As a martial artist/combat athlete the most important thing you can do to improve yourself as a fighter is actual fight training: technique drills, partner drills (like pad work and feeding), scenario drills, heavybag work, shadowboxing/kata, and (of course) sparring and competition.
However, you also need to pay special attention to your strength and conditioning levels if you really want to be your best.
All other things being equal the stronger and better conditioned fighter will win every time.
Obviously, there are a lot of opinions floating around out there as to what strength training and conditioning program is best.
Personally, I like to keep things simple.
I stick with a few basic strength moves to build full body strength and power and throw in some simple conditioning drills at the end of normal martial skills session. Bam! Your done.
If you really want a more in-depth discussion on strength training and conditioning for combat athletes you should really check out Ross Enamait's site. He's got some really great resources available. Two in particular I like are:
Strength Training For Fighters
Don't Confuse Strength With Conditioning!
Ross has great stuff. You could get lost on his site for hours.
Strength Training Posts -
4 Barbell Drills Every Fighter Needs!
Build Elite Levels of Strength and Power with No Equipment!
Speed-Strength For Fighters!
Deadlifting for MMA
Conditioning Posts -
High Intensity Interval Training (HIIT) For Fighters!
A Snatch Variation for Fighting Power!
Tabata Protocol for Martial Artists
Frank Shamrock's MMA Kettlebell Circuits!
The Unilateral Complex for Elite Conditioning!
Don't Rest...Do SOMETHING!
Train Hard,
Josh Skinner
