Now that I’ve had a chance to google a bit, my answer is:

Lincoln. And its NOT close.

If we’re talking just a pure, by the book l, round robin wrestling tourney, your order of finish is

Lincoln 1

Washington 2

Roosevelt 3

Yes they were all athletes and they all wrestled, but their degree of competent was pretty different. Teddy was an amateur. GW was well known wrestler. Lincoln was a highly renowned wrestler.

To make a very hypothetical comparison, just to use context we would understand today,

Teddy would be a guy that was on the college wrestling team.

GW would be a guy that was nationally ranked as a college wrestler. Went to the big tournaments and arguably makes “All-American”.

Lincoln would be the guy people buy a ticket to watch wrestle someone else in a promoted match. He would be true story, actually was the old carnival cliche of the guy that wins his match then calls an open challenge to the whole crowd, dares anyone who feels lucky to come climb in the ring

——

Now, thats just wrestling.

If we say who would win a plain old fight?

All in their prime? I’ll bet on Teddy.

Reason being, Best info I can find, Lincoln and GW were about 6’2”-6’4” and 175-185. Fit, lean, about even.

Teddy was only 5’10” but was likely the heaviest, and based on whst we know about his attention to sports and exercise, it wasnt soft weight. Dude knew the inside of a weight room.

So if we figure Teddy had the short end on reach but had the edge on pure ohysical strength, THEN we add skill.

His wrestling was the weakest if the three but he also boxed and later he did Judo and JiuJitsu reportedly up to 3 times a week.

(Caveat, he had one bad eye from a boxing injury and only picked up JJ after quitting bixinf because of the eye, but for the sale of argument we’re taking all three presidents at the sum of their prime ability)

So TL;DR: Teddy loses the wrestling tournament because hes the least skilled wrestler, but he wins plain out fight, because

Boxing+wrestling+judo/jiujitsu, he’s got more tools in his tool box, deliberate practice working against opponents of different sizes shapes, and a little more muscle on him. Closest thing to a modern mixed martial artist