When you throw a punch, will the opponent move straight in or back to block, or will they just cover up and cower? What is the formula for computing this? How does one quantify one's heart and fighting spirit that may vary depending on situation or emotional state at the time?
Doesn't one's spirit affect one's level of commitment in sparring/combat, and thus affect not only the choice of move, but the power put behind it? Is the opponent passive or aggressive and how does this affect one's action/reaction?
Judgement and reading the opponent is based on a variety of experiences and even more interpretations of them. After extensive studies (psychological and mathematical) a statistical model may be drawn for a large sample, but will not be reliable for any single person at any given time.
I have seen people with terrible form and inefficient body mechanics, but would be fearsome opponents as they were bat sh*t crazy. Science can explain the transmission of electro-chemical impulses in the brain, but cannot explain how or the method one uses their free will to express or execute their thoughts and actions.
The bottom line is that math can explain the physical mechanics of individual body movements and their optimum effects under a given set of criteria, but not how they are used or how one's spiritual bearing will affect them. IMO, these are variables outside the realm of physics. To think karate (and other MA) can be reduced to simple body mechanics has a very limited understanding of MA, combat, and life in general.