Mathematics Of Betting

Odds-On mathematics of betting

Betting forecasts and mathematical derivation

Walk into any bookmakers shop, in any UK high street and you will be met with an array of colorful features, posters and betting promotions. You would be forgiven for thinking that bookmaker's had lost the plot and were falling over themselves to give money away. Quite the contrary, lurking within the betting markets and betting forecasts, the mathematics and betting odds are very much against the punter.

Few professional punters make more than 10% on turnover. For the casual punter the difference between betting a horse at 6 to 4 and betting the same horse at 7 to 4 - probably appears to be insignificant. Yet the difference between these odds is 25% in outlay, and for the professional punter, always getting the lower price may mean the difference of making a profit or making a loss, long term.

Chances and Probabilities

It is normal for bookmakers to express betting odds in terms of percentage chances. To translate odds into chances, simply add up both sides of the odds and divide the number on the right hand side by this number. Thus for a horse at 2 to 1, gives 1/3rd or 33.33% and for a 6 to 4 chance, gives 4/10ths or 40% [see TABLE 1].

What the Punter is up against !

EXAMPLE 1

Imagine a three runner race where each horse has an equal chance of winning. The true odds for each horse is 2 to 1. The odds neither favor the punter nor the bookmaker. Mathematically speaking, the probability of any one of the horses winning, is a 1 in 3 chance [or 33.333% see TABLE 2, Race Example #1 ]. Adding the individual probabilities of each horses to give 1.0 [or 100%]. No matter how many runners, no matter what the individual chances of any horse, the total true probability of all the horse winning, will always total 1.0 [100%].

EXAMPLE 2

In reality, bookmakers build a bias into their betting forecasts, so in theory, no matter what the result, the bookmaker will make a small % profit. Take another 3 runner race [ see TABLE 2 ]. The total race bias is called the race over round. In this case the sum of the individual horse % chances exceeds 100 %. The betting odds are now in the bookmakers favor and the punter will no longer be "all square" if all horses are backed. The amount in excess of 100% is the degree to which the betting odds are in the bookmaker's favor. Bookmaking is founded on the principle that any horse racing betting forecast will have a certain amount of over round built into the odds.

Changes in betting over round

We randomly collected the race %over round for over 200 races run in the UK during the 2007-2008 flat and jumps season. The average over round for all these races was 1.22 [122%]. The race over round is not constant, it varies race to race for a number of reasons. These include race type, racecourse and the number of runners. If you plot all the 200 over round data against the number of runners [see TABLE 3], you can see that the over round increases as the number of runners increases. So, for a 10 runner race, the over round is approx. 1.17 [117%] and for a 30 runner race, the total over round is approx. 1.39 [139%].

Taking another fictitious race with the average over-round of 1.22 [122%]. Assume there were thousands of punters, all randomly picking horses with a pin, then these punters would lose 22/1.22ths of the total investment made [i.e. 18p for every every pound bet]. Or putting another way, the bookmaker would make a profit of 18p for every pound bet. The bigger the turnover, the bigger the field, then, the bigger the over-round, the bigger the profit. This built in race over round is the hill that the professional punter must over come in order to make a profit from betting on horses.

Seeking an Edge!

Punter's must somehow find an edge in their betting strategy. Seeking value betting opportunities is a potential weapon that punters could use to make a long term profit from horse race betting. The successful punter will seek to bet horses only when the betting odds are in their favor. i.e. only when the true odds [% winning probability] is greater than the betting odds being offered by bookmakers.

Odds-On uses a specialized horse racing software to identify value betting opportunities the profit/loss from following the betting advice is shown on the horse racing results page.