# Formation of Odds and Bookmakers' Margins

It is obvious to every gambling fan than the odds for different events are based on impeccable logic.

## The likelier an outcome to be winning, the lower the odds with the bookmaker.

And vice versa, the smaller the chances of a team to win, the higher his eventual victory is evaluated; i.e. the bookmakers’ odds are a reflection of the likeliest outcome of the event. To be able to present adequate odds the bookmaker has to collect and generalize a great amount of sports information. As a result of the analysis and study of the collected information the bookmaker specifies the likelihood for all outcomes. In practice this would look like this:

The match Stoke City – Wigan Athletic is forthcoming. As a result of the analysis of the statistic data and taking into account the present physical fitness of the team members, the bookmaker has reached the conclusion that the likelihood for the outcome of the event is the following:

Stoke City |
50% |

Draw |
30% |

Wigan Athletic |
20% |

Based on these probabilities you can easily calculate the corresponding odds. The odds for an outcome are calculated when you divide 100 by the specific percentage. For this instance we get:

Stoke City |
100/50= 2.00 |

Draw |
100/30= 3.33 |

Wigan Athletic |
100/20= 5.00 |

The odds we calculated correspond to the theoretical probabilities and are called **fair odds**. But the odds we would find with the bookmaker are actually different than the fair odds. What are the reasons for this? Let’s first go through the business model of the bookmaker in the circumstances of fair odds. On theory, the perfect option for the bookmaker is to take bets from his clients on all outcomes of the event, so that he can pay out to the winners using the money of the clients who haven’t guessed correctly. This is to say that it is desirable that the full amount of the bets on the various outcomes is balanced out according to the odds. For the specific example, if the amount of all bets is $100, then their perfect distribution would be as follows:

Outcome |
Stoke City |
Draw |
Wigan Athletics |

Odds |
2.00 |
3.33 |
5.00 |

Bets |
50 |
30 |
20 |

Pay out |
100 |
100 |
100 |

Such a distribution could only happen in theory. Things are different in practice. Being an organizer of the betting, the bookmaker has to pay out all winnings. He also needs to earn a profit in order to sustain his firm. If the bets for the fair odds are evenly distributed, the bookmaker would pay out 100% of the collected funds which would make his activity pointless. What is more, the actual distribution of the bets is very different in practice than on theory due to the punters’ preferences for teams which are favorites. This always presents a potential risk to the bookmaker. In reality, there are a lot of cases when the bookmaker pays out more than he has collected. For definite periods of time bookmaker firms could run at a loss which makes it necessary for them to have money in reserve. It is also in the interests of the punters to work with financially stable bookmakers who will always be able to pay out. It is an undeniable necessity for the bookmaker to earn a profit which is included in the odds that he offers and this profit is called a **margin**.

**Margin of the Bookmaker**

With various informational sources you can also find the terms juice or vigorish (vig). In essence, the margin (the profit) is the sum which would remain for the bookmaker in the case of a theoretical distribution of the bets in accordance with the odds. The margin is in percentage terms and is calculated as a correlation between the amount of the profit and the whole amount of the bets. Let’s go back to the example we previously discussed in the terms of fair odds. Let’s include a margin for the bookmaker and see what the difference would be.

We decrease all odds with 10% and keep the sum as well as the theoretical distribution of the bets. The table would look like this:

Outcome |
Stoke City |
Draw |
Wigan Athletics |

Odds |
1.80 |
3.00 |
4.50 |

Bets |
50 |
30 |
20 |

Pay out |
90 |
90 |
90 |

We notice that whatever the outcome, the payment would be $90 and the bookmaker would keep to himself $10 from the collected $100. In this specific case the margin is 10% but in practice it may vary. There are various factor which influence the amount of the margin. The basic ones are: the type of sport and the specific league. The margin for popular sport events played by major leagues could be reduced up to 3 – 4%. However, there are some sports for which the probability of a victory of a team/a participant cannot be specified with certainty. In such cases the margin can reach up to 15 – 20%. Still another factor for the amount of the margin is whether the prediction is for a main or some additional outcome of the event. It is difficult to give a precise prediction for some of the additional outcomes. In order to insure himself against an eventual error the bookmaker may increase the margin for these outcomes. The number of the various outcomes for an event is of great importance for the margin. If there are a lot of options, the imbalance of the distribution of the bets would be greater. When, in practice, the distribution deviates from the theoretically more balanced one which we discussed in the examples above, then the risk for the bookmaker is higher. All that leads to a higher percentage of the margin.

** **

**Reduced Margin**

American sports are usually presented with a line with 2 outcomes which includes handicap. The handicap is such that it would equalize the chances of the teams. The adequately chosen handicap also divides the punters into equal groups of supporters of the favorite and the underdog. This situation presents an opportunity to the bookmaker to use a lower margin when he presents the lines rather than a margin he would use for the soccer lines with 3 outcomes. The odds for the two outcomes are usually equal 1.91/ 1.91. This could also look like this – 1.909/ 1.909, if the bookmaker rounds the odds to 3 places after the decimal point. The amount is such since it is based on the amount 110 which is used in the American system of presenting the odds.

Since we already know how the bookmaker’s margin is calculated, let’s see exactly how much it is for a line with 2 outcomes and odds of 1.91/ 1.91. Let’s assume that the distribution of the $100 bet is equal – $50 for each outcome. The bookmaker pays out the winners 50 x 1.91 = $95.50, keeps 4.50 % for himself, which is 4.50 % of the earnings. This margin is **standard**.

As it is with other businesses, bookmakers also compete for clients. What is more the methods for analysis of information and predictions of the outcomes of the events are elaborated.

The effect of both of these factors has led to the emergence of lines with even lower margins which are called **reduced margins**. Some of the firms, such as **Pinnacle**, have offered lines with two outcomes for American sports with odds of 1.95/ 1.95.

The use of Asian handicap for soccer has led some Asian bookmakers such as **Sbobet**, 188bet, etc. to offer even more favorable terms to the punters for the lines with 2 outcomes. The odds which are offered are, for instance, 1.96/ 1.96.