I am trying to understand what does what for jumping. So I'm putting out my understanding of what's going on. Feel free to correct me. (And thanks for taking the time to read this).
We're dealing with three things here:
1a) How much force is generated
1b) How quickly that generated force can be applied
2) How efficiently that force is transmitted to the ground
1a) is improved by barbells and plain getting stronger in the squat and deadlift for the lower body and bench press for the upper body.
1b) is improved with accommodating resistance, particularly bands, that ingrain acceleration in the lift, or just by lifting more explosively.
2) is increased by things that improve connective tissue quality, things that make the tendons less "squishy" or more resistant to leaking power by deformation. Is this the quality we measure when we talk about how reactive an athlete is?
People who excel at unilateral running jumps but who cannot bilateral standing jump very powerfully: these people are very reactive, i.e. they have "good" tendons/connective tissue that absorbs and transmits force well. But they usually don't have the muscle mass to generate the force quickly in the first place. So they benefit from taking running steps in order to get the energy that their connective tissue then very efficiently stores and transmits back and forth.
Power jumpers, on the other hand, can generate the necessary force themselves without having to run to do it. They have the muscle to do it and ideally have the ability to generate that force quickly as well. BUT if their tendons are "low quality", a lot of that force will be lost. A power jumper benefits when their tendons conduct energy well like a taut string versus a slack one. Right? A lot of power could be generated by large muscles, but then lost by slack connective tissue.
So someone who has increased their squat (and to a lesser degree deadlift) strength a lot may not see as much increase in jump height as you'd initially think because squatting alone doesn't train tendons to be more efficient conductors. That's a large part of what various reactive and shock drills do...?
A high jump requires a good amount of energy on the descent and then not losing that energy on the turnaround, generating more energy during the ascent, and losing as little of that accumulated energy as possible in the deformation of connective tissue before the bones in the feet have a chance to transmit it to the ground.
Pure ability to generate force quickly is demonstrated by the paused jump or a jump from sitting. From what I understand, the rate at which force can be developed has low trainability, somewhere around 5%. Increasing the amount of force you can apply in a small unit of time is much more trainable than trying to apply the same force in a smaller window of time. In short, you're better off getting your squat from 155 to 455 than you are trying to apply 45 lbs of force in 0.4 second instead of 0.6.
So a SVJ benefits more from squat strength increasing. Same with Bilateral RVJ, though reactivity training would help this jump get a bit farther away from the base SVJ than it would naturally be.
Reactivity training would also benefit the countermovement SVJ, however, because that countermovement helps only as much as the connective tissue can efficiently store and transmit the energy provided by the countermovement.
So a 3xBW Olympic style squatter may be able to jump fairly high from sheer strength, but his countermovement jump may not be much better than his paused/from seated jump. Improving reactive strength would benefit both, but maybe for slightly different reasons? The paused VJ because the lower leg becomes better conductors; the CMJ (and running bilateral VJ) because the entire lower body connective structure is more efficient at transmission.
Again, thanks for reading all this. Your corrections will help me design my own training better.