The Art of Bookmaking

When a football team goes into battle with the opposition, their coach has usually done hours of research in an attempt to gain a winning advantage. The coach will look at how the opposition plays, the systems they have in place and what tactics they have used in the past. The coach is attempting to gain an edge over the opposition by mapping out a plan that will hopefully see his side triumph.

The same rules apply for punters who bet with a bookmaker. It's important to understand how the bookmaker works; how they set their odds, why they change them as the betting progresses, why they have maximum bet amounts and the types of bets bookmakers gain the most money from. Of course, the latter is very important because a bookmaker gains what the punter loses and just like a football coach, if we fully understand how a bookmaker works, then we can gain the edge over them.

Bookmakers have numerous ways of setting their odds but to understand it fully, we have to look at the bookmakers which are generally the first to 'price-up'. Different bookmakers scattered around the world will be the first to produce odds for certain betting markets - you won't find one being first out for everything. In doing so they will generally have a team of experts amongst them that formulate prices based on their opinion. Setting odds at the start can be a very risky business. Their opinion might differ to that of the betting public, which may result in some heavy action on the options the market determines to be mispriced. It's no coincidence, therefore, that the bookmakers who produce the earliest of odds have large bookmakers' margins.

A bookmaker's margin is basically the net return that bookmakers should profit over the long term. An example of a tennis match, priced up by bookmakers:

Rafael Nadal 1.53 (8/15)
Andy Murray 2.37 (11/8)

The bookmaker's margin here is calculated by summing the reciprocal of the odds as below.


Let's say that £6,535 was bet on Nadal and £4,219 was bet on Murray. No matter what the outcome, Bookmaker X here would make a profit of £755. Given that £10,754 was bet on this event, their profit on turnover is equal to


which, of course, is a sound position for bookmakers but a far less desirable market for punters. Bookmakers who release odds earlier than other bookmakers will usually price-up in a conservative manner by reducing their prices and thus increasing their margin. The margin can be thought of as a 'buffer'. The greater the buffer, the less their potential liability they will have as a result of pricing-up incorrectly.

Of course, in the example above, the exact amount quoted won't always be as balanced, and more often than not a bookmaker's book will not be balanced. What this means is that more money has been bet on one side than the other, to the extent that they could lose money should one of the players win. This, however, will result in an increased gain should the option that has been laid loses.

This is where we as punters come in. Bookmakers with margins of around 107% will never make 7% on turnover in the long term but will usually make an amount smaller than this because what the punters bet on will influence the bookie's price. Prices move because too much money has been bet on one outcome, giving the bookmaker a large liability should that player win. Like punters, bookmakers are always looking to reduce their liability and to do this, they will attempt to attract money on their opposition. In essence, they attempt to balance their book. To do this, the bookmaker will increase the price on the opposition to make the price more appealing to punters while shortening the price of the runner which has been well backed in an attempt to discourage further investment on that selection.

Let's assume that we had the same amount of money bet on Nadal and Murray, as listed initially above, before assuming that a lot of money has subsequently been bet on Nadal. There could be injury concerns on Murray, or perhaps other bookmakers have opened up the betting on the market, with prices leaving Bookmaker X the best price for Nadal. In other words, later opening bookmakers rate the chances of Nadal higher than Bookie X and offer prices of 1.48 and 2.5 for Nadal and Murray respectively. This will result in punters betting on Nadal going to Bookie X and bettors of Murray going to the later opening bookmakers, as these are the best prices available.

We assume £10,000 is bet on Nadal at his current odds of 1.53. At this stage, should Nadal win, Bookie X will be out of pocket by £4,544, but would gain £10,754 should Murray win. Bookie X can do a number of things. They could lay off the bets, which we will talk about later, or they can change the odds to be more in line with other bookmakers.

Let us say that they decide to change the odds, and re-price Nadal at odds of 1.45 and Murray at 2.60, which still keeps their bookmaker's margin of over 107%. If £5,884 is bet on Murray at these prices, Bookmaker X's books will be exactly balanced and they gain a profit of £1,340. Their profit has gone up because their turnover has increased. Their bookmakers' margin, however, has in fact gone down. Now out of the £26,638 that has been bet, they are only now making a profit on turnover of 5%, as opposed to the earlier 7%.

As stated before, bookmakers will never make the amount that their margin is calculated at. Of course, in the above example it might not matter how much the bookmaker decides to change his odds, he may never balance his books. In fact, bookmakers rarely do and are not fussed with losing or gaining money on any one individual event. They are primarily concerned about the long-term profit (which should be our aim as punters too!).

So what other options does Bookmaker X have if they don't balance their books? Well, they could take the risk on for this particular match and hope that the outcome will favour the side that they will gain money on.

However, it could be that one of the players is under a serious injury cloud and they decide that it's best to "lay-off" so as to eliminate any risk and potential loss. Because Bookmaker X has a high bookmakers' margin, this means that they will easily be able to find several bookmakers that have good odds that are better than their own. Let's just say that even though they changed the odds, no other bets got matched, and hence they have £16,535 bet on Nadal at odds of 1.53 and £4,219 bet on Murray at 2.37.

