When bookmakers place odds on the market, they first estimate the probability of each outcome. For example, in a market where the coin toss wins, the bookmaker will assume a 50% chance of Team X winning. When using extra odds, the fair odds of a bet are equal to the inverse of the bettor’s estimated odds. In this case, 1 / 0.50 = 2.00. To finance their operations, bookmakers adjust these odds to create a margin’s profit for the market. For example, a typical bettor’s odds of Team X winning the coin toss is 1.91. The difference between the published odds (1.91) & the fair odds (2.00) is the bookmaker’s margin.

The bookmaker’s margin is a measure of the bookmaker’s margin for an event & is a hidden transaction cost for punters. This profit is how bookmakers finance their services, but bookmakers differ in the margin they use. From a kicker’s point of view, the lower the limit, the better. The difference between 1.90 & 1.92 line odds may not seem remarkable for a single bet, but this difference has a compounding effect when betting repeatedly. It can easily make the difference between winning and losing money.

Unfortunately, the bookmaker’s margin has conflicting definitions, and synonyms are a lively concept. Even on Wikipedia, the explanation of calculating energy depends on the article you’re looking at. This website uses the definition of bookmaker’s margin (also called overround) in the Wikipedia article Mathematics of bookmaking and the meaning of Vigorish as used in the Wikipedia article Vigorish.

Bookmaker Margins Interpretation

The margin measures the bettor’s profit if they receive a bet on each outcome in proportion to the odds. Suppose a bookmaker offers odds on outcome A and b on outcome B. If a rate b/(a+b) is a bet on outcome A & a/(a+b) is a bet on outcome B, the bookmaker will receive the same profit regardless of the outcome.

For example, note that the bookmaker’s margin for the two events generated above is 3.5%. Suppose a total of $100,000 is bet on the market with the following:

 (1.64/(1.64 + 2.35)) x $100,000 = $41,102.76 wagered on Oklahoma City &

     (2.35/(1.64 + 2.35)) x $100,000 = $58,897.24 wagered on Denver.

Depending on the result, the bookmaker will pay one of the two amounts:

 If Oklahoma City won: $41,102.75 x 2.35 = $96,591.48

     If Denver wins: $58,897.24 x 1.64 = $96,591.48

The bookmaker accepts $100,000 in bets but only pays out $96,591.48 to the winner. The margin’s profit is ($100,000 – $96,591.48)/$96,591.48 = 3.5%, as the margin was calculated earlier.

A bookmaker rarely receives bets in perfect proportion to the odds, but in countless events, the bookmaker’s margin equals the average profit margin of all events.

To provide insight into how odds relate to margin, the table to the right compares even line odds (a bet with a 50% chance of winning) to the relevant margin. Note that the 2.00 odds equals a margin of 1.00 (100%) since the bettor does not make a profit on the market.

Combined Margin

A ‘combined’ margin calculates for each market by taking the best available odds across multiple bookmakers. This aggregate margin represents the realistic margin that can be earned by owning a portfolio of bookmaker memberships and trading around the maximum odds.

The combined margin is always equal to or lower than the bookmaker’s minimum margin. The greater the difference between the odds of two, three, or more bookmakers, the lower the combined margin.

In the US Open men’s singles 2021 match between Brookby and Djokovic, we observed the following markets:

bet365:

Djokovic: 1.04

Brooskby: 13.00

PlayUp:

Djokovic: 1.01

Brooskby: 18.75

For this market, the bet365 bookmaker margin is 3.85%, while the PlayUp margin is 4.34%.

If we combine these two markets by taking the greater available odds, it is:

Djokovic: 1.04

Brookby: 18.75

The combined for this is 1/1.04 + 1/18.75 – 1 equals 1.49%.

Aggregate margins are important to beating the bookies because they lower the hurdle rate needed to make a profit. The corresponding line odds for a 3.85% margin at bet365 are 1.926. To make a profit on 1,926 odds, you must win more than 51.9% of the time. In contrast, the corresponding line odds for a 1.49% compounded margin is 1.971. To make a profit on the 1,971 odds, you only need to win more than 50.7% of the time.

Note that if the combined margin is negative, there is an arbitrage opportunity.

Bookmaker Margin vs. Vigorish (Vig)

Another popular term, especially in the US, to measure a bookmaker’s margin is leverage. It is often referred to as Vigorish, for short, or juice. In this article, the term vig refers to calculating another bookmaker’s margin.

In other words, the bookmaker’s margin is the bookmaker’s profit ratio compared to the payouts to the winners. At the same time, life refers to the margin compared to turnover, i.e., of the original bets. Since the total payout is always lower than the total turnover, the bookmaker’s margin is greater than the dynamic for a positive margin.

Referring to the recent NBA example:

The bookie margin is 1/1.64 + 1/2.35 – 1 = 3.53%

while vig is (1 – 1.64*2.35/(1.64 + 2.35)) = 3.41%

If $41,102.76 is wagered on Oklahoma City & $58,897.24 is wagered on Denver, the bookmaker receives $100,000 in bets & pays out $96,591.48 to the winners, regardless of the outcome. The bookmaker’s margin is ($100,000 –$96,591.48)/$96,591.48 = 3.53%, while the bullish is ($100,000 – $96,591.48)/$100,000 = 3.41%.

Both of these measures of bookie profit margin are valid, giving you an understanding of what each one represents. You can think of bookmaker margin as meters and vigor as yards.

Remember that if the bookmaker’s margin is 0%, the life is also 0%. If one is negative, so is the other.

For a market with n outcomes, the general formula for the odds when using decimal odds is:

Where odds is a set of odds(1), odds(2), odds(3)… odds(n).

You can convert back and forth between the bookmaker margin and Vigorish using the formula below:

vig = bookmaker_margin / (1 + bookmaker_margin)

bookmaker_margin = vig / ( 1- vig)