Bookies have long had rules to eliminate “related events”, most obviously say doubling a horse in the ante-post market to win the Guineas and the Derby would not be allowed as success in the first event obviously impacts a fair price for success in the second event.
Occasionally the bookies are forced to consider joint probability, and here they stray beyond expertise and into finger in the air pricing – which we as punters have to take on.
Our ante-post Premier League recommendation is a great example. We consider Man City highly likely to defend their title, generally a 1/2 shot. Not wanting to play at that price we looked at William Hills’ market for naming league winner and top goalscorer combinations.
The obvious starting point was City-Aguero. Separately they are 1/2 and 6/1, a pure double would therefore be 9.5/1. Hills price it at 8/1. Theoretically this can be justified by considering correlation, the principle that movement in two factors are interelated, in this case that a win for City in the league makes Aguero a more likely Golden Boot winner. The difference between 9.5/1 and 8/1 suggest Hills believe a City title makes Aguero around 20% more likely to top the charts.
Inversely, City and Harry Kane are separately 1/2 and 4/1, a fair price double of 13/2, and are priced as a combo at 9/1. This time suggesting a City title win makes Kane 25% less likely to win the Boot.
This has to be taken on. Firstly consider actual correlation – the Premier League Golden Boot has been awarded 26 times and won by a player from the title winning side just 6 times, around 23%. But that’s not correlation. The players concerned would all have been priced no more than 3/1 for the Boot (think Shearer, Henry…), they win with no more regularity than they should according to the Boot market alone (Aguero’s sole win came in a losing City season). This suggests the correlation to a league title win is no more than negligible, and possibly nil.
Then think of it specifically for Kane. Spurs are 20/1 for the title- there is an implied 95% chance in the Boot market that he is winning without Spurs winning the title. That 5% chance should be the maximum negative correlation in any combo price, but Hills will pay us a 25% uplift for that risk. That has to be hoovered up hence the recommendation.