# What are 'True Odds?'

A price of \$1.85 for a horse to win gives us much more information than you would initially think. A price of \$1.85 indicates the bookmaker thinks the horse has approximately a 54% chance of winning. To calculate the chance of a horse (or any bet) winning simply divide 1 by the price. eg. 1/\$1.85= 54.1%.  The table below shows the market implied chances of each horse winning the 2016 Doncaster Mile.

Notice that the Offered Percentages in the table above total 122.5%? If there can only be one winner of the race, the true percentage chances of each horse winning should total to 1 (100%). The extra 22.5% represents the bookmaker’s percentage (over round); this extra 22.5% is basically how bookies make their money. The greater this percentage is over 100%, the more money bookmakers will expect to make from the market; the lower it is (closer to 100%), the more competitive the bookmaker is being on price and the more likely the punter should be to finding a good bet.

To find an estimation of the ‘true odds’ we need to adjust all prices so that the percentages add to 100%. A simple adjustment can be made by dividing each Offered Percentage by 122.5. From this we get what I will call the True Percentage. By converting this percentage back to decimal odds (by dividing 1 by the True Percentage) we get an estimation of the ‘true odds’ of each horse in this race. If the bookmaker’s odds are the best source of pricing information we have, then we could conclude that we need to find a price of \$2.27 on Winx to make a long-run break-even bet on the mare. Any price greater than that is likely overs.

One final thing to note regarding the Doncaster 2016 odds is the Favourite-Longshot bias. Bookmakers will always offer more competitive odds on the favourites than the longer odds runners. The table above shows that Winx’s true odds are as high as \$2.27 when we calculate the straight line conversion from the 122.5% book percentage. In Actual fact, Winx’s true odds may be closer to \$2 when factoring in the longshot-favourite bias. And the \$251 runner Aomen, is likely running at true odds of \$500 plus.

The favourite-longshot bias exists for multiple reasons. One being that bookmakers will be more competitive in pricing a favourite due to the larger flow of money for favourites. With more money flowing for and bookmakers adjusting prices more carefully for, market information is likely more efficient for the favourite. Bookmakers will offer \$251 on Aomen, basically,  because they can! The same punters who will likely back the gelding at \$500, will do the same at \$251 and the bookies have no need to risk over paying.