# Calculating the variance in throws made by a juggling machine

I have built a juggling machine. It has no sensors and moves in a consistent programed motion. In my attempts to make the machine juggle for as long as possible, I have been studying the accuracy of the throws. The machine doesn't actively catch the ball, but instead relies on the accuracy of the throw to direct the ball to where the hand will be.

A continuous run of about 3,000 throws (half-an-hour) was recorded on video. Computer vision was used to track the balls in a region of interest before the catch.

I hypothesize that the accuracy of the throws is normally distributed. Eventually, the machine makes a bad throw and the ball is dropped (usually this is because the throw is long). I will attempt to improve upon my design, but before doing so I would like to measure the accuracy of this design for comparison.

I was able to generate this image. It is a composite image that shows all the throws (only for the region of interest):

To find the accuracy, I am trying to find the variance of the throw paths. How can I calculate the mean path? How can I calculate the distance of a particular path from the mean path?