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Football’s five substitutes rule doesn’t benefit the big clubs – and here’s why | Ignacio Palacios-Huerta

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Last month I was chatting to my friend Ernesto Valverde, the former Athletic Bilbao and Barcelona coach who I got to know well when I was Athletic’s head of talent ID. For once we were disagreeing. He, like many in football, thought that the temporary rule change to allow five substitutions from an extended bench of nine players favoured the big clubs. I insisted it wouldn’t.

At the time it felt like the debate didn’t matter much either way, given the rule was only expected to last until the end of the season. Now, however, Ifab has agreed to extend it, to the dismay of many. Burnley’s manager, Sean Dyche, and Aston Villa’s Dean Smith are prominent critics – and one well-regarded journalist recently claimed it “really does not take the brains of Lloyd George to work out that it is a rule which will favour richer clubs who have squads packed with larger numbers of higher-quality players”. However, this issue really is not as simple as it appears on the surface. Let me explain why.

My starting point is this: if being able to use five substitutes favoured the big clubs, you would expect them to make more changes compared with smaller teams. However, since the season resumed that hasn’t been the case. After lockdown was relaxed in the Bundesliga, for instance, the top four teams used 4.03 substitutes per game, while the bottom four teams used 4.59 substitutes per game. In the Premier League, Manchester City and Chelsea used fewer substitutes on average than Bournemouth and Norwich.

So what is going on? My argument is that the change in the number of substitutions neither harms nor benefits the teams according to their quality, but depends on other considerations.

Let me explain using a scenario I have discussed with a number of coaches, players, and analysts in the Premier League and La Liga. It is far simpler than real life, but hopefully it captures the essence of the situation.

Let’s take two hypothetical situations. In Situation A, substitutions during the game are forbidden. Teams start and end the game with 11 players. In Situation B, meanwhile, it is mandatory to replace the starting XI at half-time, and no other substitutions are allowed. Going from A (“No subs”) to B (“All subs”) means going from 0 to 11 substitutions, something undoubtedly much more drastic than going from three to five substitutions.

In Situation B, each team experiences a change in the quality of its players in the second half. The difference between the second half and the first half depends only on how good each team’s substitutes are relative to the starting XI.

In other words, whether a given team benefits depends on how its own relative change compares with the relative change of its opponent. Note that the words “strong team” or “weak team” are not used here, and therefore whether one team has a better or worse squad than another is irrelevant.

Let me put it another way. Let’s assume that every team’s first team and substitutes’ bench has a quality that is measurable and can be assigned a number from 0 to 100, with 100 being best.

Now imagine a match between a strong and a weak team, in which all the players are replaced at half-time. The strong team has 11 players of quality 100 and another 11 who are 60. On the other hand, a weak team has 22 identical players, all of quality equal to 20.


Burnley’s manager, Sean Dyche, on the touchline during a game

Burnley’s manager, Sean Dyche, has spoken out against the five substitutes rule. Photograph: Getty Images

When the starting players have to be replaced at the break, the strong team plays with quality 100 in the first half and quality 60 in the second half, while the weak team plays with quality 20 in both halves. Contrary to what many might think, under these conditions, it is clear that the weaker team prefers the situation where there are more substitutions.

Of course Team B has a low chance of winning throughout. I am not disputing that. But, crucially, their chances of winning go up when 11 changes are made. The reason is that it has a more homogeneous squad, one with more similar player quality and is able to make more like-for-like substitutions.

Here is another scenario. All players in the strong team have an identical quality equal to 50, while the weak team has a quality of 20 in its first XI and of 15 in its 11 substitutes. Here again the more homogeneous team – which in this case is the strong team – benefits most from a situation where there are more substitutions allowed.

These simple exercises capture the essence of the impact of rule change. A team’s strength does not matter. Squads that can make more like-for-like substitutions are the ones that will benefit most from the possibility of a greater number of substitutions, regardless of their riches and thus overall level of quality of the squad. More uneven squads suffer from the rule change, regardless of how good their overall squad is.

At this point you are probably thinking: “Well, your theory sounds all well and good professor, but in practice the big clubs have more homogeneous squads than smaller ones?” I wouldn’t be so sure.

There is a well-known effect in football which economists refer to as the “superstar phenomenon” – whereby a small number of people earn enormous amounts and dominate the activities in which they engage. Of course it is not specific to football or even sports. There are countless examples from the world of arts and letters and showbiz where there is a strong tendency for rewards to be highly skewed toward the most talented individuals in the activity, with very large rewards at the top and a marked skewness in the distribution of salaries.

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Nearly 40 years ago, Sherwin Rosen, an economist from the University of Chicago, proposed a brilliant theory to explain these general patterns. Applied to football, it means that essentially the best players reap a greater share of payroll, and this reduces the spoils available to the relatively less gifted in the squad. The superstar phenomenon, therefore, tends to increase the salary inequality both within squads and across squads.

As salaries are associated with quality and performance, this pushes richer clubs to tend to have more uneven squads than lesser – in terms of money – clubs. Richer clubs would then benefit less, not more, and tend to use fewer substitutes, which is what is happening. Of course it would make sense to go through each squad individually to make sure this is the case.

Incidentally, reports have suggested that only Aston Villa, Bournemouth and West Ham voted against the rule change. But if they have a relatively more balanced squad, they should have been among those to vote in favour.

Ignacio Palacios-Huerta is professor of management at the London School of Economics

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