This is a review of the sports research conducted by Nicholas G. Polson and Hal S. Stern applying a distributional model and Brownian motion process.
Why do we like to watch sporting events? One main reason is that we can never be sure of the outcome of the event until the end. There is always a chance that the underdog will win and the favorite will lose. Uncertainty and sports go together hand in hand.
Uncertainty of a game’s outcome is assessed using the betting point spread and the probability of one team winning implied by the betting odds. The volatility of the outcome is measured by looking at the development of the game score, beginning with a distributional model for the evolution of the outcome in a sports game. The distribution of the lead of one team over the other is specified as a Brownian motion process
A method of updating implied volatility throughout the course of the game is created using real-time changes in bettor’s assessments. With on-line betting there is an almost continuous information trail available to assess the implied expectation of the probability of one team winning at any point of the game. Uncertainty of the outcome is measured as the variation associated with the final score of the game. Implied volatility is defined as the outcome for the entire game or for the remaining part of the game. The market-implied volatility is determined by bettors’ or analysts’ assessments of the game outcome. The expected margin of victory is the point spread while the probability that a team wins is based on money-line odds. Finally, the implied volatility is a market-based assessment of the level of uncertainty seen in the difference between the scores of the two teams involved in the game.
Betting and prediction markets have shown that teams who are experiencing a long losing streak and consequently are considered extreme underdogs tend to be under-priced by the market. Volatility could also be measured using index betting spreads in which bettors provide assessments of over-under lines. These lines are used to make wagers regarding the total number of points scored in a game.
The point spread and money-line odds do not have a direct correlation, as it is very possible that two games involving heavily favored teams have the same money-line odds but the point spread is very different. It is possible this is due to the idea that the market has an expectation that the volatility is much higher for the game with larger point spreads.
Looking at point spreads and money-line odds provides analysts with another measure on which to compare games. Why are some games considered to be so much more volatile than other games, even when both games have a highly favored team considered to be far superior than their opponent? This research focuses on applying the model to football games. Analysts could then apply this model to other sports to see if the results are consistent across sports or not.
Analytics Used: Distributional Model, Brownian Motion Process
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