It is halftime in a soccer game. One side is losing. Most of the time, that team’s manager decides to persist with the 11 players who started the match until well into the second half.

That lack of action actually damages the team’s prospects of making a comeback in the game. And despite the data that lays out a more prudent approach, holding on to substitutions remains commonplace in top level soccer. But it is also becoming less frequent.

Since Unai Emery became Arsenal manager at the start of the 2018-19 season, the Gunners have used all three of their substitutes in 41 out of 43 Premier League games — the third-most of any team. Under Emery, Arsenal typically makes its first substitution after 52 minutes — earlier than any other Premier League team last year. Emery’s halftime changes contrast with those of his predecessor, Arsène Wenger, who had his first substitution on average in the 60th minute from 2010 to 2018, according to the football consultancy 21st Club. In his first North London derby, at home against Tottenham in December, Emery took the unusual step of bringing on two substitutes at halftime, and both proved crucial in turning a 2-1 deficit into a 4-2 win.

Emery’s fondness for using all of his available substitutes is a snapshot of a broader change in the Premier League. The proportion of teams using all three substitutions rose from 73 percent in 2012-13 to 83 percent in 2018-19.

This rise has coincided with increased research into the potential advantages gained by teams that use their substitutions earlier. In 2012, Bret Myers, a professor at Villanova University as a professor who also works as an analytics consultant for the Columbus Crew of the MLS, published a paper based on an analysis of the top-tier leagues in England, Spain, Germany, Italy and the U.S. along with the 2010 World Cup. Myers found that if a team was losing, a manager should make the first substitution before the 58th minute, the second before the 73rd and the third before the 79th minute. The position of the substitutes didn’t matter. Additionally, if a team was ahead, the timing of its substitutes seemed to make little difference.

Teams that followed Myers’s approach to making substitutions improved their result in the match — narrowing their goal deficit — 42.3 percent of the time. Teams that did not follow his rule improved their performance only 20.5 percent of the time — so, from the same position in games, they were less than half as successful as the sides who followed this substitution pattern, and made all three substitutions before the times Myers advocated.

Players coming off the bench tend to be markedly more productive than the players they replace, as well as the players who stay on. On Statsbomb, Colin Trainor analyzed regular goalscorers in the Big Five European soccer leagues in the 2012-13 season and found that when players were substituted onto the field, they scored at comfortably the highest rate — 0.65 goals per 90 minutes — of the sample of 268 players. The rate was 50 percent more than for the players who were subbed off (0.42) and even more than for players who played the full 90 minutes (0.38). This implies not only that fresh players are significantly more likely to score than tired ones, but also that players are simply not as effective at scoring when they play the full match.

Sometimes, an element of pre-planning in substitutions may be advantageous. For instance, if forwards are told they are likely to be taken off at halftime, that may encourage them to run even more in the first half and pressure opposing defenders, rather than worrying about conserving their energy. “To turn substitutions into a proactive strategical decision rather than the reactive or habitual practice we see so often is certainly an area which teams should look to exploit,” said James Yorke, a senior analyst at StatsBomb. “The game gets ever faster, so prepping for a guy to give you all his running for 45 minutes… is just a logical idea to implement.”

Myers believes that managers don’t use their substitutions earlier because of defensive decision-making — and being too egotistical to admit their mistakes. “For the most part, the starting 11 is the perceived ‘best foot forward’ for the squad with respect to the matchup, so an early substitution is typically viewed as a plan B rather than a proactive plan A approach,” he said. “Managers also may fear backlash when pulling starters early who expect to play longer.”

Coaches might fear criticism that early substitutions, rather than being lauded as proactive, will amount to a tacit admission of their original error in picking their starting 11. After Liverpool’s manager, Jürgen Klopp, substituted a fresh Dejan Lovren following just 34 minutes of a game against Tottenham two years ago, The Times of London wrote that “Klopp must take blame for Liverpool’s comedy of errors,” and, “It comes to something when, with Liverpool 2-1 down after half an hour, Jürgen Klopp felt the need to substitute his £20 million central defender.” Managers also invite criticism if they use their third and final substitution relatively early and a player subsequently gets injured, meaning that their team will be forced to play the remainder of the match with only 10 players.

The economist John Maynard Keynes once observed that for your reputation, it’s better to “fail conventionally than to succeed unconventionally.” In such a volatile industry — the average manager in the top four divisions of English soccer lasts barely a year in each job — perhaps it is understandable that managers use their substitutes conservatively — in order to minimize criticism. But those with the courage to substitute earlier may stand to gain extra points for their team.

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