Substitute Effects Study: Part I

and away we go

This is the first edition of the Expecting Goals newsletter. If you want to know more about what Expecting Goals is, check out my introductory post.

It is a truism in soccer analytics that there is a “substitute effect” where players score goals at higher rates when they come on as substitutes than when they start matches. This effect extends to other forms of attacking performance, from shots assisted to ball progression. 

And it has an obvious logic. Players who have been waiting for an hour to come into the game will have fresher legs and and more energy than players who have been running around on the pitch for an hour. On top of that, they and their manager have been watching the match up to that point and can identify weaknesses to attack. 

If you can quantify the exact size of the benefit that an average substitute has over a player on the pitch, It should be easy to make first-run statistical recommendations to managers about how and when to use your subs. This backup striker is 20 percent worse than the starter, which means that he’ll be the better option at 70 minutes, this backup winger should optimally come on at 55 minutes, and so on. The manager could decide based on the game situation and fitness evaluation whether to deviate from those recommendations, but they would provide an objective starting point. That would be nice.

As with everything in this game, moving from a truism to any kind of actionable recommendation is incredibly complicated. But we can set our sights on a more achievable goal, which may take us some of the way to an actionable recommendation.¹ What is the substitute effect on player statistics? That is, if one player has seen an unusual percentage of their minutes on the pitch as a substitute, and another player has been almost exclusively a starter, how can we compare their performance records? What adjustments have to be performed on player statistics to adjust for this context?

Let’s start with the most obvious data and then track every point where it stops working, to identify all the different contexts which have to be accounted for.