CrossFit defines strength as the productive application of force.
Here are two scenarios that helps explain this definition and gives examples of what coach means by the productive application of force.
Imagine we have an athlete that trains legs on a leg press machine. The leg press machine is a staple of your classic body builder and can be found in most globo gyms. The leg press requires an athlete to be in a sitting position and then press weight away from the athletes body using only their legs. The weights move along guide rails, only allowing the weight to move in one direction. Every Leg day this athlete jumps on the leg press machine, loads up the weights and smashes out sets. This athlete has extremely large quadriceps muscles and can leg press 300kg. The contractile potential of his muscles is huge and looking at him, he is a tower of strength.
Then we have a second athlete that trains legs by front squatting a barbell, a typical Olympic weightlifting movement that helps build strength in the clean. A front squat requires an athlete to hold weight at the front of their body, squat hips below knees and return to a standing position. The weight can then shift forward or backward if the athlete does not have the core strength to maintain upright position in the squat. This second athlete can front squat 150kg
Now if we take the front squat guy and put him on the leg press machine and he pushes out a 200kg leg press, pretty good nothing really amazing but not bad. Then we take the leg press guy put him under a barbel and he can not even squat. He can not get his hips below his knees, he can not hold the bar in a front rack position. Even with an empty barbell he can not get 1 rep and his score in a competition would be 0kg because his ability to squat is none existent. The leg press guy does not have the productive application of force, because he has only trained on the leg press machine he has terrible mobility, his balance is way off and he does not have the ability to apply force from a squat.
In this scenario, with this movement the athlete that trains the front squat is stronger, because he has greater productive application of force.
The second scenario
We have an athlete attending a CrossFit gymnastics skill session.
She has been training CrossFit for a few years and is extremely strong. She can complete 15 strict Pull Ups and 15 strict Dips. She has the strength to complete a Muscle up but has never been taught how to. She attempts a muscle up and is no where near it. She then spends 30 minutes with the gymnastics instructor practicing her kip, her hip drive and learning to push down on the bar. After 30 minutes of practice she gets her first muscle up!!!!!!!!!
Did she get stronger???
Well her productive application of force increased. Her Muscle contractile potential did not, definitely not in a 30 minute session. But her ability to move weight improved by increasing her skill in the movement. So defining strength as the productive application of force, she definitely got stronger.
Strength has an overlap of technique, mobility and muscle contraction potential. Anyone that has attempted an overhead squat would understand this definition. In our training the movements we use must improve our productive application of force. This is why you will not see a leg press machine or why we will not do bycep curls or lateral raises. These movements do not improve the productive application of force apart from conducting that individual movement. Our strength training must use functional movements, that is movements that replicate every day life or transfer to everyday life and will improve our overall productive application of force.