A Ball screw is not a simply supported beam at both ends so I don't think it's the right equation.
> I think it's [W*L^4/(384 EI)]: 5 times less than the above prediction.
A ball screw is more clamped at both ends or maybe in some cases clamped at one end (fixed bearing) and a hybrid at the other end (floating bearing). Nonetheless there are implied moments due to the bearing blocks which will reduce the deflection vs a simply supported case.