## Monday 8 December 2014

### Weighted Shots v Unweighted Shots As A Predictor of Future Goal Difference in the EPL.

Tom Tango has recently presented an alternative to Corsi in hockey that weights shots differently depending on whether they resulted in goals, saves, misses or blocks.

One of the logical tests of the new metric is see how well it correlates to useful team information, such as future goal difference, compared to projecting from previously used metrics, such as unweighted shot differential or ratios.

The expectation voiced in many hockey circles was that because the "Tango" correlated almost perfectly to the traditional Corsi metric, the added information hoped for by weighting different types of shots would be negligible, at best.

In a typical concise and insightful post, here, Tango addresses the issue of the virtually perfect correlation between both metrics. Pointing out that using basic shot data from identical samples to test the correlation to out of sample data, such as future goal difference, gave different coefficients of correlation depending on whether the Corsi or Tango was used.

In short, weighted shots showed higher r values, despite the strong correlation between the two metrics.

r Values for Weighted & Unweighted Shot Differential and Ratios when Correlating to Future Premiership Goal Difference.

 After X Games r for Total Shot Ratio r for Shot Differential. r for Weighted Shot Differential 2 0.49 0.51 0.57 6 0.70 0.71 0.77 10 0.70 0.71 0.76 15 0.74 0.74 0.80 18 0.73 0.74 0.80 20 0.73 0.74 0.79 24 0.72 0.73 0.77 30 0.65 0.66 0.69 34 0.55 0.55 0.56

Tango's defence of his new metric can be summed up in this extract from the linked post.

"But more amazing is that even though the correlation of Corsi to Tango (both based on the same samples) was close to r=1, when we correlate each to out-of-sample data (in this case, goal differential from OTHER games), Tango correlated at r=.50, while Corsi was r=.44.  Or if you prefer r-squared, it’s .25 to .19, respectively."

I have therefore repeated the exercise for the Premiership, using three flavours of shot based metrics in one part of the season and testing the correlation between these at an individual team level and goal difference for teams in the remainder of the season.

And the weighting of shots also appears to make a difference in soccer as well as in hockey. Correlation peaks around mid-season, but at every stage, weighting proved a superior correlation to goal difference in the remainder of the season compared to unweighting.

It also makes intuitive sense to reflect the extra information present in a goal compared to just a shot.