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quote originally posted by krislee:
"Margin of Safety" as the Central Concept of Betting
A team's past ability to create quality chances is the expected number of goals that they should have produced. The expected number of goals in excess of the actual number of goals constitutes the "margin of safety". The margin is counted on to cushion the bettor against discomfiture in the event of a performance decline in the upcoming fixture. The soccer bettor does not expect the upcoming fixture to work out the same as in the past. If he were sure of that, the safety margin demanded might be small. The function of a safety margin is, in essence, that of rendering unnecessary an accurate estimate of the team's winning probability in the upcoming fixture. If the safety margin is sufficiently large, then it is enough to assume that the team's upcoming performance will not fall far below their expected goals in order for the bettor to feel sufficiently cushioned against bad luck. The safety margin is always dependent on the odds that the bettor accepts from the bookie. It will be large in certain odds, small at some lower odds, and negative when the odds is too low. However, even with a safety margin in the bettor's favour, he may lose his bet. For the margin guarantees only that he has a better chance of winning - not that loss is impossible.
Theory of Diversification
There is a close logical connection between the concept of safety margin and the principle of diversification. One is correlative with the other. Even with a margin in the bettor’s favor, an individual bet may work out badly. But as the number of such commitments is increased the more certain does it become that the aggregate of the profits will exceed the aggregate of the losses. This point may be made more colorful by a reference to the arithmetic of roulette. If a man bets $1 on a single number, he is paid $35 profit when he wins—but the chances are 37 to 1 that he will lose. He has a “negative margin of safety.” In his case diversification is foolish. The more numbers he bets on, the smaller his chance of ending with a profit. If he regularly bets $1 on every number (including 0 and 00), he is certain to lose $2 on each turn of the wheel. But suppose the winner received $39 profit instead of $35. Then he would have a small but important margin of safety. Therefore, the more numbers he wagers on, the better his chance of gain. And he could be certain of winning $2 on every spin by simply betting $1 each on all the numbers. (Incidentally, the two examples given actually describe the respective positions of the player and proprietor of a wheel with a 0 and 00.)
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