# How bookmakers calculate odds

## How are the coefficients calculated?

The coefficient, or betting quotes– is the main term in sports betting, which reflects the probability of a certain event. The bookmaker’s profit depends on the correct formation of coefficients to stay in the black in any outcome of the match.

### The principle of creating a coefficient

The main task of BC is always to make a profit. The analysts of the office calculate quotes for the event as a whole and individual outcomes, based on the real probability and laying a margin that provides income to the bookmaker.

### To understand the essence, let’s use the example with a coin.

The probability of each side falling out is 50%. Let’s say you bet 100 USD on «tails», and your friend puts the same amount on «heads». Without margin, the winner will receive 200 CU, that is, the coefficient turns out to be 2.0. In such conditions, no office can exist, so quotes are obtained not 2.0-2.0, but 1.95-1.95, depending on the margin value. And now, if you win, you will be paid 195 USD, and the remaining 5 USD will go to the treasury of the office. ### How is the coefficient formed?

The coefficient shows the probability of the outcome according to the analysts of BC. Ideally, the probability is one or 100%. It is calculated by the formula k=1/p, where k is the coefficient and p is the probability (from 0 to 1). For example, the chances of an even score in basketball are 50%, which means that the value will be displayed as 0.5 in the formula.

An analyst or a special department of a bookmaker thoroughly studies the event, analyzes statistics, applies probability theory, listens to the opinion of experts and decides on the basis of all the information that the first team will win. Forming quotes, experts are based on the real chances of the outcome. This is what an objective assessment of the probability of the result of the duel would look like (without betting margin):

• team victory 1 — 70.2%;
• draw – 15.3%;
• the victory of team 2 is 14.5%.

The sum of the real probabilities is 100%. In this case, the majority will bet on the winning of the first team, so the office hedges and artificially lowers quotes for the outcome of P1, increasing the sum of probabilities for the event. After such manipulations, it turns out the following:

• coefficient on P1 — 1.54 (probability 64.8%);
• the coefficient for X is 4.22 (probability 23.7%);
• the coefficient for P2 is 5.4 (probability 18.5).

The sum of probabilities for this market is 107%. To calculate the margin, divide 100 by the coefficient. Do this with all the quotes for the outcome (for the victory of each team and a draw, for the total more and less, etc.). Add up the results and subtract 100.Quotes for odds -1 and odds +1 are 2.02 and 1.92, respectively.

### Divide 100 by each number

100/2.02=49.5%;
100/1.92=52.08%.
Add the values (49.5+52.08), subtract the number 100 from it (101.5-100=1.5) and we get a margin of 1.5% BC.

Try to calculate the margin yourself in various markets in the image below. We will only give the correct answer to the margin on the outcome, so that you double-check the correctness of the calculations -1.83%. ### Why are the coefficients constantly changing?

After calculating the coefficients and laying the margin, the office does not stop influencing the values. First of all, the change in quotes is affected by the players’ bets. If a large flow of funds is concentrated on one outcome, the coefficient for this market is significantly reduced, and for the opposite – increases.

There may be other reasons for the movement of the line, which are associated with the appearance of new information. For example, a key performer has been injured in the team, a coach has changed, or rainy weather is expected. These factors affect both the outcome and the number of goals and other indicators of the game.

### Resume

The bookmaker determines the probability of the outcome as a percentage and expresses the value in the coefficient in which the margin is laid in order to make a profit regardless of the volume of bets on various markets and the outcome of the event.

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