Bookmaker odds are determined by the bets placed by the bookmaker’s customers. As more people bet on a given outcome, the bookmaker will adjust the odds in order to hedge its position and earn a margin. From these odds, we can estimate the probability distribution of event outcomes. Although bookmaker odds are determined by betting patterns, they are usually representative of the probabilities of event outcomes. This is due to a statistical phenomenon called the “wisdom of the crowd” – the bias of individual bettors averages out, giving a reasonable end result.
To find our picks, we look at the odds quoted by multiple bookmakers. We then identify outliers that fall outside the 95% confidence interval for the “ideal odds”, calculated as +/- two standard deviations from the mean of all quoted odds. This way, we identify bookmakers who, for some reason, represent a significantly different view on the probability distribution of a given event outcome.
We then calculate the implied event outcome probability for the inlier odds (those within the confidence interval, or in other words, the ones who have a more or less common view on the event’s outcome probability). When calculating these probabilities, we remove the margin in proportion to the odds, which is a recognized best practice.
Finally, we calculate the expected value of the potential win of placing a bet with the bookmaker who is quoting outlier odds as:
outlier odds × average implied probability from the inlier odds
For example, placing a €1 bet on outlier odds of 2.0, when the average implied probability from the inlier odds is equal to 60%, you can expect to earn a net profit of €0.2 (or 20%) over your initial investment:
€1 × 2.0 × 60% - €1 = €0.2
This approach has many benefits:
- it’s based on a sound mathematical framework and not your trust in someone’s predictions;
- you can make informed bets without having to factor any of your expectations into the formula, choosing bets with an expected profit and the probability of winning that satisfy your individual strategy;
- by taking the average implied probability of the inlier odds, we strengthen the effect of the “wisdom of the crowd”.
While no bet is certain, sticking to bets with positive expected value will likely result in a net win over time. For more information on value betting, bookmaker odds, expected value, and variance in betting, visit our article section.