Stubborn England making life harder for themselves with Gareth Southgate’s subs – here’s the proof

Where were the England substitutes? It was a nation’s refrain as Gareth Southgate took 66 minutes to make his first substitution, 84 minutes to make his second and 94 to make his third. Ivan Toney, as Southgate admitted, was “disgusted” to be brought on so late.

Of course, as Southgate would be entitled to point out, it worked. But while England were behind from the 25th minute to the 95th against Slovakia, the question was inescapable: was there a more enlightened way for England to use their substitutes?

For any specific game, the case is impossible to prove; there is no way of being certain whether making substitutions earlier would have led to a better outcome. Yet it is possible to answer a subtly different question. For teams who are trailing in matches, does using their substitutes more proactively tend to increase their chances of levelling the game?

Here, the answer is unambiguous. Sides who are trailing in matches have more chance of equalising when they use their substitutions earlier than Southgate did on Sunday night.

An academic study of more than 400 matches analysed how substitutes were used by sides who were trailing in the Premier League and leagues in Spain, Germany, Italy and the USA, as well as the 2010 World Cup. It examined whether teams behind in games had more chance of equalising if they used their substitutions earlier, or waited longer to make changes.

The research compared teams who were behind who made their first substitution before the 58th minute, the second before the 73rd and the third before the 79th minute to those who did not. In each case, a side’s results improved markedly when they made their substitutions earlier.

On Sunday night, Southgate missed this mark with his first three substitutions – even though managers are now allowed five. In the games that the study analysed, only 34 per cent of managers of teams trailing had made all three substitutions by the three times suggested: the 58th, 73rd and 79th minutes. Yet those who did drew or won 42 per cent of games, compared to just 20 per cent for those who did not.

“The overall message is that earlier substitutions are better when a team is behind,” explains Bret Myers, the author of the study. A series of other studies have suggested the same. For teams who are winning, the timing of their substitutions does not seem to be significant in determining what happens later in the game.

With five substitutions now permitted within 90 minutes, and an extra one should the game go to extra time, Myers advocates that teams who are trailing be even more proactive in their use of substitutions. “When behind, I do believe teams should use all five that they now have, as it was clear they were benefiting from using all three in the prior research.”

Such research raises the question of why sides who are losing are reluctant to use their substitutions. The simplest explanation is a very human one. To make a raft of changes early in a game amounts to tacit acknowledgement from a manager that their plan A has failed. Should the substitutions work, a manager might still be criticised for the 11 they picked; should the original team turn it around, it will amount to vindication of their starting line-up. And while earlier substitutions mean more chance of a team equalising, they also increase the risk of it going very wrong: if, say, a side replaces a defender with a forward, and their defence is then exposed.

Rather than make decisions that maximise the chances of success, humans make decisions to “cover their ass,” the psychologist Gerd Gigerenzer writes in Risk Savvy. For instance, doctors have been found to prefer treatments that are more likely to save themselves from litigation rather than those with the best chance of success. Gigerenzer calls this defensive decision-making. “The strategy is to abandon the best option because it cannot be justified if something goes wrong and to favour a second- or third-best option.”

For an embattled club manager, their team’s interests might be better served by making adventurous substitutions when 1-0 down. But their own personal interests might be better served by waiting longer – thereby avoiding their boldness backfiring, leading to the sort of result that could bring them the sack.

Managers’ reticence to use their substitutions fits within a wider pattern: of sports teams playing more cautiously than research suggests is optimal. In ice hockey, losing teams who ‘pull the goalkeeper’ – replace their goalkeeper with an extra attacker – have more chance of drawing level. In Twenty20 cricket, teams who lose early wickets are generally more likely to win when they continue to be aggressive, rather than consolidating for long periods. Yet in both cases, being more aggressive when struggling also raises the risk of being thrashed.

“Sports teams tend to undervalue attacking strategies,” observes Omar Chaudhuri from the sports intelligence agency Twenty First Group. “Making your substitutions earlier makes sense as it gives you more time to take an attacking approach.”

And so, the next time Southgate or another manager is in doubt about whether to make a substitution, or leave it another five minutes, academic research provides a clue. To turn a match around, earlier – and riskier – is better.