by Adrian Worton

Yesterday we found equations which accurately create odds for Premiership matches. To do this we used the form of each team over the last 38 matches as a measure of strength to influence our model.

However, this won't work for matches involving clubs recently promoted from the Championship, since clearly 3 points are harder to earn in the Premiership than the Championship.

So in this article, we aim to get an exact measure of how much stronger the Premier League actually is.

Yesterday we found equations which accurately create odds for Premiership matches. To do this we used the form of each team over the last 38 matches as a measure of strength to influence our model.

However, this won't work for matches involving clubs recently promoted from the Championship, since clearly 3 points are harder to earn in the Premiership than the Championship.

So in this article, we aim to get an exact measure of how much stronger the Premier League actually is.

**Relative Strength**

The value we want to find we will call

*c*, which will represent the fraction of the Premier League's strength that the Championship is. For example, if

*c*= 0.8, we can conclude that the Championship is 80% of the strength of the Premier League, and that if a team is good enough to earn 20 points in 10 matches in the Championship, they would be expected to earn 80% of that in 10 matches in the Premier League, so 16 points.

If

*c*= 1, then a win in the Championship is as good as a win in the Premiership. And if

*c*= 0, then all points earned in the Championship are worthless. Clearly these two scenarios are unrealistic, so we know

*c*will be between 0 and 1.

**Comparing Values**

Since we have already derived equations which will estimate odds for matches given the relative forms of teams, we can put all matches involving newly-promoted teams into our equations, and compare the resulting odds with the real odds given. By varying

*c*we will find the optimal value of

*c*which gives us the more accurate fit.

We will use the R^2 value as our measurement to

*c*. More detailed explanations of this measurement are available elsewhere, but essentially it is a value between -1 and 1. The further away from 0 it is, the better the relationship between two variables. compare different values for The slideshow below shows the relationships for home wins (PredH), draws (PredD) and away wins (PredA) when

*c*is set to 0.8.

The R^2 values of 0.4396, 0.3406 and 0.3840 are fairly low, suggesting that 0.8 is a poor estimate for

*c*. The graph below shows the R^2 values as*c*is varied from 0 to 1:We can see that all three curves peak between 0.3 and 0.5. As the PredD curve is the lowest and flattest, indicating it is the least sensitive to changes, we can ignore it. Below we look at the average of PredH and PredA between 0.3 and 0.5, to find the value which estimates both the best.

The highest point along the graph curve is when

*c*= 0.39, which gives us our best value. Below you can see the three plots showing the accuracy of our predicted odds when*c*is set to 0.39:This means we can conclude that the Championship is a meagre 39% of the strength of the Premiership. This means that if a team is good enough to earn 20 points from 10 matches in the Championship, they should be expected to earn 39% of that in 10 matches in the Premiership, which is 7.8 points.

If we compare this to the records of the teams within our database, the average points total of teams being promoted is 82.067, which is 1.784 per match. If we multiply this by

In real life, these teams average 38.233, which is 1.006 per match. This is far higher than the prediction, implying that bookies generally underestimate the ability of newly-promoted teams.

With our measurement of the difference between Premiership and Championship teams, all the places are in place for our Premier League 2014/15 simulator to be build, so watch this space!

If we compare this to the records of the teams within our database, the average points total of teams being promoted is 82.067, which is 1.784 per match. If we multiply this by

*c*= 0.39, we get 0.678, which is the prediction of the points per match earned by teams promoted into the Premier League.In real life, these teams average 38.233, which is 1.006 per match. This is far higher than the prediction, implying that bookies generally underestimate the ability of newly-promoted teams.

With our measurement of the difference between Premiership and Championship teams, all the places are in place for our Premier League 2014/15 simulator to be build, so watch this space!