As far as I'm aware the skill works like this:
You kill a player of equal or greater skill -> Gives you large bonus to skill (for each kill)
You kill a player of less skill -> Gives you bonus but very little (each kill)
You get killed by a player with higher skill -> Gives you moderate reduction in skill (for each death)
You get killed by a player of lower skill than your own -> Gives very large reduction to skill (for each death)
If you happen to be killed by someone in a round who has terribly bad skill (hardcore is rife with this) then you will almost always have a rubbish game from a +/- skill, point of view.
I've had games where I get 20+ kills and between 1-3 deaths... yet still 0 or negative skill because the deaths were caused by a very low skill player. I have a funny feeling also that depending on whether or not its a knife, grenade, primary weapon or secondary weapon kill matters as well, and also if its a headshot or not.
The simple way to test is play a pistol only server - your skill rating is far more stable as the sill you gain from pistols seems to be higher - so combats the horrible penalty you get from deaths.
Its a simply idiotic way of calculating a players skill and it is an entirely meaningless stat - whats better is a combination of Score per minute and K/D. Why the "Skill" doesnt work out from the other stats - K/D, Accuracy, SPM, Win%, %Headshots etc etc... is totally beyond me.