We train many variations of the barbell clean here at LOD. Powers, Hang Power, Hang Squat Clean, full olympic style clean, etc. We even shake up the training tool when doing it... barbell, kettlebells, sandbags.
The belief is that these lifts will help develop your bodies ability to generate power - defined as (force x velocity).
Hypothetically, if you train the clean and improve your numbers, you'll be able to jump higher, come off the starting line of a sprint more explosively, or drive an opponent off the line or into the mat.
The reality is that while you may become stronger with the exercise, it likely has a pretty marginal effect on your ability to create power.
Genetics plays such a large role in the bodies potential to generate power/explosiveness, your increases in likely due to improved competency in the technical aspects of the lift.
We're all born with a certain set of muscle fibers. Type I muscle fibers work long, hard, and efficiently, but don't contract quickly and therefore produce less force per contraction. Type II muscle fibers (divided into Type IIx and IIa) produce a powerful muscle contraction quickly and generate greater power. Lance Armstrong is mostly Type I, while Usain Bolt is mostly Type II. Each of us has a genetic makeup, when paired with the shape and form of our body, establishes an athletic potential ceiling.
While training can transfer the disposition of a individuals muscle fibers, it's limited. For the most part, you're born with a certain set of genetics that will dictate your performance with particular tasks.
If the ability to transfer olympic style lifts to real-life performance, why do we do it?
1. Durability: The ability to move a barbell through the air and catch it in a full or partial squat increases or ability to manage force - particularly in the catch. Your body learns how to absorb the load efficiently by aligning the joints in proper position and preparing the supporting musculature to absorb it. For athletes, this means you're likely to land from a jump safely, take a hit safely, or change direction safely. For most us, that means catching ourselves from tripping without tearing up the knee or compromising the lower back. Teaching joint alignment and force management is important to staying injury-free.
2. Coordination: Your entire body is involved in the triple extension (ankles, knees, hips) involved in the clean. This takes a level of coordination that is not experienced outside of sports. We want to train our body individual body parts to work as a whole, not as isolated limbs. Coordination is a perishable trait that can and should be improved through your life span.
3. It's Fun: For whatever reason, sticking a heavy clean feels damn good. We want to train all aspects of strength, but lets face it - squats and presses can get boring. Hitting a good clean just feels sexy.
The Division 1 football player who is the same size and height as me is probably going to have a bigger vertical jump than me, even if I clean more than him - but for most of us, that's not the point. We want to have fun with training and increase our ability to be durable and become stronger, faster, and better looking naked than we were the day before. Cleans are a important aspect to achieving that.