## Wednesday, 4 October 2017

### Quick & Dirty Strength of Schedule.

I've recently posted some xG, strength of schedule adjusted figures for the Premier League and justin_mcguirk has asked for a method.

The sos values have been intended to be purely descriptive, rather than attempting to more accurately portray underlying team quality.

But intuitively you can look at WBA's start where they've not faced one genuine title contender, in Bournemouth, Burnley, Stoke, Brighton, WHU, Arsenal and Watford and compare it to Everton's lucky seven of Stoke, Man City, Chelsea, Spurs, ManUtd, Bournemouth and Burnley and immediately think that Everton's start has been more difficult than that of the Baggies.

Strength of schedule can be calculated using a steal from the NFL, particularly so called least squares Massey ratings..

In the case of the Premier League, each teams schedule is laid out, followed by a performance parameter, such as goal or expected goal difference. The seven inputs (the teams they've played out of a possible twenty for each team) are then calculated, such that the errors arising when trying to solve each of the twenty simultaneous equations are reduced to a minimum.

The maths is doable using matrices, although 20x20 matrices can sometimes resist inversion and I'm sure many packages will undertake the heavy lifting as well.

For those who would like a simpler and probably equally informative approach you can average the goal or expected goal difference of the seven teams a side has played.

These seven teams will have played 49 matches, admittedly seven will be against the side whose strength of schedule you are attempting to estimate, but their 49 games will have been against a broadly league representation.

Here's the sos table using this method after six games. It is broadly similar to the one I posted on Twitter after 7 and using a least squares approach.

Everton still had the toughest start & WBA the easiest. Chelsea moved up towards a more taxing unbalanced schedule by hosting Man City as did Palace visiting Manchester United.

Also more information about each team and their opponents has become available after seven games.

Finally, here's the individual calculations for WBA & Everton. Stoke's xG for after 6 games was 5.2 and they'd allowed 9.2 xG.

Data from @InfogolApp