Are bigger people more likely to win fights?

Maybe, maybe not.

Many years ago, in New York’s Union Square, I came across two guys squaring off in front of a bar a little after midnight. The first was a little guy with close-cropped hair and a rough look about him. About ten feet across from him there was a much bigger guy in a nice coat. They were—as it’s sometimes put—”having words.”

I looked away for some reason. Only for a split second. When I looked up again, the big guy was flat on his back on the sidewalk, his eyes closed, and the little guy was patting his face — “hey man, wake up!”

I don’t know how the little guy closed that distance so quickly. I didn’t see what kind of punch he threw— an expert right cross? A wild haymaker? But I’ve been curious ever since: in David vs. Goliath, how often does David actually win?

A brief look at the data

The UFC fights dataset is a popular resource among the surprisingly large subset of people interested in both data and MMA. It can help us address this question because, in addition to a load of fight-specific figures and the identity of the winner, it also includes vital stats about fighters such as their weight and their height.

This highly specific dataset has its limits for my more general question, but it can get us started: for two similarly skilled opponents, how much of an advantage is size?

I was surprised to learn that, at least in the UFC data, bigger fighters don’t have much of an advantage. Analyzing the data, it appears as though height seems to have a limited impact (see my code on GitHub)— but differences in body mass don’t seem affect fight outcomes.

I restricted this analysis only to those fights where the winner emerged via knockout or submission — a "real" win. This analysis holds true for all weight classes, and even holds true when you restrict the analysis only to those fights where the weight difference exceeds 15 pounds: the heavier fighter wins fewer than half of all these fights.

This holds true even when weight differentials exceed 50 pounds, and even holds for the few “Open Weight” fights, in which all weight class restrictions are lifted and in which heavier fighters have historically won only half of all fights. The canonical example of this type of fight was 1994’s Hackney vs. Yarborough, in which the 200lb Hackney beat the more-than-700lb Yarborough:

Source

Why would bigger fighters have an advantage?

There are two primary characteristics that could theoretically give bigger fighters an advantage: reach and mass.

Reach is highly correlated with height, and it’s useful because it allows rangier fighters to literally keep their opponents at arms’ length: it enables them to hit their opponents from a distance that stubbier-armed fighters can’t cross. Same goes for legs. This is what we see in the data above: being taller really does help.

Mass is a more interesting story. When you’re trying to knock someone out, you’re trying to, well — it turns out science hasn’t totally solved this one yet. But it’s probably a safe bet that the harder you hit somebody, the more likely you are to put their lights out.

“How hard you hit somebody” is a way of describing the impact of the punch—the kinetic energy a fighter can deliver in a short period of time. Kinetic energy is described by a simple equation:

Energy = 1/2 * mass * (velocity^2)

So more impact can come from more energy, which can come from more mass. This isn’t just about the weight of your arm or fist. Boxers talk about “effective mass” — good punching form allows a fighter to “throw” his weight behind the punch, using the weight of his entire torso and even his legs to transfer energy into the punch (and into his opponent’s head).

Why wouldn’t bigger fighters have an advantage?

Of course, the equation above has two variables, and the second one is squared. This means that you get the same increase in energy from doubling your velocity as you would from quadrupling your mass. More realistically, this means that a 160lb fighter could add 50% to his punching power either by bulking up to 240lbs or by speeding up his punch by only 22%.

This means that we should probably expect punching speed to have a greater impact on fights than bodyweight does — all else being equal, of course. But it’s not at all obvious that big fighters can’t punch as fast as small ones. For starters, they don’t really need to— because they’re bigger, they can deliver the same amount of kinetic energy at lower speeds (see the equation above).

However, there is mechanistic evidence to suggest that smaller fighters could have an advantage. In order to hit the high velocity necessary to knock someone out, a fighter needs to accelerate his fist quickly; this is related to "rate of force development," a measure of explosive strength. Since longer tissues might be less capable of transmitting force, and since taller fighters have longer tissues, there is at least some reason to suspect that little guys can develop force faster.

More generally, bigger fighters will need to muster a lot more energy just to get their punches and kicks going: the more mass they have, the more energy they need to move it, and the higher their rate of force development will need to be relative to that required of a smaller fighter. This can be pretty draining!

Energetic concerns like these weigh quite heavily on fights. That’s because a fight is essentially a twenty-five minute dance around a ring punctuated by bursts of traumatic violence. Speaking very roughly, a person twice as heavy needs to use twice as much energy to get around. And people get tired.

PSA: Don’t fight big people

If you've ever watched a fight, something has probably been nagging at you this whole time: fights aren't all about hitting! And it's simply a fact of life that people with more muscle are able to exert more force, generally speaking, against their opponents. At the risk of being obvious, this is because muscle is the thing that makes the force.

By and large, given two people with roughly equivalent proportions of lean body mass and dramatically differing weights, the larger person will be stronger. That means that they are better able to grip their opponents in bear hugs, wrench their arms around, shove their faces into the mat, and yank their legs out from under them.

Moreover, if they're really big, they're essentially covered in a layer of shock absorbers that spread out the force of a punch, making it less likely that their internal organs will get knocked around even by a well-aimed strike.

So what explains the UFC data, and why might it present a different picture than the one you'd encounter in everyday life? I think there's a number of things going on:

• Since the beginning, UFC has been dominated by Brazilian jiu-jitsu, or BJJ, a martial arts style that originated with the Brazilian Gracie family (which also helped to found UFC). BJJ is grappling, which is useful in UFC because nearly all MMA fights end up on the ground, where bigger fighters, or at least taller ones, seem to have less of an advantage. BJJ is notoriously technical — it's a kind of puzzle-solving exercise that adepts view as being more about skill than strength. A classic submission in BJJ involves simply getting behind someone and choking them out, a move which, if done correctly, takes only a few seconds and benefits from speed and agility. This evens the odds in UFC fights.

• Punching fast and delivering effective mass takes training that most street fighters of any size don't have. This suggests that mass, not velocity, is probably the main determinant of punching power among untrained people, which gives big untrained people a decisive advantage against little untrained people, against whom the odds stacked against the little folk in street fights.

• Finally, the very process that generates UFC fights — the tournament structure — means that fighters who end up facing off will often be fairly evenly matched. For the matches that pair fighters with massive weight disparities, it seems likely that the bigger fighters are relatively unskilled for their weight and/or the smaller ones are unusually skilled — if one of these things weren't the case, then these pairings usually wouldn't occur.

Crucially, this last bullet is not something that is likely to hold on the street. People don't usually pick fights unless they think they can win, and, at least in the case of very large people, my advice is to trust their judgment.