Opponent-adjusted metrics: Part 4, investigating form in Premier League opponent-adjusted margin

Introduction

In previous posts, here, here, here and here the concept of opponent-adjustment was introduced and a set of  principles described. In a number of those posts, the idea of form was mentioned in the context that a shortcoming of the metrics used is that they do not evolve with a team's form. In this post, an attempt is made to correct this.

Method

The method is broadly similar to that used in the previous post. However, rather than using a single value to evaluate the performance of a team throughout the season, in this method the metric for each team changes with every game played.

Each team begins the season with a rating of 0. For the nth game, the performance for the home team is calculated by:

Home team performance (n) = Home goals(n) - Away goals(n) + Away team rating (n-1)

A corresponding equation gives the performance value for the away team.

After the nth game, a team's rating is:

Home team rating (n) = Home team performance (1) + r * Home team performance (2) +

... + r^(n-1) * Home team performance (n)

In this way, a weighted average is calculated and each subsequent game is worth r times the previous game in the ratio.

Below, different values of r are compared. Predicted margins are calculated for each match by:

Predicted margin = Home team rating - Away team rating

Following this, the average error is calculated. The value of r which produces the lowest average error best captures form throughout the season.

Results

The results are rather underwhelming. The best value of r is, in fact, 1.03. So more recent results hardly carry any more weight than older ones. In fact, the fact that the optimum value is not 1 is likely to be simply due to noise.

Therefore, the best way to judge a team's ability is simply by looking at their opponent-adjusted margin to date.

So, with a value of r = 1, we can track the form of teams throughout the season. An annotated graph of opponent-adjusted margin throughout the season is provided below, for Chelsea:

Similar charts can be provided for each Premier League team.

Conclusions

Form does not exist in the way that we understand it. This has been mentioned often in previous literature and this work supports that claim. It is, however, useful and illustrative to consider the opponent-adjusted margin to date when judging a team's ability.