A lot of how you program depends on how many hours a week you're able to train. If you're fighting 10hrs a week, and have access to another 10hrs for supplementary training (strength, cardio, efficiency, explosiveness), then you can afford to spend more time dedicated to heavy weight training. If you're fighting 4hrs a week and struggle to hit that, then don't spend any time doing anything but fighting.
Originally Posted by Mike Short
So if I'm understanding you correctly though, organizing my supplementary work should include power cleans, pull ups, maybe some deadlifting, and core work (and of course crossfit to help with metcon)? But what about bench press, shoulder press? Unnecessary? Or do the CrossFit WoDs take care of these areas?
Whether your WOD's take care of chest and shoulder strength is dependent upon your specific WOD programming.
Don't take me wrong, bench and especially press are important for fighters. Shoulder strength for striking, pectoral strength for creating distance between grappling bodies or elevating off the mat (think of pushing up off of a guy when in his guard).
My main point is about the problem with how most of the popular strength programs are structured. By and large, they are low rep, high weight, which doesn't help you keep your gloves up after 12min of fighting.
It's great for fighters to have high strength, but having a big gas tank is far more important. So you need to train both. Don't focus on going so heavy that you never go long (i.e. SS, PP, GSLP, Outlaw, 5/3/1). Handle your bodyweight a lot, whether it's your literal body, or your bodyweight on a bar. Oly lifts, with very deep catches driving up out of the hole are fantastic (think of dropping elevation and driving off the mat for takedowns).
Core strength is critical.