By Nikhil Waugh
When Keith Peacock became the first player to enter the field of play as a substitute in the English Football League on 21st August 1965, few would have envisaged the role of the substitute today. Substitutions are one of the few tools in football that managers have at their disposal to affect the outcome of a match. Planning, tactics, formation, and conditioning can all be conducted on the training field, but what happens when those plans fail during a match?
This paper explores the quantitative and qualitative aspects around football substitutions in the English Premier League over a 15-year period. The 1115 games analysed across the 04/05, 11/12 and 18/19 seasons provide a modern understanding of the football substitution (Note: the five-substitution rule was brought in during the pandemic and has changed the way substitutions work since this paper was written).
In the quantitative analysis the relationship between substitution distribution and goal distribution was investigated to see if there were any trends in the way substitutions were used and if there were any correlations to changes in scoreline. Whilst the paper goes into much greater detail, a couple of key findings are worth mentioning.
1) The average time of the first substitute rarely changes.
The table below shows the mean time for the first substitute roughly adheres to the anecdotal quip ‘managers make the first substitute at the 60th minute’. What is more significant is the fact that over a time which is roughly half of the premier league’s lifespan, the average time rarely changes (+/- 2 mins) and the difference between home and away teams is negligeable. Both these trends also apply to the second and third substitutions.
2) There is hardly any correlation between goals and substitutions.
In theory, when a team goes behind, a manager should want to change the course of the game. However, the correlation coefficient between the first goal being scored and the first substitution being made is 0.03. This is a strong indication that managers do not use substitutions in reaction to goals. Now consider a 2-0 deficit. A team leading by two goals wins 89.2% of the time suggesting that a current plan is not working, and a change should be made. After all, one point more in any match is better than any magnitude of goal difference. However, it takes teams on average 16.6 minutes to make a substitution.
Both these points lead onto the qualitative analysis and looking at decision making theory and how that can be applied to substitutions. If goals aren’t a determining factor in substitution decision making process, could biases and behavioural psychology be driving the decisions of substitutions.
Football is a sport where randomness and uncertainty play a huge part in the outcome. This, along with the scarcity of scoring actions, is a major reason why it is so popular around the globe. When uncertainty exists, by definition, there are unknowns which the decision-maker cannot anticipate when making a final decision. The effect of these unknowns increases the influence of chance, or luck, in determining the outcome of the decision. The paper looks into decision-making theory, most notably the works of pioneering behavioural psychologist Daniel Kahneman, and how human biases and heuristics apply to substitutions. Some examples include:
Hindsight bias – when something happens, it was bound to always happen. Neglect all of the other possible outcomes which did not come to fruition.
i.e. Just because a substitute scores, it doesn’t necessarily mean it was the right decision.
Framing effects – the way in which a decision is presented invokes different emotional triggers. This in turn will affect the analysis of these decisions.
i.e. The substitute could have scored, invoking people to think it was a good decision. However, the goal could have been deflected and is mostly down to chance rather than the substitute.
The applications of these, along with other facets of behavioural psychology, can give managers a better understanding of their decisions and provides them with tools to avoid common pitfalls.
The conclusion of the paper touches on how the findings can improve the understanding of substitutions as well as suggesting ways to utilise substitutions in a better way. This includes, making substitutions earlier with greater emphasis on the scoreline, for example, if you are 2-0 down, switch a defender for a striker and try and score more goals. Or, finding footballers whose defined role is an impact substitute such as, a really tall athlete (NBA player-esque) who is good at heading the ball or a very fast athlete (Usain Bolt-esque) who can terrorise a tired defence for last 10 minutes or so. Both can change the outcome of a match if applied with appropriate training on the training field.
Some clubs are employing substitution coaches and with the increased number of substitutions per match, are trying to find that edge in an ever-competitive environment.