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# Odds in Sports Betting

Sporting bets are extremely popular worldwide. The betting events are characterized by the odds. Let us find out what is behind that figure. Learn about the odds calculation and see the difference between "ideal" and offered odds.

## What Are The Odds?

The odds represent a chance that a bookmaker gives to the outcome of a specific betting event, e.g. to the result of a football match. In the recent times various exotic betting opportunities have occurred such as who is going to win presidential elections or talent competitions or whether the euro zone is going to collapse or not. Simply put you can bet on almost everything as the supply of betting events is truly manifold.

The odds, times the bet, determine a potential win. If you bet e.g. `\$100` on the victory of a home team in a football match with the odds `1.8`, the potential win is `\$100 × 1.8 = \$180`. The lower the odds, the higher is the chance – according to the bookmaker's assumption – for the outcome to happen and vice versa.

## How Are The Odds in Sports Betting Calculated?

Mathematically speaking the odds are a reciprocal of the probability of a certain outcome to happen. Therefore there are low odds for favorites (because there is high winning probability) and high odds for outsiders (since there is low winning probability). This is clearly demonstrated on the examples below.

### Odds Calculation Step-by-Step

Let us start with a simple example with only two possible outcomes that may happen, such as a football match where two teams fight for advancement in the Champions League: either Team A or Team B can advance.

The bookmaker of a sports betting company estimates that Team A is slightly better and will succeed with the probability 0.6 (or 60% if you like). The probability of success for Team B is then 0.4 (or 40%; the sum of the probabilities must equal 1, or 100%). What are the odds that will be likely given by the bookmaker?

Let us recapitulate the probabilities of success:
Team A = `0.6` (or 60%),
Team B = `0.4` (or 40%).

The odds are the reciprocal values of the probabilities, therefore the odds are calculated as follows:

Team A = `1 ÷ 0.6 = 1.67` (or analogously in %: `100% ÷ 60% = 1.67`),
Team B = `1 ÷ 0.4 = 2.50`.

These are "ideal" or completely "fair" odds that would be given by the bookmakers in ideal conditions. Since we do not live in an ideal world, the sports betting companies decrease these fair odds by their margin, which usually makes 10% (this is their expected return). In other words a betting shop will pay you only 90% of the fair odds.

However it is logical and understandable. The betting shops need to secure a specific edge or contribution to their operation and development (it is not a profit yet since there are other costs except of the winnings paid such as rents, salaries of bookmakers etc.) and also to reduce their risks of losing.

Finally we are getting to the odds that would likely be given by the betting companies. The ideal or fair odds need to be multiplied by 0,9 or 90% (i.e. 100% minus the supposed margin 10%):
Team A = `1.67 × 0.9 = 1.5`,
Team B = `2.50 × 0.9 = 2.25`.

Let us follow further examples, but first let us have a look at the abbreviations used by the sports betting companies under which the odds are provided. The above-described calculation of odds then can be done in the form of a table, which is shorter and better-arranged. There can be these possible outcomes in most betting events:

1 = home team will win (or the first player in tennis etc.),
0 = there will be a tie,
2 = visitors will win (or the second player in tennis etc.),
10 = home team will either win or tie, i.e. home team will not lose,
20 = visitors will either win or tie, i.e. visitors will not lose,
12 = there will be no tie.

## The Example of the Odds Calculation of a Supposedly Tight Football Match

In the following example we assume a football match between two teams, whose winning (and drawing) chances, according to the bookmaker, are considered to be absolutely equal. It means that the probability of win, loss and tie is still the same `1/3` (or `0.33` or `33.33%` if you like, but the usage of fracture for calculations is more accurate in this case). Let us put it in the table below and calculate the odds for all possible outcomes.

The Odds CalculationOutcome and Corresponding Odds
102102012
The probability of the outcome1/31/31/32/32/32/3
Fair odds (= 1 ÷ Probability)3331.51.51.5
The odds offered by the betting company2.72.72.71.351.351.35
[= Fair odds × (100 % – Margin)], the margin is supposed to be 10%

## The Example of the Odds Calculation with a Favorite Team

At last let us calculate the odds of a match, where one of the teams is a great favorite. We can use the match Manchester Utd – Wigan as an example. The bookmaker estimates that the probability of Manchester Utd to win the match is `0.75` (or `75%`), the probability of a tie is `0.15` (or `15%`) and the probability of Wigan to win the match is merely `0.1` (`10%`); sum check: 0.75 + 0.15 + 0.1 = 1 (or 100%).

Note: To be exact the probability in math is set in the decimal form (it is defined in the interval 0 to 1), not in percentage. However there is nothing against multiplying it by 100 and it may be clearer for some of you. For an illustration the odds calculations below are done in % and, of course, there is no impact on the result (1 / 0.75 is the same as 100% / 75%).

The Odds CalculationOutcome and Corresponding Odds
102102012
The probability of the outcome75%15%10%90%25%85%
Fair odds (= 1 ÷ Probability)1.336.67101.1141.18
The odds offered by the betting company1.26913.61.06
[= Fair odds × (100 % – Margin)], the margin is supposed to be 10%

For completion: The probabilities of the outcomes 10, 20 and 12 are acquired by a simple summarization of the individual probabilities, e.g. in the case of the outcome 10: 75% + 15% = 90% etc.

## The Calculation of Winning Chances from the Given Odds

The whole course of action can be turned around. What is the winning chance – according to the bookmaker of a sports betting company – if the odds are for instance `1.8`? If we suppose the margin to be 10% then the winning chance is `(100% – 10%) ÷ 1.8 = 50%`. Universally speaking:

`Winning Chance in % = (100% – Margin) ÷ Odds offered`.

In case of the 10% margin the formula can be shortened to: `90% ÷ Odds offered`.

The winning chances for common odds are calculated in the following table.

The Odds OfferedCorresponding Chance of Success According to the Bookmaker
1.181.82%
1.275.00%
1.369.23%
1.464.29%
1.560.00%
1.656.25%
1.752.94%
1.850.00%
1.947.37%
2.045.00%
2.142.86%
2.240.91%
2.339.13%
2.437.50%
2.536.00%
3.030.00%
3.525.71%
4.022.50%
10.09.00%