[Ether]

Originally Posted by Alon

we built a table for speed-distance, plug it into excel and used polynomial regression...it is a little time consuming...
maybe someone did it with a different approach

You don't need to turn the table into a polynomial. You can use a lookup table, or a carefully-chosen piecewise-linear function.

i know some teams did it with physical calculation but i have always thought that air drag / ball spin (magnus effect) are really hard to predict and calculate.

Gathering empirical data for your specific shooter and using that data as you did is likely the most accurate approach.

maybe someone ...explain how?

Here's a paper for students interested in the physics, math, and computer simulation aspects of this problem: Free-body force diagram, derivation of differential equations of motion, and C pseudo-code for trapezoidal numerical integration.