Sports statistics - results and odds for soccer

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Studysoccer.com has a database containing details of over 70,000 matches. If you were to bet on the home win on everyone of those matches, you would lose approximately 9% of what you'd staked. This is because of the bookmakers overround.

Bookmakers accept bets on events where the outcome of the event is unknown in advance, and for which there are a number of mutually exclusive outcomes. Imagine if a bookmaker took bets on the toss of a coin. The probability of a tossed coin coming up heads is .5, and the probability of the result being tails is also .5. Both results are equally likely.

The odds offered by bookmakers on an event are inversely proportional to the probability of that event occurring. The higher the probability the outcome to an event is, the lower the odds offered by a bookmaker on that outcome will be (and vice versa). The odds for a particular outcome to an event are:

Odds=1/Probability

In the coin tossing example, the probability for both heads or tails is .5. Therefore, the odds for both heads and tails are 1/.5, which is 2.0 (or evens). For every unit staked on an event, in the case of the wager being successful, the bookmaker returns 2 units. This is the original stake, plus the winnings. However, offering odds of 2.0 on a coin toss will not make the bookmaker money. A coin toss is an event with a random outcome. Over the long term, punters will be successful 50% of the time. Assume that over a large number of coin tosses (eg 1000) half of these will result in wins for the punter. The bookmaker will have to return the punters stake, plus the same again in winnings, which is a loss of 500 units. The punter will lose 500 times however, which results in gains of 500 units (the punters stake) for the bookie. The 500 unit loss cancels out the 500 unit gain. The bookie is not ahead.

In order to make money on the bets, the bookie uses an overround. The overround is also called "juice" or "vigorish/vig" in the United States. Remember in the coin tossing example that the odds offered by the bookmaker are dependent on the probability of that event occurring. The sum of the probabilities for all possible outcomes to an event should equal 1.0. The sum of the probability of heads (.5) and the probability of tails (.5) is 1.0. Bookies offer odds however that do not offer value. Instead of offering 2.0 for heads and tails, bookmakers will offer 1.9. Just as we can determine the odds from the probability, we can also determine the probability from the odds, using this formula:

Probability=1/Odds

If the odds on an event are 1.9, the probability associated with this event is approximately 0.525 (1/1.9). There are only two possible outcomes to a coin-toss. If we add the probabilities implied by the odds offered by the bookmaker now, we do not get 1.0, we get 1.05. The extra .05 is called the "overround", and it is how bookmakers make money on a market. We say in this case that the bookmaker is running a book with a 5% overround. Look what happens when bookmakers accept bets on coin-tossing, but only offer odds of 1.9 for successfully guessing heads or tails. Over 1000 bets, 500 will result in wins for the punters. The bookmaker will have to return their stakes, plus their stake multiplied by .9. Over 500 bets, the bookmaker will pay out 500*.9=450 in winnings. But the punter will lose 500 times, and the bookmaker gets to keep their stakes. The bookmaker is taking in 500 units, but only paying out 450 units. The profit of 50 units over 1000 wagers is a consequence of the lower-value odds offered by the bookmaker. The winnings of the bookmaker are proportional to the overround on their markets. In this example, the bookmaker is in profit to the tune of 5% of what the punters wagered. This is because of the 5% overround on the odds they offer.

How does this apply to soccer betting?

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