How to use odds to predict football?

There are many ways to determine the relative strength of teams; recent form, world ranking, value of squad, past meetings, and so on. However, rather than spending huge amounts of time trying to tie all these factors into one model, bookies’ odds can be used instead, since they take all these factors into account when creating their odds. Therefore, we just need a way of converting the odds into an actual expectation.

• HOW ODDS WORK

For the opening match of the World Cup, between Brazil and Argentina, the odds for the result of the match are:

Brazil win: 3/10
Draw: 18/5
Argentina win: 9/1

So for a Brazil win, £10 placed on that result will profit by a mere £3 if that outcome comes to fruition, whereas £10 placed on Argentina to win will make a profit of £90.

If the bookies created the odds to exactly reflect the probability of that outcome,  10/(3+10) = 76.9% will be the probability of Brazil’s winning. However, they need to make a profit, so the odds are shortened slightly.

However, the odds will all have been shortened by the same proportion, such as 5%, for the bookies to try and people to bet on each result proportional to the chance of it occurring, in order to guarantee a profit. Therefore, we can still assume that the odds are a fair representation of each result, compared to the other outcomes.

• MEASURING TEAM STRENGTH

The odds currently give the lower score to the better team, however, we need values which are higher when a team is better, so in order to find those the reciprocal of each odd is found.  This is simply a case of turning the odds upside-down.

Example, Brazil’s 3/10 becomes 10/3.

If we switch the resulting values from fractions to decimal form, It will be;

Brazil win: 10/3 = 3.333
Draw: 5/18 = 0.278
Argentina win: 1/9 = 0.111
(to three decimal places)

We will call these three values the coefficients for each result.

• FINDING THE PROBABILITIES

It is very simple to translate these coefficients into the probability of each outcome happening.

To find this, we divide each value by the total of all values. So for our example, the total of the three coefficients is 3.722, and our three probabilities are:

Brazil win: 3.333/3.722 = 89.6%
Draw: 0.278/3.722 = 7.5%
Argentina win: 0.111/3.722 = 3.0%

(that the three probabilities add up to 100.1% is a result of rounding, the true probabilities add up to 100%)

• SIMULATING RESULT

We will find the winner of the match based on these probabilities. To do this we find the cumulative probability for each result:

Brazil win: 0.896
Draw: 0.896 + 0.075 = 0.970
Argentina win: 0.970 + 0.030 = 1.000

(again, rounding counts for the discrepancy in the draw calculation)

These values can now provide boundaries:

0.000 – 0.896: Brazil win
0.896 – 0.970: Draw
0.970 – 1.000: Argentina win

If we now draw a random number between 0 and 1 we can see which range it fits into, giving us our result.

Running five random simulations gives values of 0.0659 (Brazil win), 0.6236 (Brazil), 0.3970 (Brazil), 0.9752 (Argentina win), 0.0207 (Brazil). In the long run, Brazil will win 89.6% of matches, and 3% will be won by Argentina.

• SUMMARY

Bookies’ odds are in probability and statistics. However, they are weighted in order to guarantee them a profit. These can be transformed with relative ease into the actual probabilities, at least according to whatever analysis the bookies have used, of each possible outcome.