Good and interesting test 

I'm pretty sure their algorithms just report the highest "velocity" recorded.

Altthough I don't know all the guts, in essense, the unit pulses a radio signal out, it reflects off the traveling object and then it receives a radio signal back. It then takes a Fourier transform of that (giving frequency) and whatever the highest/lowest frequency it sees, it reports back the shift from the initial frequency as the speed (converted to velocity of course). If the object is traveling toward you  the frequency shifts up, if it's going away, the frequency shifts down.  So, as long as it can detect something far enough away, it should just report the highest velocity "seen".

I'm not sure how it determines what amplitudes of signals to filter out (like noise or other weak radio signals), but that can cause issues.

The other thing that could potentially cause issues is the end of the sling itself. The geometrical problem that if something is moving at an angle away from the radar gun, if it goes fast enough, the velocity away from the radar gun could be fast enough to be the fastest thing picked up. I thought I wasn't having this problem, but the above graph makes me unsure at this point. I'm going to have to do some more testing.

One thing that I can determine is that if i'm 1 or 2 m behind the radar gun and sling over the top, It affects the speed by 1 or 2 m/s (seems to be about 1m/s per m at the beginning).

This data set is very similar to what I’ve experienced as well.
Tennis balls have very rapid decay in velocity.
And I get slightly higher readings in front of the radar compared to over the top .

Nicely done IG!
So the ball loses roughly half its energy over 35m.  Now I want to know what the velocity dependencies are.  Assuming the air resistance loss is a function of velocity, is there a sweet spot? Or just an asymptotic relationship with diminishing returns?

Science! 

great work!