Sparring and wrestling in the martial arts can get quite intense especially with novices who might rely on strength because lack of knowledge and technique. It can get quite competitive just for the sake of satisfying egos. The experienced martial artist should be past this stage but it may take years for most people to really understand that relaxation is the key to success.
People relate power with strength when it should be based on speed and technique, power being the by-product. We have to keep reminding ourselves POWER = MASS x ACCELERATION so it stands to reason the muscles must be relaxed to maximise speed, however, many of us already know this but fail to preach it.
Sparring and wrestling should be done at a 'slower pace so you can make conscious decisions' (thanks, Richard). This can give you a chance to learn and apply as many of your techniques whilst getting feedback from your opponent. You can get into 20 rounds and still get up and go to work the next day! I have never seen a professional boxer or kickboxer spar anything near as hard as they do in competition so it does not make much sense when students are just going all out. BJJ coach and friend, Steve Perceval made a very valid point about wrestling 'what's the point of doing competition if you are going to go that hard in class'? BJJ and full contact Karate can be a playground of frustration if the environment is too competitive. I have to keep reminding students there are no 1st place prizes.
To improve sparring (wrestling), relax and slow it down. World class experts recommend sparring/wrestling be done at a slower pace on a 'give and take' basis. John Will uses the 'half a bottle of scotch' theory before you wrestle. You will then have no choice but to be relaxed before a roll. However, I don't suggest anyone turn up to class smelling like a brewery. Remember, no one thinks big of you if you go fast!