Using data from the Big 5 European leagues and studying the goal scoring rates for all players that scored at least 6 league goals.
The use of this filter gives a list of 268 players that scored a combined total of 2,782 goals in 617,331 minutes of playing time. This equates to an average scoring rate of 0.41 goals Per 90 minutes for the sample of players.
It is a fact that more goals are scored in the second half of games than the first half, and the apportionment in the Big 5 leagues is no different with just 44% of all goals scored in the first half and 56% in the second half.
The goal scoring rates increase in line with the time elapsed during a match.
Forwards coming on as substitutes score at a higher rate than starting forwards. But when we consider that more goals are scored in the second half than the first half then this is no great surprise. Substitutes spend a greater proportion of their playing time in the second half (when goal expectation is higher) compared to the first half than a starting player would.
The fact that substitutes have a higher scoring rate means that you can’t directly compare Goals Per90 figures between players that regularly start and those who make frequent substitute appearances. Very simply, the substitute will have his numbers inflated and we would expect his Per90 numbers to drop in the event that he was handed a starting position.
However, “fatigue among forwards is a more powerful force than fatigue among defenders”. That sentence strikes a chord.
We have established that the longer a match goes on the greater the goal expectation. This is one of the reasons why substitutes score at a higher rate than starting players. So, by this logic we would therefore expect players who are substituted to score less Per90 than players who played the full 90 minutes.
Not only would the substituted player be playing at least as many first half minutes as second half minutes when the goal expectation is at its lowest, but the fact that he is substituted may also indicate that he hasn’t played a great game thus far.
That second suggestion certainly isn’t true all the time. The player may be injured, withdrawn for tactical reasons or just tired.
Even ignoring the suggestion that the substituted player has been having a less than stellar performance, due to the increasing goal expectation it is reasonable to assume that the Per90 goal scoring rates would look as follows:
- Substitutes who come on
- Full 90 minutes Players
- Players taken off
How does that compare with what actually happens?
Each game that the 268 players took part in last season was divided into the 3 categories: Substitutes on, Full 90 and Players off and a total of the number of goals and minutes that the group of 268 players as a whole racked up in each category.
As expected, substitutes coming on scored at the highest rate of the three groups. This group scored at a rate of 0.65 Goals Per90, however players that played the full 90 minutes actually posted the lowest Per90 numbers of 0.38 with the players that were substituted off in between with a rate 0.42 Goals Per90.
This is an interesting finding and it appears that the suggestion of fatigue being a big issue in the rate that forwards score goals is true. The sample doesn’t specifically just include forwards as it includes the leading goal scorers, it will obviously be forward biased.
It looks like the fatigue factor is so strong that it is even able to overcome the fact that more goals are scored in the second half than the first half. It shows that a player who starts the game and is withdrawn scores at a higher rate Per90 than a player who completes the full 90 minutes.
When you think about this, it is common sense. Players tire and it’s better to replace them with fresh legs, but the impact of tiredness is interesting to say the least. Theres no doubt that clubs and organisations like Prozone have data that records the physical drop off in player performance due to fatigue but It is surprising that the impact is so strong for goal scorers that it outweighs the benefit of playing the entire second half of a game with its increasing goal expectation.
All 5 of the leagues follow exactly the same trend. The substitutes coming on comfortably post the highest Per90 scoring rates. This group being fresh as well as spending more of their playing minutes in higher goal expectation periods of the game. The players that were withdrawn have a slightly higher Per90 figure than the footballers that played the full 90 minutes with the benefit of freshness outweighing the back ended scoring bias.
Therefore we can conclude that, not only do substitutes score at a higher rate than starting players but that the players who are subbed off score at a higher rate than their teammates that play the full 90 minutes.
Unless there is a large difference in quality between the starting 11 and his substitutes any manager that doesn’t use all 3 substitutes are giving up some expected value.
Obviously managers may need to hold a substitute back to cover the chance of injury later in the game, but leaving that aside there really should be no reason why managers don’t ensure that they use the bench in enough time to get the full benefit of the fresh player.
50% of all first substitutes played at least 30 minutes, 50% of second substitutes play less than 20 minutes, and only approx 15% of second substitutes play at least 30 minutes.
50% of the time, a third substitute plays 6 minutes or more and 1 in 5 managers wait until the 89 minute to make their last change. In fact, during the first 20 weeks in the Premier League there was a total of 98 possible substitutes that were not used. Managers have a desire to finish the match with a full complement of players, but there is a trade off where this prudence has the opportunity cost of not making maximum use of fresh legs against a tiring opposition.
This analysis has shown that the fatigue impact is large enough to overcome the difference in the scoring rates between the two halves, so with that in mind there is really no reason for a manager not to avail of all of his available substitutes.