probability and betting

This section is under development and will be updated regularly

We saw in our earlier article - Probability - The Basics that a probability of 0.5 should give us a 50% strike rate, if we have calculated our P value correctly and are confident that a large enough 'sample' of data was used to arrive at the P value.

In another article we showed that when the bookmakers made the home team favourite then we would expect to achieve a strike rate of 54% - Home Favourites, Results Anlysis. These figures were based on 17 complete Premier League seasons, covering 6.460 matches so we can be confident that our P value will be above 0.5, it will be o.54. But, the bookmakers will of course not be offering us decimal odds of above 2.0 ( evens in fractional odds ) so we will be looking at man empty wallet if we decided to blindly follow home favourites. If we worked on an average price offer of 1.5 we would receive £75 back on every 100 £1 bets we made but those bets would cost us £100. That's not good.

If we were to only pick those matches where the bookmakers were offering decimal odds of more than 2.0, the strike rate drops to 40.96%. They are fiendishly clever these bookies!

Results where home favourite > 2:0:

the odds

How do we calculate the true odds of a result from the probability? The formula is simple:

Decimal Odds = 100 / P (Probability)

So, if we were to take a simple coin toss, the P value is 50 (%), 100/50 = 2. Our true odds for a coin toss resulting in heads or tails is 2.00. With a 'three horse race' which is how football match could be seen because there are three possible results - home win, away win or draw the decimal odds would be 100/33.33, a decimal odds value of 3.00. Of course the probability of any particular result in football is not an even split, the top team in the Premiership playing the bottom team would make the P(robability) values very different! Taking an imagined educated guess of P's our calculations could look something like this:

  • Bestchester United Probability of home win : 70%, P 0.7
  • Wobbly Wanderers Probability of away win : 10% , P 10
  • Draw Probability : 20%, P 0.20
The sum of the P percentage values will always add up to 100 or a probability of 1, because one of those results will always happen giving us anabsolute certainty that one of these three will happen. Of course nothing is absolutely certain, a match may be abandoned but then bets will be void so we can ignore that 'probability' and give it a value of 0!

The true decimal odds of home win, any wish and draw for our imagined match are:

  • Bestchester United home win : 100 / 70 = 1.25
  • Wobbly Wanderers Away Win : 100 / 10 = 10.00
  • Draw: 100 / 20 = 5.00

These sort of odds will be seen quite frequently, but the bookmakers will want to make a nice wheelbarrow full of money and to do that they need to add an 'overround' factor to the odds to make sure that in the long term they win whatever the results. There will also be factors like team popularity to be taken into account as more punters may bet on Bestchester United than the opposition even when they playing like a schoolboy team! More on bookmakers tactics later in this series of articles.