At Melwood, the club’s training complex in a residential Liverpool neighborhood, Graham works in a white-walled room, down a corridor from the coaches and the cafeteria. Tim Waskett, who studied astrophysics, sits to Graham’s left. Nearby is Dafydd Steele, a former junior chess champion with a graduate math degree who previously worked in the energy industry. The background of the most recent analyst to be hired, Will Spearman, is even less conventional. Spearman grew up in Texas, a professor’s son. He completed a doctorate in high-energy physics at Harvard. Then he worked at CERN, in Geneva, where scientists verified the existence of the subatomic Higgs boson. His dissertation provided the first direct measurement of the particle’s width, and one of the first of its mass. Another club might conceivably hire an analyst like Graham, or Steele, or Waskett, and maybe even Spearman. But it’s almost impossible to imagine any but Liverpool hiring all of them.

As often as possible, the analytics staff arrives at Melwood in time for breakfast. The food in the cafeteria includes locally sourced eggs and five or six kinds of salad greens and beef aged in a glass locker. Players sit at one of two tables with coaches and trainers. The analysts, who look like nobody else in the building, sit at an adjacent table. Greetings are cordial, even friendly. But there’s little evidence that the players know one analyst from another. The morning after the Leicester game, Graham sat with his back to Keita, their chairs touching. Hours before, he’d been shouting at Keita from the stands. Now he was within a foot of him, eating the same poached eggs, yet there was no interaction between the two of them. “If he wants to talk about the game to me, he can initiate that, and I’d be delighted,” Graham said. “Otherwise I’ll leave him in peace.”

At one point, Spearman went to get coffee. He returned with a question rooted in the intersection of breathless fandom and mathematical geekiness: Who would be the most accurately regarded player in soccer? Not the most underrated or overrated, but the one whom conventional wisdom comes closest to gauging correctly.

“It has to be Messi,” he said. “Because if he isn’t the best player in the world, he’s second. So the most that opinion could be off is one place.” As if to punctuate his point, Spearman suddenly spilled his coffee so that it streamed down the middle of the table. The analysts erupted in good-natured jibes. “You’re not doing a good job at convincing anyone that you’re not a nerd,” Waskett said.

Spearman hasn’t had much to do with Liverpool’s recent success. He does almost none of the work that Klopp sees, and he’s rarely involved with discovering players. His mandate is more ethereal. Spearman knows just enough about the sport, or just little enough, to try to change it. “We’re just starting to ask the question, ‘Why don’t we try to play football in a slightly different way?’ ” Graham explains. Soccer is the sum of thousands of individual actions, but the only ones Graham’s model can evaluate are the passes, shots and ball movements that are downloaded from the official play-by-play. “There are still fundamental limitations in the data we have,” Graham says. “It’s still like looking through a very foggy lens.” By working to get the mathematical rendering closer to reflecting what actually happens on the field, recording not just that a defender kicked a pass to a midfielder but how hard it went and what happened when it was received, Spearman is looking to find a path through the fog.