Question: From so far away, what indications can we see in patterns of recorded of data that signals whether a supernova will form a white dwarf, neutron star, black hole or something else? Or do we think it is purely chance? If so, then does that still allow for an explanation?

Heather Campbell answered on 16 Nov 2014:

Whats left behind after a supernova (a core collapse supernovae) depends on how massive the star was which exploded. Smaller explosions leave behind neutron stars (dense balls of neutrons). This could be a spinning neutron star, called a pulsar.
If the core which is left behind after the explosion is more than 3 times the mass of the sun then it can over come neutron degeneracy forces, so it continues to collapse forming a black hole.
Type Ia supernovae (the ones which come from a white dwarf and a companion star) blow off all the material in the explosion and probably nothing is left afterwards.