PITCHf/x release points are generally recorded at 50 feet. I say generally, because in the early years (2007-2009) they varied from 40-55 feet while they were trying to determine the best location. In late 2010, Mike Fast published an article arguing that 55 feet is more representative of true pitcher release points (every pitcher is a bit different in reality). Since then, it has become standard practice to renormalize all pitches to 55 feet to make analysis more consistent. The procedure to do this, while alluded to by Alan Nathan, is never really spelled out explicitly. That is what I aim to do here.
The procedure is fairly straightforward (and hence probably why it isn’t normally shown). The equations for the position of the ball at time t are (remember high school physics?):
The equations for the velocity of the ball at time t are the first derivative of the position, so:
Where is the release point as reported by PITCHf/x, is the initial velocity at that release point, and is the acceleration.
First, you need to calculate time t for when the ball was at 55 feet. Using the quadratic equation, you can derive t:
Now, using the equations above, you can calculate position and velocity at y = 55 feet.
Finally, to recalculate start_speed: