Note also and importantly that the stick force at contact does have a strong relationship to the eccentric strength of the hamstrings. This is because the extension moment created about the knees via the quads etc must first be "checked" or slowed down prior to contract so that the player does not hyperextend the keen and cause injury. I suppose the cruciates are assisting the brain with some angular velocity information during this phase.

Therefore a strong quads group will only be as good as the hamstrings are to slow them down. If the hamstrings are weak then they will break earlier during the knee extension and the contact force will be less. Increase their eccentric strength and they can break later, thus permitting more power at contact. The message is: that without training any quads at all, but doing some "through-range" eccentric hamstring training, you can increase the contact force at you kick the ball. This of course assumes the individual is not already highly trained.

It is not really any different in concept to eccentric Wikipedia reference-linkrotator cuff (external rotators) strength in a throwing arm. The stronger they are (and the better the trunk follows through) the less likely you are to feel that you threw your humerus out of the shoulder joint along with the ball.