Dzeko Revisited.

There has been some insightful recent tweets concerning the problems associated with per 90 players stats. Notably from Ian Baldwin who noted the difficulty presented by added time when assessing the amount of playing time attributed to all players, but most tellingly those who are subbed on usually during the second half of games.

The difficulties are compounded by even larger discrepancies that arise due to the different amounts of time the ball is actually live and in play.

Added time only allows compensation for a narrow band of officially sanctioned stoppages, usually injury treatment, substitutions and restarts and it has been shown by Colin Trainor that actual playing time differs between teams.

Soccer doesn't stop their watches while the crowd is playing head tennis with the match ball and so a nominal 90 minute game almost always runs to nearly two hours including a break for Bovril.

Sometimes games just seem to go on forever.

The clearest disconnect between the official duration of a sporting contest and the actual time it takes to complete a game is seen in the NFL. The game lasts for four 15 minute quarters, but stopping the game clock on some plays and a half time interval extends the time spent in the stadium to nearly three hours.

Therefore Per 90 figures, even in soccer can quickly become tainted.

Even if we ignore the considerable difficulty caused by how long the ball is in play, accounting for added time merely adds an additional layer of potential error.

Consider a hypothetical example of six individual substitutions made between the 60th and 80 minute.

The first substitute plays for 30 minutes from the start of the 60th minute to the end of the 89th, but he's left twiddling his thumbs for five subsequent substitutions. He is then compensated for this enforced idleness with 150 seconds of added time.

In this case the crude 30 minute value is probably a better indicator of playing time for the first substitute on the pitch rather than if we include added time to his total playing minutes.

Not so for the last sub to enter the game. Five subs have already been made and the ref has taken note of this adding 30 seconds for each transaction, but sub number six wasn't on the field during these stoppages.

When he does arrive on the field for the final ten minutes and assuming there is no other stoppage, he potentially plays for twelve and a half minutes of normally punctuated play.

In his case adding added time to his playing time is likely to be more accurate than simply crediting him with the ten minutes from the start of the 80th minute to the end of the 89th.

As Ian points out this is most evident for substitutes and couple of years ago I looked at the scoring exploits of substitutes, inevitably choosing Edin Dzeko.

Evaluating the performance of subs is fraught with problems, not only relating to time played, but also the goal scoring environment in which they compete. It is both team and time dependent, with scoring rate increasing as the game progresses and the season trend is shown below.

To bypass these issues I simply looked at the proportion of all team goals scored by Dzeko when he was on the pitch playing as a starter and then as a sub.

This only gave a crude comparison.

Goals are rare enough when looking a teams, never mind individuals and even a player who was found on the bench as often as being in the starting 11 would  provide only limited sample size.

 Armed with more data I instead looked at the proportion of expected goals contributed by Dezko compared to the rest of the team, again first as a starter and then as a sub.

I looked only at the 2013/13 season during which there were 252 non penalty goal attempts taken by Manchester City whilst Dzeko the starter was on the field. 59 were from the Bosnian and in terms of expected goals his contribution was 29.5%

Dzeko the sub took 32 of 117 attempts while on the field and his expected goal contribution ticked slightly upwards to 30.7% of the team's total output during that period.

Hardly evidence in isolation that subs, probably due to freshness, contribute more than tired starters, but at least we may not have to deal with obviously flawed time data or require time stamped play by play data to inch towards a conclusion.

Check out Colin's Statsbomb post here, Dan Altman's take here and Ian's original post here.