The Conversion of Money Lines Into Win Probabilities

Abstract

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.

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

“…The DraftKings betting odds for teams to make it to the 2022 Final Four, commonly referred to as Futures Lines, was collected on July 8, 2021 and reported in Table 2. Berkowitz et al (2018) discuss the different approaches for converting betting lines into subjective probabilities and note the standard normal probabilities as preferable as we do not have a favorite-longshot bias in our data. (see Berkowitz, Depken, and Gandar for discussion on the conversion of betting lines into subjective probabilities).…”

“…10 This means if you purchase an option for the field, your option is in-the-money and can be exercised for a ticket to the semifinals as long as one of the teams without a line makes it. 11 For a discussion of converting betting lines into probabilities see Berkowitz et al (2018).…”

“…Through the Efficient Market Hypothesis (Fama & French, 1996), the price of the option cannot exceed the amount that one would have to bet in order to receive a payoff great enough to buy the tickets at market price when the games occur. Thus, the price of the option is a function on the odds of a team making it that far in the tournament, which is a simple conversion of the money line (see Berkowitz et al, 2018).…”

Behavioral Biases in Daily Fantasy Baseball: The Case of the Hot Hand

“…12. https://sportsbookreviewsonline.com/scoresoddsarchives/mlb/mlboddsarchives.htm 13. A general discussion of money line to implied win probability conversion techniques is available in Berkowitz et al (2018). 14.…”

Exploiting the “Win But Does Not Cover” Phenomenon in College Basketball

“…In the absence of transaction costs, money lines reflect the fair probability of each team winning. However, because the bookmaker charges a vigorish, an adjustment to the actual money line is needed to calculate the fair odds (see Sauer, 2005;Berkowitz, Depken and Gandar, 2017a). The money line for a game is posted as negative (positive) number for the favorite (underdog) as (−125, +110).…”