# Analytics: It’s more than the maths…

Last night we landed a nice 7/1 return when Eden Hazard netted his brace, as recommended against West Brom.

We profited mainly from a Betfair sportsbook price of 7/1 in a market where most other bookies were pricing between 4/1 and 5/1. Did Betfair get it wrong? Here’s where it gets mathematical…..leave now if you hate numbers…you have been warned!

Hazard was generally evens to score at anytime. We can convert that to a probability of 0.5, then correcting for the bookies margin percentage (say 10%) we can estimate the true probability as 0.5/1.1= 0.455. And by extension, not scoring has a probability of 0.545.

We then break a game into 90 divisible discrete minutes, assuming there won’t be two goals in a minute (which is fair). The probability of Hazard failing to score in any given minute is the 90th root of 0.545, which is 0.993, and hence scoring in any minute is the inverse i.e. 0.007.

It’s relatively simple statistics therefore to compute the probability of Hazard scoring just one goal (0.993^89 * 0.007 * 90 combinations) = 0.331.

Given scoring at all was 0.455, then scoring more than one is the differential 0.455-0.331= 0.124 which equates to a 1 in 8 chance, or fair odds of 7/1.

Statistically the maths may suggest Betfair were right. However, this analysis assumes that the probability of a Hazard goal remains constant throughout a game.  Intuitively we know this is not true, and statistically we know there is data to say this is not true.

In football, goals breed goals. Any goal in a game immediately increases goal expectation in total for the remainder of the game, and for the individual. In simple terms when Hazard scores once, his chance of scoring a goal in each subsequent minute is higher than it was at the outset.

This is mathematically extremely hard to compute (you need to factor in timing of the first goal etc), and we believe bookies effectively create their market intuitively rather than statistically, which is why the herd mostly trimmed a statistical outcome of 7/1 to a gut outcome of around 9/2.  Betfair didn’t, and it’s our job to keep trying to find these anomalies.

Of course it helps when Hazard does then spank in the two goals!!