Subbing Your Striker.

Substitutes provide a fascinating look into the changing dynamics of a football game.

Scoring accelerates as the game progresses and in this post from 2012 I looked at the tag of "super sub" that had become attached to Edin Dzeko and how it owed much to the higher goal scoring environment in which he commonly played.

Individual players may tend to produce elevated scoring rates as a substitute not only because of the higher goal environment, but also because they will usually be playing against a minimum of seven tired opponents. Playing time for substitutes also tend to result in smaller sample sizes, leading to extremes of good or bad scoring rates.

Small sample sizes will inevitably throw up prodigious scoring rates for individual players, whereas those which inevitably fall well below normal scoring rates will tend to be neglected. The former, high scoring group of players will therefore often be used to represent the scoring feats of substitutes as a whole.

To attempt to remedy this, it seems sensible to firstly compare the records of all starting strikers who play for the entire game, all those who are subbed out and all those who take their place, to see if there is the expected benefit from playing exclusively during the later minutes of a match.

Peter Odemwingie looks forward to a period of elevated match scoring.

These results are taken from the 2011/12 EPL season and are restricted to players who were designated as out and out strikers. I looked first at the scoring rate per 90 minutes for the three different groups of strikers, as well as their conversion rates.

Striker.	Goals Per 90+ Time Allowed.	Goals Per Attempt.
Plays Entire Game.	0.356	0.126
Subbed Out.	0.346	0.139
Subbed In.	0.387	0.113

The average amount of playing time for the subs in this sample was 18 minutes, added time probably stretches this to 21 minutes. And as suspected, as a group they score at rates that are above either those of the strikers who were substituted and those whom played the entire game.

However, there are a multitude of factors that may alter the scoring rate of this minority group of strikers. They may be thrown onto the pitch in place of a midfielder to help chase an game, which may lead to them scoring at a high rate than usual, even allowing for the late stage of the game. But additional goals may be ceded at the other end.

Similarly, strikers subbed out of a match may have been replaced by a defensive midfielder, to help close out a game where more goals and the possibility of an increased scoring rate were there for the taking.

Allowing for these micro details of game state and managerial intention would require painstaking analysis of each individual match, but we can perhaps design a proxy to reduce the effect of goal environment and these other variables.

There does appear to be some method behind substitutions in the EPL. In this post I suggested that younger, less experienced players are proportionally substituted out of a game more frequently than more experienced players, even with such likely factors as a fitness advantage.

So there may be perhaps a systematic overall approach from EPL managers to substitutions.

Therefore, I looked just at substitutions where a striker replaced another striker, matched the pairings together and treated the combined statistics of the departing player and the newly introduced substitute as those of a single 90  minute + injury time playing event. Albeit made up of two different individuals.

This partly eliminated occasions where a side was aggressively attacking their opponents. If we compare this composite "player" combined from a subbed out and subbed in striker to a striker who plays for the entire game, we might see if the manager is getting optimum return from his ability to make substitutions by looking at like for like changes.

There were just over 300 occasions where a striker replaced a striker in 2011/12. We could speculate that more often a less talented striker was replaced by another less well thought of attacker, but with fresher legs, while the side's premier striker remained for the entire 90 minutes.

The "subbed out/subbed in" group of matched attacking players scored 115 goals in 309 matches of 94 minutes allowing for injury time. A rate of 0.356 goals per 90 minutes.

Strikers who played the entire 94 minutes, scored 277 goals in 746 games. Also a rate of 0.356 goals per 90 minutes.

Either through accident, design, a quirk of this data set or a combination of all three, in 2011/12 EPL managers were able to get goal scoring returns from a substitute striker and the striker he replaced that were identical to those returns from a striker who was considered worthy of the full 90 minutes, under broadly similar match conditions.

A case of expertise and experience eking the optimum return from a side's strike force?