I saw this picture on fallout wiki(on the bottom of the page) and I wonder if I can do any boxing in fallout or is it as useless as it looks?
P.S. Is that picture a hack or are there any boxing possibilities with the Legion?
So, there's two seperate questions that could be answered here.
Can you fight unarmed, using primarily punches, and wear boxing gloves? Absolutely. In fact, Unarmed is among the stronger combat specializations in the game, though Boxing Gloves are somewhat weak specifically, because they cause only subdual damage - meaning they will knock your opponent over, but not kill them. Useful sometimes, but rarely.
Can you fight in a 'boxing match'? Well, not per se, however, there are two opportunities for you to engage in a sporting fight for some caps. The Thorn in westside is home to one such opportunity, where you'll have the opportunity to fight off various monsters of the Wasteland such as Radscorpions, Giant Mantises, Deathclaws and Cazadors. Any weapon is fair game in the Thorn, though you're welcome to go in unarmed if you're looking for a challenge.
Male (and only male, the legion are nothing if not chauvinistic) Players aligned with Caesar's Legion meanwhile, have the option to fight in The Arena, located at The Fort. In the Arena, the only weapons permitted are Machete's. All your other weapons are confiscated at the beginning of a match, and you are of course free to use your bare hands instead if you so desire.
I'm specializing in unarmed combat in Fallout NV and so far it's a riot. I've beaten supermutant with machine gun on level 7 with nothing but brass knucles and without breaking a sweat. First punch - gun flies away, second punch - crippled hand...
The trick is to have high strengh, endurance and luck (at least 7-8) - it all affects unarmed combat. You cannot target body parts in VATS, but you CAN target them without VATS. For example, guns aren't much use to your opponents after you cripple their hands. Someone comes after you with a melee weapon? Cripple or trip his legs and deal with shooters first. It's quite a different style of combat from shooting and it's definitely worth a try.
However, it's not much use against wild beasts. For example, a boxing match with a radscorpion is a bad idea.