Actually, I think some other skills could affect things as well.
Skills, Event, Effect
Clinch (Arm Wrestling, mild)
Heart (all, but especially the direct competition ones, 100m and Arm Wrestling)
Conditioning (all, but particularly 100M and Long Jump)
Kicking (Long Jump, mild)
Aggressiveness (Arm Wrestling)
Arm Wrestling, I can even see KO Resistance, Submissions & Submissions Defense and Control being a part of that. I do agree that the ones you name are likely to at least be primary qualities required.
Well, except for Dodging for Long Jump. The bar you mention, are you actually thinking of High Jump perhaps? Where you leap up and jump over a bar at a set height? Long Jump is the run up a line on the ground and then jump forward as far as you can.
I would probably be no good at the three Strength categories, as I did not give myself good Strength and most of the guys on the other team are bigger than me. I am agile and have good conditioning and control, so I think I would be best at 100M and Long Jump.
I think Schmidty is pretty small and agile, IIRC, so he might be the guy to go with the 100M. So I am probably best used for the Long Jump.
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