Mathematical rates. Betting on an outsider – what is the reason?

Mathematical rates. Betting on an outsider – what is the reason?
For those who have not yet experienced the effects of overbetting, we will briefly tell you what the point is.
In the simplest case, when there are only two outcomes: a and b, we can determine the bookmaker margin by the formula:
M = (1 / a + 1 / b) ∗ 100%
But in what proportions is this margin distributed between the two outcomes? For TB 2.5 and TM 2.5 with the same fair bet of 2, we can expect the same betting odds in the vicinity of 1.95. This happens most often in practice.
It is quite another thing when the outcome is almost a foregone conclusion, that is, the chances are far from equal. Take, for example, the odds ratio of 80/20, which gives their respective fair rates of 1.25 and 5.0 on two outcomes. It can be expected that, taking into account the bookmaker’s margin, real bets will be between 1.19 and 4.75, in case the margin is distributed evenly between two outcomes.
In fact, the bookmaker often earns the lion’s share of profit from an outsider, and bets can settle at around 1.23 and 4.35. The bookmaker discounted the favorite rate by only 2%, while the outsider rate by as much as 13%.
Recall the very first article about our professor of mathematics, the author of the book Soccermatics, and the player David Sumpter, who, in pursuit of a successful strategy, revealed longterm tendentious expectations of this type. In the end, he managed to capitalize on the underestimated draw results, but perhaps he should not go into details again.
So, the excess and the tendency to overbet at risky bets is obvious, and perhaps because of it, bookmakers can not worry about their profits. After all, if somewhere the banknotes wane, then in another place they will arrive, right. This is confirmed by common sense, mathematical simulation on a computer and analysis of historical rates.
While football statistics, like the game itself, are rich in trends for every taste with proper lighting – horse racing is a classic example for the subject of our discussion. Here it will not be superfluous to bring a scifi schedule of honest money taking from lovers of dark horses.
Bet income falls as risks increase.
Bet income falls as risks increase.
Explanations:
along the horizontal axis the log is a probability scale;
the vertical axis returns, or rather the loss of a player from one dollar;
the selection was made from an array of data on horse racing in the period 1992 – 2001. ;
the sample included 5 610 580 races;
thick black line – all leaps;
green solid line – small sample at exotic rates;
broken line – last run of the day
It is immediately clear that dark horses bust players much more proven. Rates with 1% chances caused a total loss of 61%, random or blind bets – already 23%, and favorites rates – only 5.5%.But then the jumps, and is it the case in football. Not everything is so simple and there is some dependence on the time, place of research and the impartiality of the researcher himself.
David Sumpter found trends in one season, and in the other – they changed to the opposite, i.e., to overbetting a favorite. Football statistics benefactor Joseph Buckdal found tendentious bets in favor of an outsider for European club tournaments during 2005 – 2012.
In football, as well as in races, this is not a harmless phenomenon from the field of statistics, or behavioral psychology, or rather not only that. Betting on unlikely outcomes is also unprofitable for the player. Randomized outcome bets with a coefficient of ≥ 5 allow you to return only 80% of the invested funds, while randomized bets ≤ 1.50 are almost breakeven.
I myself have repeatedly encountered a similar phenomenon, but due to inexperience of bookmaking tricks, I prescribed this effect to the imperfection of the collective mind, or random fluctuations. Of course, all this takes place, the collective mind of the fans lends itself to emotions, as well as random deviations are inevitable.
However, there are more solid reasons for the mass of sufficiently mature players to make a bad deal over and over again, not paying attention to alarming monetary signals. You will learn about these reasons shortly, and yes, they are relevant to our list of useful books.