“Who would win?” is one of the more fun, divisive debates that fans have — in sports, sure, but also in comic books and movies. And with “Captain America: Civil War” — a film that pits a whole bunch of costumed heroes against one another — taking that question to its logical conclusion this weekend, this is a great time to take a stab at figuring out which Avengers would actually win in a fight. There’s a vast amount of discussion on the internet about superhero matchups, but the kind of rigor that is applied to the question of “who would win” in the sports world isn’t used in the debate surrounding fictional characters who punch one another.

So we jumped into this minefield, with the full intention of objectively doing it right. None of that cowboy “I think Hawkeye could totally beat Black Panther” crap I tried to pull during March Madness last year. I turned to the wisdom of the crowd, controlling for notoriety to ensure that this wasn’t some gauche popularity contest. For some help, I reached out to friend-of-the-site James England, who by day is the chief technology officer at 321Forms but by night maintains a college football analytic system and develops killer Oscar predictions. He set up a site that asked users to identify which of 14 Avengers they were familiar with, then cycle through matchups of those Avengers and identify the likely winner of a fight between the two.

We got 1,158 FiveThirtyEight social media followers to weigh in on 47,503 head-to-head matchups. Here’s how the matchups break down according to our respondents:

I then calculated a numerical power rating for each contender based on their record using a system called maximum likelihood that is used in things like basketball and football analytics. We’re going to use math to figure out how likely each Avenger is to win a fight, just like we’d do with college football: We’ll use the same methods to ascertain Hawkeye’s comparative strength that we use to evaluate the University of Iowa Hawkeyes football team.

Here are the power ratings, plus each of the 14 character’s estimated win percentage against an average opponent.

CHARACTER RATING WIN PERCENTAGE VS. AVG. OPPONENT Thor +1.94 87% The Vision +1.68 84 The Hulk +1.56 83 Iron Man +1.08 75 Scarlet Witch +0.91 71 Captain America +0.67 66 Black Panther +0.04 51 Spider-Man +0.03 51 Ant-Man -0.74 32 Black Widow -0.75 32 The Winter Soldier -0.89 29 War Machine -1.07 26 Hawkeye -2.08 11 Falcon -2.37 9 Source: JAMES ENGLAND

The ratings confirm a lot of what we already know, including that there are different tiers of Avengers. You have heavies like Thor, The Vision and Hulk in a class of their own. Next comes a powerful group of artificially enhanced humans and several possessors of suits: Iron Man, Scarlet Witch, Captain America, Ant-Man, Black Widow, Winter Soldier, Black Panther and Spider-Man. Rounding out the list is a group of regular guys who are kind of good at a thing: Hawkeye, War Machine and Falcon.

But we can also use these individual ratings to see how every character would do one-on-one against every other character (using the maximum likelihood ratings to calculate individual matchup-level probabilities gives us a vastly larger sample of data to work with and provides a more holistic sense of each character’s power; for example, how Thor performed against the Vision informs his chances against Ant-Man):

Based on his rating, Iron Man beats Captain America in a one-on-one fight 60 percent of the time. The Hulk, an unstoppable force of nature, beats Falcon, a nice man who can fly, 98 percent of the time. Ever wonder what would happen if Spider-Man fought Ant-Man? Me neither, but Spidey wins the bug fight 68 percent of the time. Thor stomps everyone, which makes sense because he is Thor — a god — and everyone else is not.

Indeed, one immediate takeaway from this analysis is that there is a very good reason that Thor and The Hulk go off on their own at the end of “Avengers: Age of Ultron,” getting them out of the way for “Civil War.” They’re tanks. Here’s what Ant-Man did to Falcon:

Imagine a god of thunder messing with the winged guy. But then that raises a larger issue, one that has plagued fans of the Avengers franchise: The presence of The Vision — who can fly, shoot beams of radiation from his head, phase through stuff and has an Infinity Gem powering the whole shebang — makes Team Iron Man way too powerful. According to our ratings, he ranks somewhere between Hulk and Thor in power.

