The optimal angle of Release in Shot Put

We determine the optimal angle of release in shot put. The simplest model - mostly used in textbooks - gives a value of $45^\circ$, while measurements of top athletes cluster around $37 - 38^\circ$. Including simply the height of the athlete the theory prediction goes down to about $42^\circ$ for typical parameters of top athletes. Taking further the correlations of the initial velocity of the shot, the angle of release and the height of release into account we predict values around $37 - 38^\circ$, which coincide perfectly with the measurements.