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What are Fixed Odds Betting?

A few days before a sports match, say football, the bookmakers will set the betting odds for the match. Traditionally, high street bookmakers such as William Hill or Ladbrokes prepared on printed coupons odds for the upcoming weekend's matches. Once these odds are set in print, they cannot be changed, hence these are known as fixed odds coupons. More recently, with the advent of internet, online fixed odds betting are becoming more and more common.

What are odds?

Before we look at an example, let's look at how odds are interpreted. If the odds for a team to win a match is 3 to 2, or 3/2. What this mean is that for every £1 you put in, you win £1.50 (3/2 times £1) plus your original wager, which is £1. Therefore your total return is £2.50. Sometimes, in order for punters to compare the chances of winning more easily, bookmaker also provide decimalised odds (common in mainland Europe), e.g. in the above example, the odds of 3 to 2 is identical to as 2.5 in decimal format, i.e. (£1.5 + £1)/£1.

Also, the more likely an event is going to happen, the smaller the odds, i.e. the odds given above might be 1 to 2 rather than 3 to 2 if the team is very likely to win. Therefore your profit margin is less than 100% (50% to be exact in this case).

Outcome of Football Matches

Most football leagues utilise a points rating scheme. The points which a team is awarded is dependent on the outcome of previous matches that team has played. The more matches they play and win, the more points they score. Consequently, a higher team points rating means the greater winning potential the team has for forthcoming league match.

The outcome of a match between two teams are generally expressed in terms of probability distribution rather than making a specific prediction. For example, consider a match between Manchester Utd. (home) and Arsenal (away). There can can only be three possible match outcomes with the following probability distribution:

Therefore the most likely outcome of this match is a Home Win for Manchester United. However, given the average probability distribution of all league matches outcomes is 46% Home Win, 28% Draw and 26% Away Win (based on English league data 1994 to 1999), it's far from certain that betting on Manchester Utd. will be a good financial decision. One need to access what odds are being offered by the bookmaker in order to interpret prediction of this match in a more meaningful way.

The Bookmaker's Odds

The bookmaker also sets his odds based on how he thinks the match will be decided. A possible set of fixed odds for the match set by the bookmaker could be:

From the odds/decimals given, we can determine the bookmaker's estimated Home Win-Draw-Away Win probability distribution. This can be done by taking the inverse of the decimal odds:

The total probability distribution come to more than 100%, in fact it is 116%. Since there can be no greater than 100% certainty for the outcome of any event, this is therefore a measure of the bookmaker's profit margin. The bookmaker has artificially shortens the odds, i.e. make it "less likely" to happen; or conversely increases the estimated probability of the outcome of a match. Therefore odds provided by bookmaker are not true or fair odds, i.e. the expected return of the bet is negative, just as with any casinos games and all forms of lotteries.

Concluding Remarks

So, if the bookmaker's odds are unfair odds and weighted in their favour, how is it possible to make money from fixed odds betting? One such way is to improve one's forecasting system and identify whether the bookmaker's forecasting system is over-predict or under-predict certain outcomes.

In the above example, the decimal odds for a Home Win is 1.67, but historical data has shown that a Home Win is more likely to be 2.17 (inverse of 46%). Therefore the bookmaker has significantly increase the odds of a Home Win (by paying out less winnings). However, if the bookmaker is offering a decimal odds of 2.5, then this would represent a good value bet.

Written by Henry Tang.

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