Impact of the ‘Overround’ on Accumulators, Multiple Bets, and Parlays

Betting odds are supposed to reflect the probability (statistical expectation) that a particular event will happen.

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 known as ‘multiple bet’, ‘parlay’, ‘combo’, or ‘acca’), 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

On 10 of the bets, the overround (profit margin) was between 6.28% and 38.89% (red).

Five bets were offered at negative ‘value’ which ranged between 4.31% and 16.21% (green):

Table 4: Bookmaker overround for each bet – Swiss Cup, Scottish Cup, Champions League Final, Portuguese Cup, Coppa Italia, 2012

Why do bookmakers love accumulators, multiples, or parlay bets?

In the article The Permutations of 5 Cup Finals in 5 Days I explained:

To compute the overall probability of a certain combination of results, simply multiply the individual probabilities together. Thus, the combined probability that all five favourites won was:

52.8% x 45.9% x 64.9% x 54.7% x 43.7% = 3.76%

Effectively speaking, the 3.76% combined chance of all five favourites winning means this would statistically happen only once in every 25 seasons.

The above calculation is based on the REAL chances.

If you take Tipico’s probabilities (Table 3) then the equation is as follows:

The accumulator’s odds for all five favourites to win would have been (Table 1):

This means that a winning accumulator would have paid the bettor 17.63 times his stake as a return.

However, based on the true probabilities, all five favourites win only once in every 25 betting rounds (3.76%), which means that the bettor will lose his stake 24 times.

Winning 17.63 times his stake just once in 25 attempts is just not a prudent investment!

The overround (profit margin of the bookmaker) in this example is 42.8%:

Interpretation

The exponentiated overround for an accumulator as in this example (five-fold multiple bet on five favourites to win) gives the bookmaker a profit margin of more than 40%.

Of course it happens now and then that the bookmaker pays out, because a chance of 3.76% is not zero.

Tipico encourages accumulators by publishing daily lists of ‘lucky’ winners and the amounts they have won to encourage even more people to put their hard-earned cash into multiple bets, where the odds are definitely stacked in favour of the bookie.

Conclusion

Bookmakers just LOVE accumulators, multiple bets, and parlays, but people with dollar signs in their eyes continue to play..!

Amen.