Outcome Uncertainty and Fan Interest in Nascar

Using data from the 2007, 2008, and 2009 NASCAR seasons, this paper shows that the uncertainty of outcome hypothesis pertains to both race attendance and television audience, with the former only responding to race-level uncertainty and the latter responding to both race-level and season-level uncertainty. Of the other contributing influences, the price of gasoline and the unemployment rate were both unrelated to race attendance during the sample period, counter to conventional wisdom expressed during the declining attendance and ratings of the 2009 season. We also find that NASCAR broadcasts lose audience when competing against other big-interest sporting events and that declines in both television ratings and audience size during the NASCAR season were not unique to 2009, again contradicting conventional wisdom. Overall, the empirical evidence suggests that declining competitive balance might have been the common factor that reduced both television audiences and race attendance during this period.

An Online Appendix to 'The Conversion of Money Lines into Win Probabilities: Reconciliations and Simplifications'

This online appendix accompanies the paper “The Conversion of Money Lines into Win Probabilities: Reconciliations and Simplifications” by the same authors.Full paper available at: https://ssrn.com/abstract=2658335

Real Options Applied to Consumer Goods: Maximizing Profits and Fan Welfare

This paper demonstrates that both consumer utility and event organizer profits increase when tournaments played at neutral sites sell tickets via options, which are exercisable only if the desired team reaches a given round of the tournament, and advanced selling; rather than just utilizing an advance selling strategy. This approach yields a separating equilibrium pricing strategy. Through this ticket pricing strategy, the organizer can realize a significant increase in profits as a result of a separating equilibrium. Simultaneously consumer welfare increases as fans know, with certainty, they have tickets to the game if their team makes it. If these options were offered by participants instead of organizer it allows them to smooth their revenues over time.