How to Calculate Bookmaker Margins
26 April 2019
Many bookmakers claim to offer the best odds or best value on different sports or markets. However, it’s quite difficult for the punter to know if this is true or not. This is unless they calculate the bookmakers margins.
What are Bookmaker Margins?
Basically, a bookmaker margin ensures the bookmaker gives themselves the best chance of making a profit by pricing up the betting market to above 100%. This gives them a margin to pretty much guarantee a profit regardless of the outcome of an event.
To explain this fully we will use a simple coin toss.
A normal coin has two sides, heads and tails, so if you tossed that coin the odds of it landing on heads are 50% and on tails is the same 50%. If betting odds were offered to represent the chances of each outcome in a fair market, the bookmaker would give you 1/1 (2.00 in decimal odds).
This means that if you bet 100 on heads and predicted the correct outcome, you would make a profit of 100. But, if you predicted the wrong outcome you would lose 100.
Lets say 10 people placed a bet, with 5 saying heads and 5 saying tails.
Regardless of the outcome, the bookmaker would take stake money of 1000. This is 500 on heads and 500 on tails. However, the bookie also has to pay out 1000. The 500 staked on heads at odds of 2.00 is a payout of 1,000 and the same for tails. This doesn’t give the bookie any profit at all, and profit is what they are in business for.
So, the bookmaker will add a margin to ensure they make a profit.
If the odds offered on each outcome were lowered to 4/5 (1.8), it would mean each winning bet would only receive 180 back instead of 200. This means the bookmaker still takes 1000 in stake money but only pays out 900, meaning a 100 profit from each coin toss.
However, the punter who wins the first coin toss may turn a profit but the same people may bet 10 times and the outcome is 50/50 with the coin landing heads five times and tails the other five. Each punter would lay out a total of 1,000 in stake money (100 x 10), and only receive 900 back from their five wins. This means that every punter would be down 100, or 10% of their total stake money.
The bookmaker, on the other hand, ends the ten coin tosses with a total profit of 1,000. This is despite the fact that the chances of each outcome were 50%.
How to Calculate Bookmaker Margins
Now you know what a bookmaker margin is, you need to be able to calculate how much of a margin has been set so you know which bookie is indeed offering the best odds available.
This can be done using a simple mathematical equation that works out the total margin for an event. As you will see, the equation uses decimal odds instead of fractions. Many online bookmakers will give you the option of viewing odds in decimal or fractions, but there are resources available to give you this information if the site does not.
(1/decimal odds for A) x 100 + (1/decimal odds for B) x 100 = bookmaker margin
We can give an example using a match from the world snooker championship.
Player A odds – 3.50
Player B odds – 1.30
So, (1/3.50) x 100 + (1/1.30) x 100 is the equation which gives 28.57 + 76.92 = 105.49%.
So, the bookmakers margin here is 5.49%.
For events with three possible outcomes, such as a football match, you use the same equation but with the odds for home win, away win, and draw all added together.
Home Team odds – 1.80
Away Team odds – 5.00
Draw odds – 3.40
So, (1/1.80) x 100 + (1/5.00) x 100 + (1/3.40) x 100 = Bookmaker margin
Meaning, 55.56 + 20 + 29.41 = 104.97%. This gives a bookmaker margin of 4.97%.
How to Calculate Commission
Obviously, once you’ve worked out the bookmaker margin for each market you can then work out how much commission you are paying on your bet.
To do this you take the overall bookmaker margin, 104.97% from our football example above, and use it in another equation but by putting it as decimal odds.
(1 – (1 / Market Margin)) x 100
So, it would be (1 – (1 / 1.049)) x 100
Which is, (1 – 0.95) x 100
Therefore, betting commission for this market is 5%. Meaning that for every 100 you bet, 5 of that is basically going to the bookmaker as commission.