on the player’s effort and performance during training activities, observable by the club
coach but typically not by the national coach.22
The fact that some players spend much more time on the field than others implies that
comparing total outputs such as number of goals of different players could be misleading.
Not surprisingly, the correlations between some per match output measures and minutes
played reported in Table 4 are strong. A way out of this would be to exclude observa-
tions of players who were substituted (out or in), but in the many matches with three
substitutions this would make us lose 6 out of 14 observations (with field appearance) per
team.
To disentangle the two performance dimensions ‘time spent on the field’ and ‘perfor-
mance while on the field’, our approach will be the following. First, we run regressions
with minutes played as the dependent variable. Second, we run regressions for various
outputs per minute played ; one issue with per minute played measures is however that, as
reported in the lower half of Table 4, for outputs such as shots on goal there is a negative
correlation between output per minute and minutes played. This can be attributed to
physical exhaustion as well as associated energy management strategies. Interestingly,
though, the correlation tends to be positive for output measures more strongly related to
team play. This points to the fact that players need some time to get involved into the
team’s game.
To rule out that our findings are driven by differences in minutes played via such
correlations, we keep only observations associated with at least 71 minutes, the median
substitution time for starters conditional on being substituted out.23 The average number
of shots on goal per minute is about 0.022 for players who play 71 minutes or less, but only
0.014 for players who play more than 71 minutes. The difference between the averages for
players who play more than 71 and those who play more than 90 minutes is very small on
the other hand: 0.014 versus 0.013. By adding the condition that minutes played exceed
the median substitution time for starters, we can hence substantially alleviate the problem
of comparing observations based on appearances of different lengths without losing too
many observations.
22 Even famous players may have to work hard to convince the coach to let them play. A point in case
is Lukas Podolski, a star of the German national team during World Cup 2006, who had just five league
starts between August 2007 and September 2008 at the Bayern München team.
23 The results would be very similar if instead we kept only observation of starters. If we adopted the
stricter conditions of no substitutions, some but fewer of our results would be significant.
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