# How to determine the probability of the outcome of an event by the odds: theory in sports betting

Learn to determine the likelihood of an outcome based on odds. Because of the margin, you will have to take a calculator.

Some of the world's bookmakers place odds in their line in British or American formats, which are unusual for us. First of all, you should be able to convert odds from one format to another, which will help in calculating the probability of the outcome included in the odds.

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## Odds formats in the bookmaker's line

Coefficient - the probability of a particular event, taking into account the bookmaker's margin. Bookmakers use the following odds formats:

• European or decimal.
• British or fractional.
• American.

The result of multiplying the European odds by the size of the bet is the payout amount in case of the event.

The British ratio is written as a fraction, for example, 15/4, therefore it is called fractional.

Calculate the payout for a bet on an event with UK odds using the formula :

V = (S x Kb) + S , where V is the payout, S is the bet amount, Kb is the UK odds.

When betting on a particular outcome with American odds, there are two options:

• The US plus ratio shows the possible net profit at a rate of 100 conventional units.
• The negative US coefficient shows the amount that must be wagered in order to get a net profit of 100 conventional units.

For example, in a football match Portugal - Croatia, the bookmaker set the following odds: -111 for the home win, +244 for the draw and +330 for the away win.

• With a stake of 111 rubles on the hosts, you will receive 100 rubles in net profit if Portugal wins. The payment will be 211 rubles: 100 + 111.
• In the event of a tie with a stake of 100 rubles on this outcome, the net profit will be 244 rubles, and the payout will be 344 rubles.
• If Croatia wins with a stake of 100 rubles per guests, you will receive 430 rubles, and the net profit will be equal to 330 rubles.

Sports betting odds calculation: How Bookmakers Calculate Sports Betting Odds: Types, Line and Adding Margin

## How to calculate the probability of an event based on odds

To convert the UK rate to the European rate, use the formula :

K = Kb +1 , where Kb is the UK rate and K is the European rate.

For example, British odds of 5/2 are equal to European odds 3.50: 5/2 + 1.

Convert American odds to European odds using the following formulas :

• K = Kap / 100 +1 , where Kap is a positive American coefficient.
• K = 100 / (-Kao) +1 , where Kao is the negative American coefficient.

For example, the US odds +280 corresponds to the European odds of 3.80: 280/100 + 1. The

US odds of -200 is the European odds of 1.50: 100/200 + 1.

Determine the probability of an outcome using the formula:

P = 1 / K, where K is the European odds , P is the probability.

The odds include the bookmaker's margin. This must be taken into account when calculating the real probability of the outcome based on the statistical data of the bookmaker's analysts. To do this, subtract the margin from the probability.

## What is bookmaker margin

Margin is the bookmaker's commission on the betting market.

Determine the bookmaker's margin using the formula :

M = (Ps - 1) x 100%, where Ps is the sum of the probabilities.

For example, in a hockey match between the Philadelphia Flyers and the Boston Bruins, the bookmaker offers the following odds: 2.70 for the home team, 4.00 for the draw and 2.40 for the away team.

We calculate the probability taking into account the margin:

• Philadelphia Flyers win 0.37: 1 / 2.70.
• Draw 0.25: 1 / 4.00.
• Boston Bruins win 0.42: 1 / 2.40.

In total, we get 1.04: 0.37 + 0.25 + 0.42.

The bookmaker's margin is 4%: (1.04 - 1) x 100%.

We subtract this extra 4% proportionally from each probability. That is, minus the bookmaker's margin, the real probability of outcomes is as follows:

• P1 - 0.3558: 0.37 x 100/104.
• X - 0.2404: 0.25 x 100/104.
• P2 - 0.4038: 0.42 x 100/104.

After placing quotes for an event, the bookmaker gradually corrects them. Most often, the coefficients are changed in the following cases:

• New information has arrived that affects the balance of power.
• When analyzing the odds of other bookmakers, an arb was noticed.
• Loads for a certain outcome are observed.
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