As other bookmakers have better odds despite the odds changing, Bookmaker X has found odds for Nadal and Murray at 1.5 and 2.75 respectively. By matching the £10,000 bet on them with £10,000 of their own at odds of 1.5 they eliminate any risk that they might incur. It is also quite often that bookmakers will 'lay off' on betting exchanges, so even though you believe you are betting against other punters, you are in actual fact also betting against other bookmakers on the exchanges.

Bookmaker X no longer has any liability for this event and will make a profit of £456 if Nadal wins and a profit of £754 if Murray wins.

Bookmaker X also offer odds for set betting for Nadal vs. Murray and the odds given are as shown below:


If we calculate the bookmakers' margin for the odds listed above, we obtain a result of 120.6%. This is a lot larger than before and means that punters have to be 20% better than the bookmakers in order to start gaining a long-term profit by betting on these results. This ultimately means that it is very hard to find an edge betting in such markets. In fact, the more possible results there are in a market, the higher the bookmaker margin will be. This is because if there are more options to bet on, generally the odds will be higher. The added bookmaker's percentage insures against the potential liability from the bookmaker's perspective.

What you will find is that bookmakers make a large amount of money from punters betting on events where there are a large number of betting outcomes possible (e.g. Correct Score, First Goalscorer). This is no surprise, as the bookmakers' margins are so high. Unless one can pick obvious errors in the bookmakers' prices, punters are best to stay away from such high percentage markets.

This leads us to the favourite / long-shot bias that is found in bookmakers odds. As we mentioned above, bookmakers compensate for the larger liability by increasing their margin, so as to gain a large amount in the long term. The same actually happens when we have events where there are big outsiders.

Let's suppose that Bookmaker X are pricing up the odds between St. Helens and Castleford in the Super League, the former a traditional powerhouse, the latter a regular struggler. Let's presume that they believe St. Helens has a 90% chance of winning. Given this, they should price St. Helens at 1/0.9 = 1.11 and Castleford at odds of 1/0.1= 10. The market here is 100%. The bookmaker will then want to add their margin in and as such, they decide to make the odds 1.05 and 8.50. Notice here that if someone were to place a large bet on Castleford at odds of 8.5, then they would be exposed to a large liability whereas if the same amount was placed on St. Helens at odds of 1.05, the risk would be minimal in comparison.

To counteract this, bookmakers work a favourite/long-shot bias into their odds. Instead of offering 1.05 and 8.5 on the two teams, they might offer 1.1 and 6.2 on St. Helens and Castleford respectively, hence reducing the risk of Castleford's large price. Bookmakers in general want to lay the favourites as they are the most popular with punters, and the risk is far less than taking on the outsiders.

In fact, this favourite/long-shot bias is prevalent in just about every betting market. As a very general assumption, this means that proportionately the odds for an underdog are not as good as the odds for a favourite. This doesn't mean that we should only bet on favourites. It does, however, mean that we only need a smaller advantage to gain in the long-term betting on favourites (with bookmakers) than what we do betting on the underdogs.

So how does a bookmaker set his original odds? We mentioned before that most of the early bookmakers will have a number of experts in each sport and they will come to a decision as to the opening prices. However, it is important to note that the odds they set are not based on the true probability of the teams winning, but rather what the general betting public perceive the true probability to be.

This important difference is subtle but extremely important. In fact, it is the reason why professional gamblers can make long-term profits out of bookmakers. The goal for most bookmakers is to balance their books, and in doing so ensure a guaranteed profit. Let's just say, however, that they thought that Nadal was an 80% chance to win versus Murray. A probability of 80% is equivalent to odds of 1.25, but the bookmaker would not want to be too obvious about what the bookmaker's intentions are, especially considering that all other bookmakers are around the 1.45 mark. Instead a bookmaker moves his prices slightly so that he might get more bets on Murray than Nadal. He might offer 1.4 for Nadal, which in turn would push Murray out to, say 2.75. In this case, if you fancied Murray, then these odds of 2.75 are the best you can get. However, if you fancied Nadal, then the current bookmaker doesn't have the best odds at 1.4.

Here we have a situation where a bookmaker is deliberately moving his odds away from the norm in order to make the amount of money bet on each team lopsided. So this particular bookmaker is not trying to balance their books but rather is having a bet themselves with the bookmakers' margin still on their side.

Of course, it is impossible to work out the actual true probability of a team winning; if we could, then we would be amazingly rich! But one can attempt to approximate it. Whenever we bet we are approximating probabilities in our heads. Even if you don't understand what probabilities are, you are still making a judgement that the odds offered are greater than that of which you believe and hence, you bet on them.

And this is the gambling game which we play. The better the judge you are at approximating the true probability of a team winning, the more profitable a gambler you will be.

The original version of this article was written by Matt Elliott - co-owner of Australian based leading sports and racing forum PuntingAce