The Bookmaker and his Overround

Loosely speaking, anyone offering odds on an event is known as a bookmaker, or bookie for short. Daniel and Joseph in the example above could both be considered bookmakers, setting odds for each other in a friendly wager. But the term properly applies to persons or businesses that provide an odds market for one or more events, with betting prices available for all possible event outcomes, adjusted according to the demand of the bookmaker’s customers, the punters. “Bookmaking” technically refers to the management of betting probabilities for the purposes of making a profit over a large number of events for which odds are offered. A “book” is simply the full record of betting transactions at all the available odds made with the punters for a particular event.

Unlike the “fair” wager on England between Daniel and Joseph, a bookmaker will never offer a book where the expected probability of all possible betting outcomes on a single event adds up to 100%. The word “fair” is shown in quotes because unlike for pure games of chance like roulette and dice, where the probabilities of one or another result occurring are known exactly, the probability of particular sporting outcomes can only be estimated. Daniel and Joseph can never truly know what the chances are of England or Brazil winning. In a sense, then, “true” or “fair” odds in sporting contests are merely estimations of the expected probability, or chance, of something occurring, rather than exact calculations. The key to profitable betting is the quality of those estimations. If they are accurate (or at least more accurate than the bookmaker) we might make some money. If they are not, we’ll most likely lose some.

Bookmakers’ odds, however, are generally speaking “unfair”, not because they may be better at estimating the probabilities than their punters (although most typically they are), but because they need to take a cut or commission from the wagers they accept. Bookmakers are not charities. Neither do they exist just for the fun of it. They operate to make a profit, and they only way they can achieve this, once they have covered all their operational costs, is to manipulate the odds.  By shortening the odds for each betting outcome the bookmaker will pay their punters less than the expected probability of results suggests they should be paid if they win their bet. If the bookmaker manages his books correctly he will make a profit no matter what the outcome of the sporting event. By manipulating the odds in this way the totality of expected probabilities is increased above 100% (since shortening each price increases the associated probability of each result). This excess above 100% provides a measure of the bookmaker’s theoretical profit margin, and is sometimes referred to as the bookmaker’s overround.

Let’s go back to our original example of England versus Brazil. Suppose this time Daniel and Joseph decided to place their bets not with each other but their favourite bookmaker. What odds could they expect to be offered? Again, let’s assume that that Brazil is twice as likely as England to win the game. If the bookmaker offered fair odds of 3.00 (or 2/1) and 1.50 (or 1/2) for England and Brazil respectively, and if Joseph and Daniel bet £1 (on England) and £2 (on Brazil) respectively on these prices, the bookmaker will make no profit at all, regardless of who wins the game. If England wins, he pays Joseph £2 in winning profit and collects £2 lost stake money from Daniel, breaking even. If Brazil wins, he pays Daniel £1 in winning profit and collects £1 lost stake money from Joseph, again breaking even. After paying his staff their wages to collect these bets, he’s out of pocket; time to manipulate the odds.

Thinking about his profit margin, the bookmaker decides he’s going to offer odds of 2.50 (or 6/4) for an England victory instead of 3.00, paying a profit of £1.50 for a £1 stake. Similarly he shortens his price for Brazil from 1.50 (1/2) to 1.25 (or 1/4), paying £1 for a £4 stake. The implied probability for an England victory is now 40% (or 1 divided by 2.50), whilst that for a Brazil win is 80% (or 1 divided by 1.25). Remember decimal odds and probabilities are interchangeable: one is the inverse of the other. For both results the bookmaker has increased the estimated probability by a factor of 1.2, and together these total 120%. Of course this is not to say that there is a 120% probability of either England or Brazil winning, how could there be. This information is merely informing us that the bookmaker is manipulating the odds (to build in his profit margin) by suggesting either team have more chance of winning than they really do. This time if England wins, the bookmaker will only pay Joseph £1.50 in profit money, whilst collecting £4 from Daniel for an overall profit of £2.50. On the other hand if Brazil wins, the bookmaker will pay Daniel £1 whilst collecting £1 from Joseph, to break even. True, 2 times in every 3, the bookmaker will still not make any money in this scenario, but on the 1-in-3 occasions where England wins he will, in this case £2.50. Consequently, on average after 3 games the bookmaker will see £15 of turnover (3 games multiplied by £5 turnover for each game) to make a £2.50 profit. To put it another way, for every £15 of action the bookmaker sees, he will only have to pay out £12.50 (taking £2.50 profit for himself), which expressed as a percentage is 120% (or £15 divided by £12.50) – the overround.

Of course, more usually punters will stake volumes roughly in proportion to the estimated probabilities of all possible results. If Brazil is expected to be twice as likely to beat England, we would normally expect punters to bet twice as much money on Brazil. If they didn’t then this implies that either they or the bookmaker have miscalculated the fair chances of either side winning. In this case, if Joseph was betting £1 on England, Daniel would reasonably be expected to bet £2 on Brazil. In this instance, whatever the result the bookmaker sees a profit of £0.50 from a turnover of £3, again a profit margin of 120% (or £3.00 divided by £2.50). Such a scenario where the bookmaker manages to balance the books and secure the same profitable outcome regardless of who wins the match is something that he is always striving to achieve. Anything less, and particular where he actually faces a loss on one side of the book given a particular result, is something the bookmaker would prefer to avoid. Intelligent bookmakers just see themselves as middle men, balancing action between competing punters. They generally don’t want to be part of the action themselves, although in the final lesson in the Academy we’ll look at why some bookmakers might actually choose to do so.

Different bookmakers have different overrounds. For straight home-draw-away football betting, Pinnacle Sports for example, has an overround as low as 102%, whilst Interwetten might have one of 110%. Different overrounds exist for different sports too and different betting markets. Generally speaking the more possible outcomes a particular event has the larger the overround will be. This is because the likelihood of any single result occurring is smaller (since there are more possibilities to choose from), and to guard against the threat of mistakes (through for example some insider knowledge held by the punter), the bookmaker will build in a larger profit margin into his book. The average overround for a tennis match, with only two players, is about 106%. For half-time/full-time football bet with 9 possible outcomes, that figure is about 120%. For a golf tournament winner market with potentially over 100 runners listed it will be much higher still. The size of the overround is something a punter should always keep in mind when looking for profitable betting strategies. The bigger the overround, the more unfair the odds will be and the larger the disadvantage he will potentially face, unless he happens to know something that the bookmaker has missed about one of the runners or possible outcomes. Undeniably, however, punters who lack any form of betting skill at all – let’s call them mug punters – will always lose more money in the long run betting markets with larger overrounds.