I wrote a program to simulate the beam pattern of a LED in a (SMO) paraboloid reflector, here's a screenshot for an S2+ (blue) and S2 (red) comparison.
It uses a ray tracing method and simulates about 50 million (depending on reflector size) rays to calculate the angular beam distribution.
You can see spot, corona and spill - just with a perfect parabola; for the deep S2 reflector the corona is nearly as wide as the spill.
And it shows an effect I didn't expect to be that strong: Deep reflectors reduce flux output (lumens) due to the higher fraction of reflected light and the reflexion losses (I calculated with a reflectivity of 85%).