Matchups are fun, but this is Civil War, not “Captain America: One-On-One Skirmish.” If you’re going to do a statistical analysis of the Avengers, you may as well go all out, so I designed a simulation that uses those matchup probabilities to try to figure out what the expected outcome would be of the Team Cap vs. Team Iron Man brawl.

Based on the trailer, Captain America is evidently leading a team with Scarlet Witch, Ant-Man, The Winter Soldier, Hawkeye and Falcon. Iron Man has The Vision, Black Panther, Black Widow, War Machine and Spider-Man. The simulation randomly paired each member of one team against a random member of the other squad and then continued to schedule such fights until one squad was entirely defeated. (I spent two hours writing the simulation out in Python because I have completely lost control of my life.)

According to a cool one million simulations, Team Iron Man is triumphant 81 percent of the time.

At the insistence of FiveThirtyEight sports editor Kyle Wagner, who is, I promise you, a larger Marvel nerd than I ever will be, I also adjusted the simulation to accommodate several non-random seeding scenarios — my best guy versus your best guy and so on; the inverse of that; my best versus your second best and so on — just trying to squeeze out an ounce of tactical advantage for Team Cap. But the effect was minuscule. Messing with matchups does not save Cap’s cause. Also, why is a master tactician staging the big fight in an open airport when the majority of his adversaries can fly?

These minute differences underscore the larger point: Captain America is a bad recruiter; his team is deliriously outgunned, and his only real asset on the team is a reality-warping tyro (Scarlet Witch). It’s going to be very, very hard to balance these teams out, mainly because of The Vision.

But there are some things that the power ratings — which essentially describe an individual character’s strength against the average adversary in the set — cannot capture, so it’s interesting to look at the differences in win percentages between what the ratings estimate and what the respondents to our survey said:

Here’s a good example: According to the power ratings, Scarlet Witch would beat the Hulk 34 percent of the time. However, the voters picked her to win 44 percent of the time (227 of the 511 Hulk vs. Scarlet Witch matchups). That 10 percentage point gap, I’d argue, is probably because we got to watch Scarlet Witch mind-warp the Hulk in “Age of Ultron.” Voters had Hulk beating Thor more often than the ratings system did — 50 percent vs. 41 percent — probably because they saw “The Avengers,” in which that sort of happens on a helicarrier. Given that there was a whole movie on the subject, it should come as no surprise that Captain America’s win percentage over The Winter Soldier from the voters came in 10 points higher than the expected wins. I can’t explain why Ant-Man might do better against Hulk among our voters than the ratings imply, but I shudder to think it’s because of a soda commercial.

And now, a selected analysis of several potential fights in the film, based on various trailers and using the matchup win percentages derived from our power ratings:

Captain America vs. Iron Man

Ah, yes, the marquee event. Iron Man wins over Captain America 60 percent of the time. It’s a little surprising to see Cap doing OK here, but, again, the location of the brawl appears to be an enclosed space — so who can really say.

Scarlet Witch vs. The Vision

This is an upset. Or perhaps The Vision is jobbing. Scarlet Witch would beat Vision one-on-one about a third of the time based on our analysis.

Black Panther vs. The Winter Soldier (Bucky)

Bucky is very, very fortunate that the helicopter has entered the fight, as Black Panther wins this 72 percent of the time.

Hawkeye vs. Black Widow

https://www.youtube.com/watch?v=o6JY7V83J3A

Hawkeye is screwed here. Black Widow crushes him 79 percent of the time. I realize that any article I write that mentions Hawkeye is going to be biased — me writing about Hawkeye is like Nate talking about La Taqueria — but here I must concede that everything people have said about Hawkeye appears to be correct and maybe he is slightly out of place in a brawl like this. Perhaps he should have swapped out with The Hulk and joined Thor on his buddy-cop Ragnarok and then Cap would have a snowball’s chance in Hel to win this war.