I’m not sure which sportsbook you’re quoting for the 5000-1 odds, but I would suppose that it is parimutuel and the house “sets” the game and takes a percentage off of the top (known as the rake or vigorish) as does the local government in taxes. The odds are then determined by the number of betters and the teams for which they’re betting. If the pool of betters (presumably all having the same information) is “right”, then the odds set are typically “correct” and the proper/fair payouts follow.

In cases where the betting pool is overly biased (perhaps there are more die hard fans for Man United who are betting with their hearts and not their brains) this can create situations known as “overlays” in which careful gamblers who notice the shift can take advantage of the situation and potentially have better-than-usual margins on their bets. Naturally these margins need to be big enough to overcome not only the inherent risk of the initial gamble, but also cover the loss of the houses’s rake and the subsequent taxes. Serious handicappers will use all of the best available information available in making their gambling choices, but will then only proceed to place bets on which they perceive to be overlays. In the long run this will give them a slight edge (not over the house, but) over their fellow gamblers. They also typically place their bets just before the close of betting so that they have the most updated odds available (and can ensure their bet is still an overlay) while keeping in mind that their bet and other last-minute bets can potentially sway the ultimate odds. (example: If someone comes in at the last minute with several million pounds on Leicester City then the odds shift away from them, potentially creating overlays for other teams.)

In most cases, longshots with terrible odds like these, are longshots for a reason, but if a careful gambler has (preferably solid information creating) reason to believe that the odds shouldn’t be as bad as they are, then it creates an overlay which makes the bet more valuable in comparison to all the other gamblers.

For statisticians, think of it as a normal curve whose local x-value along the y-axis is shifting (usually slightly) over time. If there’s a huge bump in the outlying choices just before betting closes, then one’s statistical likelihood of winning is better and it’s a good bet with a better-than-average payoff. In practice, there are so many people gambling (usually intelligently) that these local shifts (sometimes called “noise” in engineering parlance) are fairly small and that in aggregate averaged over time most gambling situations are the mathematical equivalent of a numerical lottery.

As a similar somewhat related example, in US baseball, sabermetricians are gathering large amounts of data to attempt to find otherwise unseen inequities in forecasted player talent and then leverage that to try to win more baseball games. In the early days of applying these methods, one team could statistically do better than others, however over time, as more teams begin using the same methods, the information gap is overcome and everyone is on equal footing again. The trouble in most sports is that coming up with accurate measurements of performance isn’t easy (or even statistically significant) and thereby adds a large enough layer of noise on top of the process that gambling on them is again relatively equivalent to the lottery.

]]>Calling him a crackpot is not correct, because he has several correct and interesting publications (e.g. the wrong two pages paper mentioned above refers to a correct paper by the mathematician in question).

Also relevant is this question from a few days ago …

]]>Even more, in my experience mathematicians in general (as opposed to probabilists and statisticians) tend not to think beyond expected value calculations when analyzing uncertain events. Many of them seem hardly to be aware that probability theory has even developed more sophisticated ways of looking at things (although some have heard the word “variance”).

]]>And now, to address whether it would have been a good idea to bet £20 on them mid-season if you think that you knew the odds better than others, depends on your utility function, i.e., how much different quantities of money are worth to you. Most bettors would use the Kelly formula, which says that if you think the odds are 100-1 instead of 1000-1, then you should bet about 1% of your bankroll, i.e, the money that you can afford to loose and might occasionally use for betting. So, if you have £2000 to spend on bets (which is realistic), then it would have been a good idea.

*Thanks — I’ve changed “bed” and “championship”.*

https://en.wikipedia.org/wiki/2003%E2%80%9304_in_English_football#League_tables

]]>What you really want is the mirror image of that – a program that will monitor all the odds being offered, and work out a combination of bets you can place, perhaps with several different bookies, such that you will win overall, whatever happens (finding the arbitrage opportunity). But again, if that were easily done, lots of people would be doing it already, and the odds would shift accordingly. (The obstacle to doing it is presumably not the computation, unless someone is going to tell me that the problem is outside P, but the poor odds on offer.)

]]>