As part of a PhD program one has to conduct research and publish findings in conferences and academic publications. I am lucky enough to have had the opportunity to focus some of my research on betting markets after noticing a major missing lacuna in academic research.
There is no standardised way of describing odds and very few look at it from the perspective of a bookmaker.
In this article, I discuss my latest publication Expected Values and Variances in Bookmaker Payouts: A Theoretical Approach Towards Setting Limits on Odds which is now available as Open Access thanks to a contribution from Pinnacle.
Those with a quantitative background will realise that the techniques presented here are relatively simplistic, not beyond first year undergraduate mathematics. My intent, however, is to explain it in layman terms, for an individual with little to no mathematical know-how.
In my literature review, I did not find anyone who standardised the key concepts of betting; hence my paper starts off by defining the needs in this respect. The second section titled Evaluating Odds is intended for an academic reader, who may not be knowledgeable of how to convert odds into probabilities.
Pinnacle uses two formats of displaying odds (European and American). For more information on how to calculate probability, odds and payout read our article on What do betting odds represent. My section on Evaluating Odds is in essence a more academic take on these descriptions, also extending to other formats.
When adding the probabilities implied by betting odds, we tend to find these add up to more than 100%, with the difference being called many terms (vig, betting-margin, over-round).
The section Bookmaker Margin explains that this represents the expected profitability of a bookmaker; such that the expected profitability is the betting margin divided by (1 + the betting margin).
Pinnacle are popular for their low bookmaker margin. Assuming a 2% betting margin, Pinnacle expects to make 2/102 = 1.96% profit on every wager made.
In a previou article I have explained the way betting margins affect your profitability in greater detail using the example of a coin toss in.
This section proves a well-known theory; the conditions for the possibility of arbitrage betting. It also derives an estimated variance in the range of the payouts for a bookmaker.
The remaining part of the paper points out three necessary conditions for a bookmaker:
- A bookmaker does not need to know the exact probabilities of each outcome but needs to make sure that each odd implies a higher probability than the real outcome. Traditional bookmakers tend to sort it out by using the highest betting margin they can allow for, which derives my admiration of Pinnacle for offering such low margins.
- Bookmakers can ‘balance-the-books’ and obtain a definite profit if it can keep the ratio of wagers on each wager in proportion to the implied probabilities.
- Bookmakers tend to make higher profits in multiples or accumulators.
By way of conclusion
I want to thank Pinnacle for paying the Open-Access fee. If you have any questions, feel free to tweet me @domcortis. And if you happen to cite me in an academic publication, I owe you a drink.