Is it easier to score as a sub?

Recently I’ve seen some discussion about the existence of the “supersub” in soccer. There’s no doubt that a few players, notably Edin Džeko and Javier Hernández in the English Premier League, have great scoring records as substitutes. But would they do as well as starters?

I decided to start with the basics: did subs score more than other players? To find out, I made the following graph using Opta data from the Premier League in the 2012-13 season:

Sub Goals

Subs were much more likely to score than other players. As soon as subs started coming on, usually after the first half, they scored a disproportionate share of their teams’ goals. In fact, their advantage was pretty constant from the hour mark until the end of the game.

But the initial evidence didn’t tell the whole story. Imagine that all subs were forwards. Since forwards were more likely to score than other players, the percentage of goals by subs would have risen faster than the percentage of players who were subs. This is an exaggeration, but in reality forwards were 36% of subs last season – more than the usual proportion of forwards among outfield players. In other words, a given forward was more likely to be a sub than a given midfielder or defender.

To see whether this dynamic affected scoring by subs, I repeated the analysis by position. Here is the same graph for forwards:

Striker Sub Goals

Subs did not score a disproportionate share of goals among forwards. Rather, the likelihood that a forward’s goal was scored by a sub was roughly equal to the likelihood that any given forward was a sub. The subs did have an edge when they first came on, but they gave it back after about 25 minutes. The same was true, somewhat less dramatically, for midfielders:

Midfielder Sub Goals

If anything, defenders underachieved as subs. Only one – Ryan Bennett, then of Norwich City – scored as a substitute last season. I’m not going to add another graph just for him.

Though subs started strong, over their entire time on the field they weren’t much better at scoring than their starting counterparts at the same positions. Of course, some of the starters who stayed on the field probably did so for good reason. But any difference in subs’ scoring rates versus starters probably had little to do with their inherent talents.

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    1. Are subs not on average worse players than non-subs? I would suggest that controlling for this would make subs scoring rates look better than non-subs given this data.

    2. “For the next graph, I compared the actual scoring rate to the scoring rate with the personnel effects removed…So I ran the logistic regression again, controlling for the time the forwards had spent on the field. ”

      Can you explain more explicitly how you controlled for ‘personnel effects’ and ‘time the forwards spent on the field’? Did you just add these variables to your regression? What is your resulting regression formula?

      I don’t expect a stat lesson, just a brief explanation. I’m just curious…


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