Odds and Probability

Lets explore what is behind the fixed odds posted by the bookmakers and how these are determined. Fixed odds betting is all about chance, or probability. The odds, for example, of Spain winning the Euro are related to the probability of Spain winning the Euro. If the betting odds are equal to the true odds that an event will occur, then they are said to be "fair" odds.

Of course, unlike the flipping of a coin, where it is known in advance exactly what the true chance of each outcome (heads or tails) will be, it is no simple task to estimate exactly what the true probability of Spain winning the Euro will be. For coin flipping or dice rolling, the probability function that describes the chance of one or another result occurring can be calculated from first principles. In sports prediction, by contrast, the probability function can only be estimated by observation of a team or player's past performance, and other influencing factors. Furthermore, for extended events, future influencing factors like the weather may very well affect the chances of one particular result occurring.

Determining the fair odds for Juventus to win the Serie A, 9 months before any of the games have been played, must, surely then, be even more complicated.

Profit Margin: Lets analyze the game of Liverpool vs. Manchester City. Assume that the returns provided for the game by the betting company are:

Result 1: 1,40 Result X : 3,75 Result 2: 5,00

Book Profit= (1/Result 1)+(1/Result X)+(1/Result 2)=1/1,40 + 1/3,75 + 1//5,00=1,18

The amount of 1,18 Euro is the revenue of the betting company if the players bet 1 Euro on each outcome of this game. Based on this, we can calculate the profit margins for the betting company as well as how much of the money gets distributed to the players (the Pay Out).

Pay Out = 100 * 1/ Profit = 100 * 1/1,18=84,75%

Profit Margin = 100- Percentage of Pay Out=100-84,75=15,25%

15,25% is simply the profit margin for the bookmaker. A lower margin means that the bookie makes less profit and distributes more money to the players. In this case the players benefit and are allowed to enhance their profits.

Calculating Probabilities from Odds:

The odds are calculated based on probabilities on the potential outcomes of the game. Looking at the odds, the punter is able to determine the underlying probabilities. The betting companies are based on these probabilities to make their calculations. This process allows the bettor to compare the probabilities of the betting company with the ones he/she has calculated for any of the potential outcome of the game.

The formula to calculate the underlying probability for each potential outcome of the game is:

Probability = Percentage of Payout/Return (e.g. Probability for Result 1 = 84,75/1,40=60,53, Probability for Result X = 84,75/3,75 = 22,60, Probability for Result 2 = 84,75/5,00=16,95)

The above calculations indicate the underlying probabilities based on which the betting company makes its calculations (quantifies the betting company’s assessment of the potential of any outcome). Our clients should always compare the underlying probabilities of the betting companies with the probabilities they calculate on their own. This comparison will indicate the opportunity to bet on any specific point.

In a sense, then, true or fair odds in sports are estimations of the expected probability, or chance, of something occurring, rather than exact calculations. Bookmakers have their own opinion about what the fair odds for each event should be. If they are wrong, and the punter spots the mistake, this is where the profit can be made.Based on the above formulas and on the odds of the various bookmakers included in the Comparison Tables of Oddsandstats (e.g. Odds Matrix), you will be able to choose the point and the company that will maximize your profits.

Good Luck!