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The First Rule of Book Club …

by Noel Hayes |  Published: Oct 01, 2007

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If something seems too good to be true - it probably is! A punter's first reaction to bookmaking is usually that it's money for old rope, but those who think this likely misunderstand the fundamentals of the profession.

A bookmaker's "book percentage" or "book," as it is colloquially known, is defined by the venerable industry publication the Racing Post as the "sum of the quoted probabilities across all horses in a race." Bookmakers assign each horse in the race a probability of winning, which is represented by the odds. To translate these odds into the book percentage, you add one to the odds and divide it into 100. So, 3/1 contributes 25 percent to the book, (100/(3+1) = 25 percent), while 4/1 contributes 20 percent to the book, and so on.

In its simplest form, the book percentage is designed to serve as an indicator of the level of bookmaker profitability on a given race. If a book is 125 percent, the bookmaker can expect to make a profit of 20 percent (125/25) on that race. However, the principle upon which this rests is that the bookmaker can lay each horse in the race for an amount proportional to the amount it contributes to the overall book. Furthermore, the favourite/long-shot bias also dramatically distorts the book percentage.

Consider the hypothetical situation in which the bookmaker's aim is not to make profit but rather to provide a service such as a five-horse race in which each horse is deemed to have an equal (20 percent) chance of winning. In a fair market, each horse would be priced at 4/1. If the bookmaker were to accept a bet on the horses' equal in value to their book percentage, in this case 20 percent, a bet of €20 per horse, at 4/1, he would have an evenly matched book. He would know that regardless of the outcome of the race, he must pay €100 to the holder of the ticket on the winning horse. In this case, the bookmaker makes zero profit and the betting public as a group also makes zero profit.

By the Book
In the real betting world, it is likely that one of the horses would be 6/4, another one maybe 2/1, and the remaining three horses 4/1. In this instance, the book would be 133 percent. Again, if the bookmaker accepted a bet equal in value to the respective horse's contribution to the book percentage, he would accept a bet of €40 on the 6/4 shot, €33.33 on the 2/1 shot, and €20 on each of the 4/1 shots. The bookmaker has a maximum liability of €100, but has generated turnover of €133.33. Regardless of the result of the race, the bookmaker has generated profit of €33.33 on his turnover.

Sounds easy, right? Sadly, it's not! The concept of book percentage is dependent on having an evenly matched book. The bookmaker is at the mercy of laying each horse for the amount that it contributes to the overall book. This evenness of match - that is, the ability to lay horses equal to their respective book percentage - is, in truth, never achieved. This results in a bookmaker having an uneven book, and in this instance, the reported book percentage is no longer a true reflection of the market, and reliance upon it as an indicator of the market is ill-advised.

Many people, not armed with an understanding of the fundamentals behind the concept of book percentage, are too quick to jump to assumptions that a bookmaker is offering poor or even no value in a given market. They look at the reported book percentage and are very quick to use this as a stick with which they beat the bookmakers for offering punters no edge. From the above example, it is easy to see that the book percentage is a weak measure. It is balanced upon the concept of evenness of match, and it should be easy to understand that this is almost impossible to achieve.

Bias and Book Percentage
Another reason why the book is not a true reflection of the market is due to the favourite/long-shot bias. Bookmakers will tell you that they are unable to lay certain horses regardless of their price - whether that is 20/1 or 100/1. With that in mind, when pricing a horse, they err on the side of caution, in case a shrewd stable decides to go for a gamble.

Inasmuch as punters who want to back an outsider are as likely to back it at 14/1 as they are 40/1, the bookmaker will serve to limit his potential liabilities on outsiders without unduly compromising his perspective turnover on a race and offer outsiders at odds shorter than what they perceive to be their true price. In this instance, it is important to consider that the punter, armed with more information than the bookmaker, considers the price available to be fair and accepts the available price.

Revisiting the earlier example of the five-horse race, we see how the favourite/long-shot bias affected the reported book percentage. The book was 133 percent, which included the three horses priced at 4/1. Let's suggest that the real price of these horses should in fact be bigger, say 5/1, 7/1, and 12/1. This would generate a book of 110 percent.

Exchange Odds
With the above in mind, a punter should be aware that the value prices are often to be found at the front end of the market, as these horses' odds are not unduly biased. This is why you will see the outsiders trade much higher on exchanges such as Betfair than on-course. In general, exchange layers price horses and not a book, so in order to get a taker at the offered price, they need to offer odds that reflect more closely the true odds of the horse; in other words, they need to offer unbiased odds.

With this knowledge, punters begin to understand that there is much more to bookmaking than setting odds that appear unfavorable to the punter and sitting back to reap the rewards. Successful bookmaking requires skill and judgment. Evenness of match is crucial to the use of book percentage as an indicator of bookmaker profitability. Not only will bookmakers fail to have an even book, they will very often have markets in which they have been unable to lay some of the horses.

In the five-horse race example, assume that the bookmaker was successful in finding customers to back only three of the five horses - the 6/4, 2/1, and one of the 4/1 shots. If the bookmaker lays each horse evenly, he has a liability of €100 on turnover of €93 - which is hardly an ideal situation for him, and in practice, more extreme situations are regularly found.

Judgement Books
This market behavior is often displayed in large-field non-handicap races. Take a 25-runner maiden hurdle or a 20-runner flat maiden. If you examine the market in these races, you often will see that only the front two or three horses in the market are wanted by punters. This leaves the book in a sorry state, and whether or not a bookmaker profits on the race is a result of his judgment call. Despite a huge reported book percentage of sometimes close to 200 percent in these races, the bookmaker is often running a judgment book and fighting a hard battle against the punters.

A recent example of this was the Nassau Stakes run at Goodwood, in which Peeping Fawn defeated Mandesha and Light Shift. This race had eight runners and a reported book percentage of 113 percent. Market activity centered on these three principals, priced at 2/1, 3/1, and 7/2, respectively. Others in the race ranged from 6/1 to 80/1. The book of the first three was 76 percent, and all were well-supported. This looks like a lose-lose situation for the bookmakers, before you even take account of the each-way wagers on the placed runners.

This is a real example of where bookmaker judgment is crucial to profit, and if nothing else, it shows that punters should be less hasty about jumping to conclusions of a lack of value in betting markets. Remember, there are two sides to every story, and to be able to tell the story properly, you need to understand them both.