Real Madrid's Champions League mystique: Can science explain their magical run?

Real Madrid have completed miraculous comebacks in every knockout round of the Champions League to reach the final. Are they just lucky, or something else?

It's either magical or biological. At least, that's what they'll tell you.

After Real Madrid lost 4-3 in a first-leg Champions League semifinal against Manchester City that easily could've produced a bigger deficit, Karim Benzema evoked the supernatural. "A defeat is never good," he said. "The most important thing is we never gave up until the end. ... Now we have to go to the Bernabeu. We'll need the fans like never before. We'll do something magical, which is to win."

And what better way to describe what unfolded in the second leg?

City went up 5-3 on aggregate with a goal in the 71st minute, and Madrid didn't come close to threatening the opposition goal during regular time. Then in injury time, Madrid scored with their first two shots on target of the game to send it to extra time. In ET, City defender Ruben Dias, then the defending Premier League Player of the Year, quickly gave up a silly penalty, and it was game over.

After advancing to the final, Luka Modric reached for a more organic explanation. "The most difficult one was the one against Manchester City because there was almost no time left, but the team and the fans believed until the end because it's part of the DNA of this club." He didn't shy away from the paranormal, either, adding, "The most fun was the PSG game; it was 15 or 20 minutes of madness because it's very difficult to explain what happens on Champions League nights at the Bernabeu. It was the start of many magical nights that have taken us all the way to Paris, and hopefully we can win another Champions League."

In the round of 16, Paris Saint-Germain dominated Madrid in the first leg in France, then did the same in the first half in Spain, roaring out to a 2-0 aggregate lead thanks to a pair of goals from Kylian Mbappe. VAR and a couple inches of space were all that prevented the gap from being even bigger ... and then Madrid scored three second-half goals in 17 minutes to flip the tie on its head. In between, Madrid blew a 3-1 lead at home and went down to Chelsea 3-0 at the Bernabeu -- only to score in the 80th minute to salvage some extra time, where the DNA or the magic took over once again, and Benzema scored the winner.

A couple of questions ahead of Saturday's Champions League final against Liverpool: Is this improbable run actually magic? Is it dumb luck? Do players gain some sort of innate ability to execute at the highest-leverage moments possible when they put on the all-white kit?

The beauty and terror of it all is that no one knows for sure.

"Luck" vs. "DNA"

If you want your brain to experience physical pain, and if you want to feel like your intellectual capacity is truly inadequate, you should fly to New Mexico and go hang out at the Santa Fe Institute. Founded in the 1980s, SFI is a research center that focuses mainly on complex systems science. As they describe themselves: "Our researchers endeavor to understand and unify the underlying, shared patterns in complex physical, biological, social, cultural, technological, and even possible astrobiological worlds. ... As we reveal the unseen mechanisms and processes that shape these evolving worlds, we seek to use this understanding to promote the well-being of humankind and of life on earth."

At SFI, the evolutionary biologist Jessica Flack studies and teaches the specialties of collective behavior and natural computation. Put in her words: "I study how nature computes solutions to problems & how these computations are refined over evolutionary and learning time." Put in my words: We have a good idea of the way collective groups of organisms behave, and there's a lot of research behind why they behave a certain way, but Flack's work is focused on the nitty-gritty of how those groups behave. What is actually happening when a group of individuals combine to overcome a problem, and how do you rigorously describe it?

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Back in November of 2020, Flack co-wrote an essay for Aeon magazine with Cade Massey of the University of Pennsylvania titled "All stars." The sub-headline: "Is a great team more than the sum of its players? Complexity science reveals the role of strategy, synergy, swarming and more." The essay delves into all of the things we don't know about team sports, whether they be unknowable or impossible to measure. It cautions against just writing off unmeasurable phenomena as "luck" and, well, based on what's measurable in soccer, Madrid's current run is filled with luck.

Among the 44 teams that have reached the Champions League semifinals over the past 11 years, this year's Madrid have the fifth-worst expected goal differential at minus-2.5. Only three teams allowed more goals than the 11 Madrid have conceded, and their field tilt -- share of all the final-third passes completed in a match -- is 36%, the third-lowest among all 44 teams. The only finalist that grades out worse by xG differential or field tilt is 2012 Chelsea, who of course won the title ... but finished sixth in the Premier League and beat Bayern Munich via penalties in one of the most improbable soccer games of the past two decades.



When I asked Flack -- not a soccer fan -- about Real Madrid this season, I described them as a team that would get outplayed for the vast majority of their matches, only to suddenly coalesce at the last second to produce enough decisive moments and win each match-up by the bare-minimum margin.

"We see that some individuals in other domains are very responsive to positive reinforcement or negative punishment and change their behavior in response to that kind of reinforcement," she said. "And so it just could be that when this group of guys get a little positive feedback, they really ratchet it up."

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This jibes with the "Real Madrid DNA" that all of the players talk about -- and also with the management style of Carlo Ancelotti, who is the ultimate "players' coach," as shown by Mark Ogden this week. There's clearly some positive reinforcement that the players get purely from playing for Real Madrid. If you keep telling yourself that your team is special and all your teammates are telling you that your team is special, you eventually start to believe it.

After Madrid beat Atletico Madrid in the 2014 final, thanks to a last-second Sergio Ramos goal that sent the match to extra time, fullback Alvaro Arbeloa said: "This is what Real Madrid is all about. When everyone thinks we are dead and buried, we go and win the Champions League. Real Madrid is synonymous with the Champions League. That is why we are the best." A year later Toni Kroos, who wasn't even on the team in 2014, said, "we are Real Madrid and being successful is part of our DNA."

It might sound hokey, sure, but athletes aren't just a set of static and consistent inputs that produce an output. Their performance varies from game to game, and often from minute to minute.