OK, let the clarification begin:
apjunkie is basically right about the biases he's listed; they are kinda generalized but nevertheless is right: speedballers tend to be non-believers, rec-ballers tend to believe to some degree, and the scenario gamers and backyard Tippman champs believe 100%.
As far as the military definition of the sniper goes, Cadet2005 is completely right, but no matter what people do the term sniper will always be used to label players who should, in reality be called marksmen. The only reason I use the term sniper is that it is widely recognized and associated with accurate shooting. Anyways, it isn't really possible to create these formula's, like you said, but instinct and training in snapshooting along with a little mental math can simulate this to the needed (IMO) extent, as headshots and extreme accuracy are only necessary in the real world.
Suprisingly the post I found most relevant was Coenen's, I think he's on to something, after all we have all seen someone call themselves a sniper (I have yet to see our area's sniper in action though, still too cold) but quite frankly most of the ones I've read about here seem kinda n00bish, like the backyard Tippman champs
, with their 21" barrels and "sniper scopes" i.e. a Crossman pellet rifle scope. Also his comment on speedball being prohibitive of sniping tactics is dead on, unless the game is all but won and it is becoming a mop-up operation.
Also I noticed a slight problem in your reasoning Cadet2005:
I can hide with a bright hunter's orange jacket just as well as with camouflage. It depends on how much movement you have to catch your opponent's attention.
Basic combat in woodlands also forces you to use camouflage (in fact, it is outlined in my ROTC manual), so does that make every soldier a sniper?
Basically the two quotes contradict, but when viewed individually make sense...BTW no offense is intended, I understand what you mean but it illustrates one of my points which was originally questioned, when you are hiding from people who want to light you up its best to err on the side of caution and have camoflage, just like it tells you in the manual for the most powerful Military in the world.
Anyways...I will update my definition again, check it out, maybe someday we will be able to get some agreement.