by Adrian Worton

We have been slowly building a Premier League simulator. To do this we first needed to work out a relationship between two team's form and their chances of beating each other, before moving our focus to the Championship and calculating how much weaker than the Premiership it is. All this was enabled by our comprehensive database giving us results and odds for all Premier League games from the 2004/05 season to the 2013/14 season.

We have been slowly building a Premier League simulator. To do this we first needed to work out a relationship between two team's form and their chances of beating each other, before moving our focus to the Championship and calculating how much weaker than the Premiership it is. All this was enabled by our comprehensive database giving us results and odds for all Premier League games from the 2004/05 season to the 2013/14 season.

With these elements in place, we can now try and put together our simulator, and see if it's up to scratch. A downloadable version of the simulator is available in

These help us calculate the coefficients for each outcome in a match (C1, C2 and C3, where C3 should always be 1). The result of a match in each simulation is worked out by generating a random number, and seeing where it falls:

*Appendix 1*.**Results of matches**

For each match, we use a system similar to that in our World Cup simulator, where odds are inverted to give an idea of each team's strength. However, we make a small change. In the previous system, an odd was inverted, so we used 1/[odd]. This time, we are going to use the formula 1/[odd+1]. A full explanation of this is in*Appendix 2*.These help us calculate the coefficients for each outcome in a match (C1, C2 and C3, where C3 should always be 1). The result of a match in each simulation is worked out by generating a random number, and seeing where it falls:

- Between 0-C1: Team 1 win
- Between C1-C2: Draw
- Between C2-C3: Team 2 win

**Tiebreaker**

As with our final World Cup simulator, whenever two teams finish level on points, we will generate a small random number to separate them, as our simulator does not take goal difference into account.**Results**

We now can investigate the results of our simulator. Below are the results from ten simulations:Results highlighted in red are ones which seem very far-fetched, from a subjective viewpoint. We can see that each simulation has an unlikely result, in fact the fifth simulation has six unlikely results, including the top three in the table.

This clearly isn't good enough, there seems to be too much random fluctuation within the model. Next time we will try and work out what causes the model to be so unpredictable.

This clearly isn't good enough, there seems to be too much random fluctuation within the model. Next time we will try and work out what causes the model to be so unpredictable.

**Appendix 1 - the simulator**

tgiafpremulator.xlsm |

**Appendix 2 - change in odds conversion**

Previous we simply used the inverse of odds in order to work out coefficients. For example, if a match had odds of:

- Team 1: 1/2
- Draw: 3/1
- Team 2: 5/1

However, this slightly misses what odds represent. Imagine a game where the true probabilities of each team winning are:

- Team 1: 50%
- Draw: 25%
- Team 2: 25%

For Team 1, the chance is 50%, so when putting money on that outcome you would expect to win the same amount if Team 1 does win as you would lose if they don't win, which in other words is evens, or 1/1.

Similarly, if you bet on Team 2, they are three times more likely to not win as they are to win, so you would expect to win three times as much if they won than if they lost. In other words, these are odds of 3/1. (The same obviously also applies to a draw).

Therefore, our bookies would give these teams odds of:

- Team 1: 1/1
- Draw: 3/1
- Team 2: 3/1

[profit for winning]/[stake]

However, when you win, you get your stake back. Therefore, we need to use the following formula:

[profit for winning + stake]/[stake]

Since we turn all our odds into decimal values (e.g. odds of 1/2 become 0.5), this formula becomes 1/[odds + 1].