A New Metric – Deserved Goals

In a given season of 38 games, we can break down goals scored as follows:

Goals Scored = Shots x Conversion %

Both of these components have an element of skill and an element of luck.

Goals Scored = (Deserved Shots + Effect of luck) x (Deserved Conversion % + Effect of luck)

The effect of luck can be positive or negative, depending on whether a team was lucky or unlucky.

We can add some numbers to this formula, based on statistics from the last 16 Premier League seasons from which we can calculate average shot and conversion rates. We can also calculate how much of the variance from the average is attributable to luck, by calculating how much they regress to the mean between seasons.

What we know:

Average shots taken per season = 453
Average conversion rate = 11.09%
Shots taken above or below average = 80% skill, 20% luck
Shots against above or below average = 81% skill, 19% luck
Conversion % above or below average = 46% skill, 54% luck
Save % above or below average = 40% skill, 60% luck

Adding in those numbers to our formula produces the following:

Goals Scored = (453 + 80% x (Shots – 453) + 20% x (Shots – 453)) x (11.09% + 46% x (Conversion % – 11.09%) + 54% x (Conversion % – 11.09%))

When producing a metric we can use to predict future performance, we cannot predict future luck. We therefore only want to measure the goals produced due to skill, i.e. the Deserved goals.

This is the problem with traditional Goal Ratio, as it includes the luck element along with the skill. Total Shot Ratio is similarly flawed, as it includes the luck in terms of producing shots, and removes finishing skill by assuming a constant conversion rate.

Removing the luck element produces the following formula:

Deserved Goals Scored (DGS) = Deserved Shots x Deserved Conversion %

Or with numbers:

DGS = (453 + 80% x (Shots – 453)) x (11.09% + 46% x (Conversion % – 11.09%))

Using the same method for Deserved Goals Against (DGA), we produce the following:

DGA = (453 + 81% x (Shots – 453)) x (11.09% + 40% x (Conversion % – 11.09%))

We can then produce a Deserved Goals Ratio (DGR) metric, as follows:

Deserved Goals Ratio = DGS / (DGS + DGA)

As this only includes the skill element of shots and conversion %, this metric should be better at predicting future performance than traditional GR or TSR, both of which include past luck and try to use it to predict future skill.

We can test this by looking at how well the metrics for one season correlate with points scored and goal ratio achieved in the following season.

All data is from the last 16 Premier League seasons.

Deserved Goal Ratio (DGR)

Total Shot Ratio (TSR)

Goal Ratio (GR)

Conclusion: DGR is better at predicting next season’s performance than GR or TSR.

We can also test within a season, to see how well the metrics so far predict future points at each stage in the season.

Conclusion: DGR is better at predicting future performance within a season than GR or TSR.

Feedback is much appreciated.

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Many thanks go to the work of James W Grayson, 11tegen11 and FootballData.