Lani and I have been working hard on our Olympic lifting since the Strength Specific Seminar and I really feel it has paid off in big ways. For one I feel I have better control over my body and can exert a lot of force in gymnastic and kettlebell movements now.
CrossFit says your fitness is based on your competency in the 10 general physical skills being:
1. Cardiovascular/respiratory endurance - The ability of body systems to gather, process, and deliver oxygen.
2. Stamina - The ability of body systems to process, deliver, store, and utilize energy.
3. Strength - The ability of a muscular unit, or combination of muscular units, to apply force.
4. Flexibility - the ability to maximize the range of motion at a given joint.
5. Power - The ability of a muscular unit, or combination of muscular units, to apply maximum force in minimum time.
6. Speed - The ability to minimize the time cycle of a repeated movement.
7. Coordination - The ability to combine several distinct movement patterns into a singular distinct movement.
8. Agility - The ability to minimize transition time from one movement pattern to another.
9. Balance - The ability to control the placement of the bodies center of gravity in relation to its support base.
10. Accuracy - The ability to control movement in a given direction or at a given intensity.
Now the first two...Cardiovascular/respiratory endurance and Stamina may not play a lot of influence in a 1 rep max but believe me the following 8 general physical skills are completely involved in oly lifting especially the Snatch. No other movement you can find in life requires as much as this lift. Nothing but Strength, extreme amounts of Flexibility (If you think you are flexible just try an overhead squat), Power (huge range of motion in a extremely short time frame), Speed, Coordination (Moving something fast and heavy requires lots of cooperation between a lot of different muscles), Agility (All explosive power moving straight up only to transition to a squat in a matter of nano-seconds) Balance, and finally Accuracy (This movement you need to have an accuracy of millimeters to complete a heavy lift).
So in conclusion, if you want to improve your fitness you need to work on your Oly-lifting. Enjoy the PR's by Lani and I of 95 and 185 lbs respectively along with our misses at that weight.