How does a neck brace work? I've done a bit of research but can't seem to find much information on how neck braces actually work to protect the neck. There are many views on whether they are actually effective in reducing serious injuries (in the same way it took a long time for ski snow board helmets to be proven). 

Neck Braces are a recommended safety item by the UCI for downhill events, unlike full face helmets which are mandatory, but all racers wear them.

What do they protect and how do they do that?
A neck brace limits range of motion to protect the neck and spine  

BikeProducts


  A neck brace restricts any extreme movement of your neck during a
  crash. In other words, it prevents your head from tilting too far
  forward, backward, or to the side, all of which can damage the spinal
  cord. A spinal cord injury can, at best, keep you off the bike for six
  to eight weeks or, at worst, put you in a wheelchair. Why take the
  risk of serious injury?


As for statistics Nascar instituted HANS like 13 years ago and they feel they have statistics that demonstrate that it is effective.
HANS
I get Nascar is not the same as a bicycle but once you protect the head the next thing you need to protect is the neck.