Converting probability and odds explained

If you want to assess bets, you need to be able to convert back and forth between odds and probability. The formulas are short:

• Probability = 1 / odds
• Fair odds = 1 / probability

Odds of 2.50 therefore stand for 1 / 2.50 = 0.40 = 40 per cent. If you think an outcome is 60 per cent likely, the fair odds are 1 / 0.60 = 1.67.

Implied and fair probability

The figure calculated directly from the odds is called the implied probability. It still contains the bookmaker's margin. You can see this when you add up all the outcomes of a match: the total is above 100 per cent. To get the market's fair assessment, you divide each implied probability by this total. That is the simplest way to strip out the margin. There are more precise methods, because bookmakers often put slightly more margin on underdogs than on favourites, but simple normalisation is enough for everyday use.

What you need it for

Converting lets you compare bets that would otherwise be hard to compare. A prediction of your own, for example from a Poisson model or from expected goals, produces probabilities. Only when expressed as odds can you see whether the offer is above or below them. If the odds offered are above your fair odds, it is a possible value bet. If they are below, the bookmaker is paying too little for the risk.

Typical errors in thinking

A probability of 70 per cent does not mean the bet is "safe". Out of ten such bets, three lose on average, and sometimes five in a row. Conversely, an underdog at 20 per cent is not without a chance: it wins one time in five. Probabilities only show themselves over many bets, not in a single match.