How many games does it take for a position player/pitcher to have in their rookie season for them to become arbitration elgible after their third full year.

More specifically, I'm in the middle of year 15 and I want to push my #5 SP off of a ledge because he's terrible.  I have a 21 year old stud who's in his first year in AAA and he's throwing very well.  If I were to pull him up, would he be arbitration eligible after 2.5 years? or after 3.5 years?  If I do pull him up, I want to make sure that I get him for 3 full season in the bigs at the rookie salary rate.

Also, for a position player, is the number of games the same?  Does it differ from pitchers?