Jürgen Klopp was in his third week as Liverpool’s manager, in November 2015, when the team’s director of research, Ian Graham, arrived at his office carrying computer printouts. Graham wanted to show Klopp, whom he hadn’t yet met, what his work could do. Then he hoped to persuade Klopp to actually use it.

Graham spread out his papers on the table in front of him. He began talking about a game that Borussia Dortmund, the German club that Klopp coached before joining Liverpool, had played the previous season. He noted that Dortmund had numerous chances against the lightly regarded Mainz, a smaller club that would end up finishing in 11th place. Yet Klopp’s team lost, 2-0. Graham was starting to explain what his printouts showed when Klopp’s face lit up. “Ah, you saw that game,” he said. “It was crazy. We killed them. You saw it!”