Betting odds are supposed to reflect the probability (statistical expectation) that a particular event will happen.
Image: Elnur (Shutterstock)Because bookmakers are profit-making enterprises who offer bets on the market, it is understandable that they build-in a winning margin to their odds computations. This margin is called overround.
The overround differs from bookie to bookie and can be at its lowest around 2.5% (e.g. Pinnaclesports pride themselves on being the bookmaker with the highest odds and the lowest margins) but can reach 12% or even higher (e.g. Ladbrokes, and most of the other high street bookmakers).
The overround is the bookmaker’s mathematical advantage and ensures in the long run that they will collect more money (stakes) than they will have to pay out to bettors.
It should be obvious that a bookmaker needs this margin in order to pay staff and running costs, and of course to make a profit.
In an accumulator bet (also called ‘multiple bet’ or ‘parlay’), the overround is exponentiated, which increases the profits of the bookmaker by multiples.
Exactly how does this work?
Here’s an example: If the overround is, for example, 6%, then in a five-fold accumulator bet the compound interest is 33.8%.
The above calculation means that a five-fold bet containing individual bets each with an overround of 6% generates a profit margin of 33.8% for the bookmaker. But what does this mean in reality?
Bookmakers overround example
Here is a table for five cup finals in mid-May 2012 (Swiss Cup, Scottish Cup, UEFA Champions League, Portuguese Cup, Coppa Italia), and the odds offered by the bookmaker, Tipico:
Table 1: Bookmakers betting odds (Tipico)
(Swiss Cup, Scottish Cup, Champions League Final, Portuguese Cup, Coppa Italia, 2012)
You will find the mathematically correct probabilities calculated for these five cup finals in our article The Permutations of 5 Cup Finals in 5 Days, and the following table shows the corresponding true odds (or ‘zero’ odds):
Table 2: Calculations Soccerwidow - conversion probabilities to true odds (without an overround)
(Swiss Cup, Scottish Cup, Champions League Final, Portuguese Cup, Coppa Italia, 2012)
Comparing the above tables, you can see straight away that the true odds differ dramatically from the bookmaker’s odds. For example, Basel’s true odds of winning their match were 1.89, but the bookmaker offered this bet at 1.67. The draw in the Swiss Cup final had true odds of 4.05, whereas the bookmaker offered only 3.80, et cetera.
Sometimes bookmakers odds are higher than the true odds. Using our example again, betting on Bayern to win was available at 1.8, although their true odds were nearer 1.54. However, of the 15 home, draw and away bets only five were offered at higher prices than the true odds, and 10 were lower.
Tipico’s average overround was between 4.13% and 6.22% per match:
Table 3: Bookmaker odds converted to probabilities (1 divided by odds)
(Swiss Cup, Scottish Cup, Champions League Final, Portuguese Cup, Coppa Italia, 2012)
After giving it some thought I am not sure if it is completely accurate. In one of your examples you say bookie has 6% overround and then compound it for accumulator and get 1.06 ^ 5 – 1= 33.8%. But bookie will only get 6% overround if its books are perfectly balanced. However I don’t see how bookies can balance accumulator bets, I mean so many different games involved in one bet. If they can’t balance accumulator bets, doesn’t it mean that the overround will be much lower, i.e. just from one outcome and not whole game?
Hi Eldar,
the overround increases as explained in the article and the likelihood to win the bet (accumulator) decreases hugely. Please see here an article on Combinatorics and Probability Theory in Football Betting
Bookmakers don’t balance bets in the way as it is widely believed by simply trying to sell the same amount of bets on each outcome. It’s far more complex.
If you haven’t bought the course book yet you may give it a thought to get it; in that I explain things like that (and many others) in great detail.
Should you be in doubt… here’s a recent comment from a German reader on the book (English readers unfortunately are spare in commenting on benefits once they bought a product)…
“As you say correctly, sports betting is and remains a risky affair with a lot of variables, the best course can’t change that. But thanks to your book “Fundamentals of Sportsbetting”, I now have some insight into how the bookmakers tick and can incorporate this knowledge into my bets.
Finally, I have to say that this was my best investment into betting in recent years.”
I did the math and if you have the edge on the bets in the accumulator (big if!) they can actually be slightly better than singles. However this is negated by the fact that with an acca you cannot pick and choose your odds like with singles. Hence I rarely use them except for fun.