How to approach betting on football: prices and markets

The video below is about football betting strategy. It presents one approach to betting on football matches.

How odds express probability

Any football betting strategy starts with the price, and a price is a probability written in a different form. British bookmakers have long quoted fractional odds such as 5-1 or 6-4, while decimal odds such as 6.00 or 2.50 are standard across much of Europe and online. Fractional odds show the profit on a winning stake; decimal odds show the total return per unit staked, including the stake itself. A fractional price of a/b therefore converts to decimal odds of (a + b) ÷ b, so 6-4 becomes 2.50 and 5-1 becomes 6.00.

The implied probability of a price is the reciprocal of its decimal odds. Evens (2.00) implies a 50 per cent chance, 5-1 (6.00) implies one chance in six, or about 16.7 per cent, and 6-4 (2.50) implies 40 per cent. Reading prices in this way turns a list of numbers into a statement about how likely the bookmaker considers each result to be.

The bookmaker's margin

If a bookmaker priced every outcome at its true chance, the implied probabilities of a market would add up to exactly 100 per cent. In practice they add up to more. The amount by which the total exceeds 100 per cent is called the overround, also known as the bookmaker's margin or the vigorish, and it represents the bookmaker's expected profit.

A textbook example uses a three-way football market with fair prices of evens, 2-1 and 5-1, which imply 50, 33⅓ and 16⅔ per cent and total 100 per cent. Shortened to 4-6, 6-4 and 4-1, the same market implies 60, 40 and 20 per cent, a total of 120 per cent. If stakes of £60, £40 and £20 are taken on the three outcomes, the bookmaker receives £120 and pays out £100 whichever result occurs, keeping £20, or one-sixth of the money staked. Real football markets carry far smaller margins than this illustration, but the arithmetic is identical: the lower the total of the implied probabilities, the closer the prices are to fair.

Common football markets

The basic match market is the 1X2, or three-way bet: 1 is a home win, X a draw and 2 an away win. Several other markets are built around it:

• Double chance covers two of the three results at once (home or draw, away or draw, home or away), so its odds are lower than those of either single outcome.
• Draw no bet removes the draw: if the match finishes level, the stake is returned.
• Over/under 2.5 goals is decided by the total number of goals. Over requires at least three goals, under requires two or fewer, and because no match can contain half a goal, the line can never be a tie.
• Both teams to score is a yes/no market on whether each side scores at least once.

The Asian handicap takes the idea of removing the draw further. One team receives a goal start, or concedes one, so that the three outcomes of a 1X2 market are reduced to two. On a half-goal line such as −0.5 or +1.5 there is always a clear winner. On a whole-goal line such as −1, a one-goal win produces a tie after the handicap, and the stake is refunded. Quarter-goal lines such as −0.75 split the stake equally between the two neighbouring lines, so a bet can be half won and half refunded, or half lost.

Expected value and variance

Expected value describes the average result of a bet if it could be repeated many times. For decimal odds D and a true probability p, the expected profit on one unit is p × (D − 1) − (1 − p). When the bookmaker's implied probability is higher than the true chance, the expected value is negative, which is exactly what the overround is designed to achieve across a whole market. A selection only has positive expected value when its true probability is higher than the probability implied by the price, and estimating that true probability is the hard part of any football betting strategy.

Expected value says nothing about a short run of results. In the mathematics of gambling, the spread of outcomes over a small number of bets is many times larger than the average expected gain or loss, and only over a very large number of bets does the average start to dominate. A sequence of winning or losing weekends is therefore weak evidence about whether a method works.

Rules and responsible gambling

In Great Britain most commercial gambling, including betting in shops and online, is restricted to people aged 18 and over under the Gambling Act 2005, and operators serving British customers must hold a licence from the Gambling Commission. Since 31 March 2020 every online operator licensed in Great Britain has been required to take part in GAMSTOP, a scheme that lets a person self-exclude from all of those operators with a single request. Setting a fixed budget in advance and treating any stake as the cost of entertainment, rather than as a way to earn money, are the basic principles behind responsible gambling.