Dan,

That is an interesting and well-written piece attempting to correlate pitcher’s velocity with long-toss distance.

However, I think there are still issues to consider more deeply with regard to using Alan Nathan’s distance-velocity calculator for your purposes.

One of these is: Pitching velocities are almost exclusively measured as “peak velocity”, also called “release velocity”. Because of the decelerating effect of air resistance, a pitched ball that comes out of a pitcher’s hand with a peak velocity of 90 mph will only be traveling about 82 mph by the time it crosses home plate. So, the average velocity for that pitch would be (90 + 82)/2 = 86 mph.

Prof. Nathan’s calculator takes air resistance into account (otherwise it would give completely unrealistic answers for the real world) but, more importantly for the sake of this discussion, it gives an average velocity required for a ball, launched at a given angle, to travel a distance of interest.

Since pitchers’ velocities are measured at release it makes better sense to correlate long-toss release velocities with long-toss distance. As mentioned in your analysis the release angle and the spin rate do matter and so it would be very difficult to make a really accurate correlation that fits all pitchers.

However, on an individual basis it is possible to deduce a pitcher’s release velocity correlation with his long-toss distance. You just need to actually measure his release velocity with a radar gun and correlate that to the distance that he can long-toss.

There is a widely-held belief among coaches that a pitcher long-tossing with an optimal trajectory angle needs to release the ball at 90 mph to throw the ball 300 feet. From measurements I’ve made on individual throwers (on mild, windless days) I think that is a pretty good estimate.