Expected values, unexpected results

Like any good school, the Betting School here on BetPreviews.com likes to make you think where possible. It’s all very well to make recommendations here and there, but rather than fishing for value and handing you our catch, sometimes it’s nice to teach the reader to fish as well!

An issue we’d like to touch on today is the difference between medians and means – most likely outcomes vs expected values, if you like.

The inspiration for this topic was a current hot topic in the world of sport – the poor form of Rory McIlroy since moving to Nike. The young Northern Ireland golfer has hit a real wall on the course since changing his clubs and while there is no shortage of speculation as to whether the reasons are scientific or psychological, the simple truth of the matter is that until Rory gets this issue sorted out, he’s an average tour golfer. Golfers are measured by the numbers they shoot and yesterday’s 73 in the first round of the Cadillac Championship was merely in keeping with the standard of golf we’ve seen from Rory since the switchover from his old clubs.

Yet his outright price to win of 12/1 would suggest that he was a front runner to win this week and while that may seem counter-intuitive, there is logic to that price too. So how can a golfer be fairly priced as one of the leaders of the field, and yet still be highly likely to finish in the middle of the pack?

The answer is the difference between mean and median. Rory’s short price to win has to account for the fact that while his form is terrible, we all know that on form, he’s the best golfer in the world. Nobody knows heading into the tournament if this is going to be the week when he’s finally got the hang of his game, or the moment when he’s finally got to grips with his new equipment. If it is, he’s the front runner and should be no bigger than 4/1 or 5/1 to win – and that has to be allowed for. Yet that may open up opportunities in match, group and 2/3 ball betting.

To go back to the maths of first principles – let’s take the example of a game, where a gambler is given 5/1 about his chances of rolling a six with a die in one attempt. He stakes €2, and from a statistical point of view, the bet is perfectly fair. From the bettor’s point of view he has a 1/6 chance of winning €10 and a 5/6 chance of losing €2. The expected value, or mean, is .1666*10 + .83333*(-2) = 0. However if we’re betting on whether the gambler will win or lose money in a single throw, of course we want to bet on a loss. The median outcome is the one in the middle, which is -€2.

It’s a similar situation with a golfer like Rory. Because he has the ability to go to a higher level than all other players, the bookmakers have to respect that fact and keep him comparatively short in their win betting. However there are ways to oppose him in markets such as group, 3 ball and match betting and these are markets where his potential to win doesn’t concern us as much. His mean performance is less important than his median. If he plays well enough to finish in the top ten, he’ll scupper our bet anyway, but if he continues to struggle, we could be on to good thing.

Very often in things like group and match betting, compilers will simply lump in a lot of golfers that are in or around the same price into their betting heat. Many are more sophisticated than that of course, but opportunities still exist out there to take advantage of such lazy pricing. If they do, always be aware of the difference between the most likely outcome, and the average outcome.

About Kevin Egan 130 Articles
Kevin Egan is one of Ireland's leading GAA tipsters. He has previously served as GAA odds compiler for a number of major bookmakers.

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