Balls curve as a consequence of asymmetries in the resistance of the air through which they pass. - Robert Adair

The maximum Magnus force on a ball spinning at a rate of 1800 rpm is seen to be about one-third of the weight of the ball, so we cannot expect a ball spinning at that rate to curve more than one third of the distance it will fall under gravity.

Almost all of fluid dynamics follows from a differential equation called the Navier-Stokes equation. But this general equation has not, in practice, led to solutions of real problems of any complexity. In this sense, the curve of a baseball is not understood; the Navier-Stokes equation applied to a base ball has not been solved.

The American ash from which bats are made has an unusually high strength-to-weight ratio. Ash was celebrated in medieval times as the only proper wood from which to construct the lances of knights errant; an ash lance was light enough to carry and wield and strong enough to impale the opposition.