About Bookmaker Margins and Kelly Criterion
The bookmakers’ margins on sports betting odds is easily the most important information that a sports bettor should have in order to score long-term profits at lower margins for himself. It goes without saying that bigger bookmaker margins can eat considerably into your long-term sports betting returns. Let’s go over a simple guide that will tell you how to easily calculate bookmaker margins on the 1x2 odds.
Smart bettors unlike novice bettors, who simply compare odds, are aware that the real price charged by a bookmaker is including his betting odds’ margins.
Following is an example of a soccer match that can have 3 possible outcomes – draw, visiting team win, home team win. In a certain week of the Premier League season, Bet365 had offered the opening odds of 3.41 for Team A to win against Team B in a home game. The visiting Team B was priced at 2.39, while the offered odds on the possibility of a draw were 3.19.
Possible outcome / Offered odds
Team A win / 3.41
Team B win / 2.39
Draw / 3.19
The 1x2 odds’ margin can be calculated using the following 2 simple steps:
– First, carry out the conversion of odds of all the 3 possible outcomes into their corresponding decimal probabilities
– Solve the following equation once you’re done with that:
Margin = (1 / draw odds) + (1 / away odds) + (1 / home odds) – 1
As mentioned above, the first step involved in calculation of margins applicable on the 1x2 odds is conversion of every 1x2 market into its corresponding decimal probability. That’s actually the equation within every set of brackets above, i.e. (1 / odds)
For the home team win, which in this case is Team A, the decimal probability can be worked out to:
1 / 3.41 = 0.293
Which is equal to 29.3% winning probability
The possibility of a draw can be worked out to:
1 / 3.19 = 0.313
And the possibility of a Team B win can be worked out to:
1 / 2.39 = 0.418
So the table now reads:
Possible outcome / Offered odds / Decimal probability
Team A win / 3.41 / 0.293
Team B win / 2.39 / 0.418
Draw / 3.19 / 0.313
Now, all that you need to do is simply substitute the above provided numbers into the remaining formula, and calculate the bookmaker’s margin as follows:
Bookmaker’s margin = (0.313) + (0.418) + (0.293) – 1
Bookmaker’s margin = 0.024 or 2.4%
Comparing margins offered by different bookmakers
Let’s say another bookmaker, for example Pinnacle, had offered the following odds for the same game:
Team A win = 3.10
Team B win = 2.10
Draw = 2.90
If you calculate the margin applicable to these odds, you’ll figure that it is a whopping 12%, which is almost 5 times higher than the margin of Bet365! Practically speaking, this means that if you had placed £ 100 bet on Team A win on 1x2 market, you’d have bagged an extra £ 31 by placing your bet at Bet365 than placing it at some other major online bookmaker.
How to use Kelly Criterion in soccer betting?
It’s important for sports bettors to always seek a mathematical edge, instead of depending solely on their impulses. Understanding and mastering the Kelly Criterion for instance, is an excellent method for sports bettors to figure out their exact betting amounts. Read on to learn more.
Every sports bettor must pay heed to the following 6 very important questions before placing his bets:
Talking about the context of this write-up, we’ll focus only on the How? question, that is, how much should you bet?
Let’s say you’re contemplating placing a wager on an upcoming English Premier league match. The above listed questions can be adapted in this scenario in the following manner:
– Who to place your bet on? Answer - Chelsea
– Where should you place your bet on? Answer - Bet365, as it offers the best odds
– What should you bet on? Answer - A top 4 finish
– Why to bet on them? Answer - They seem underpriced
– When exactly to bet on them? Answer - Right away
– How much should you bet on that outcome? Answer - This is what we’ll work out!
Majority of sports betting related articles focus only on the first 5 questions, using some statistical or mathematical justifications for the answer to the ‘why’ question.
Talking about it in context of financial decisions, one of the key issues therein is not just finding the right financial products for investment, but also deciding how to shape up the portfolio. In a similar manner, when we talk about the sports betting field, it’s very important for a sports bettor to figure out how much he should bet?
Several papers suggest using Kelly Criterion method, or some derivative of it, for figuring this out. At core, the Kelly Criterion method is used for calculating a certain percentage of your bankroll that should be bet on the concerned outcome, whose odds are normally higher than expected, in order to ensure that your funds grow constantly and significantly.
Kelly Criterion formula:
(bp – q) / b
Q = failure probability, which is 1 – p
P = success probability
B = decimal odds – 1
Let’s take the example of a coin to explain Kelly Criterion-based betting
Imagine you’re placing a bet on the possibility of getting tails from a coin toss. The offered odds are 2.00. But the coin is slightly biased and there is a 52% chance of it turning up on tails.
In this scenario:
Q = 1 – 0.52 = 0.48
P = 0.52
B = 2 – 1 = 1
In this case, the calculation of Kelly criterion will work out to:
((0.52 x 1) – 0.48) / 1 = 0.04
Hence, as per Kelly Criterion, you should bet 4% of your total bankroll. The fact that it’s a positive percentage means that the edge is in your favour, and hence there is a chance of your funds growing exponentially.
Eventually, the Kelly criterion formula provides a unique advantage over other commonly used betting methods like Arbitrage and Fibonacci as there is a lower percentage of risk involved. However, you must keep in mind that it does require very precise calculation of the chances of a particular event’s outcome.