# How bookmakers calculate their odds

## How bookmakers calculate their odds

We provide some insights on how the bookmakers calculate their odds and we explain how it works and what's the bookmaker's profit.

Although everybody knows the terms **odds**, it is not always clear what the term means. In fact, odds are a numerical expressions, and refers to the likelihood of some event happening or not.

Odds can be displayed in two ways – as a **fraction** or as a **decimal**. Fractional odds are displayed typically in forms such as 3/1, 5/2, or 11/4, and allow a gambler to calculate how much they will win in comparison to their original stake.

For example, at odds of 9/1, for every €1 bet, they will win €9. This can also be calculated as 1/(9 +1) = 0.1 which means that there is a 10% chance that the bet will succeed. Equally, at odds of 5/2, they will win €5 for every €2 bet, which equals to a 2/(5 =2) or 29% chance of winning.

Decimal odds, by contrast, show a player how much they will win if their bet succeeds. So odds of 9 indicate that they will get back, for every euro bet, €9, consisting of winnings of €8 plus their original €1 staked.

Both methodologies have their merits, but the fashion is trending towards decimal odds because they are easier to understand. This is because factional odds report winnings, and do not take into account the fact that, if a bet succeeds, the punter does not only get their winnings, but also gets their original stake back.

In terms of **how a bookmaker calculates their odds** then it is important to understand implied probability, a concept which can be found also in many market-based transactions, including swaps, futures, bonds, and currency markets. Implied profitability, in essence, is merely the conversion of odds into percentage terms.

Normally the sum of **2 probabilities occurring is 100%.** If a coin is tossed, for example, there are only two outcomes, heads or tails, and the sum of betting on either will always equal 100%. Where **sports betting differs in that**, if all the odds for a particular bet are added together, the total of the probabilities exceeds 100%, This incremental element represents the bookmaker’s profit.

This is best represented by examples.

For a Premier League fixture the following odds might be offered by a bookmaker:

Chelsea – 3.5 (1.91); Liverpool +3.5 (1.91).

Ignoring the possibility of a draw, if we bet Chelsea win, we either have a pay-out of €0 if they lose or €191 if they win.

Equally, if we bet on Liverpool, we either have a pay-out of €0 if they lose or €191 if they win.

To calculate the implied probability for each outcome, we take the amount staked and divide it by the total pay-out:

Chelsea wins 100/191 = 52.4%

Liverpool wins 100/191 = 52.4%

Both outcomes added is 104.8% which means that to cover both bets, a player would have to spend €104.80 to win back €100. The €4.80 is the bookmaker’s profit.

The same principle applies when the odds differ. For example:

Chelsea 1.53, Liverpool 2.6.

Betting €100 on Chelsea, we gain nothing in the event of a loss, but win €153 if our bet succeeds. Equally, if we bet €100 on Liverpool, we either win nothing or €260. Again, ignoring the possibility of a draw, the two implied probabilities are:

Chelsea wins 100/153 = 65.4%

Liverpool win 100/260 = 38.5%

Adding the two together gives a total of 103.9%, with the incremental part representing the bookmaker’s margin.

The odds offered by different bookmakers on the same event may vary. All leading firms employ statisticians and complex computer models to calculate probabilities, but no two algorithms are the same, which is why you will find marginal differences in the odds offered by the leading firms for the same teams, horses, and players.

Generally bookmakers make anywhere between 5% and 20% profit, depending on the type of sport. When choosing your bookmaker, therefore, try and choose the one that is taking the lowest margin in total, as they are likely to be offering the fairest odds.