Course Handicap = Handicap Index * (Slope / 113)
we get for the 16.5 hcp index player:
16.5*(139/113) = 20.296
16.5*(135/113) = 19.71
Which both rounded to 20 course hcp, which then feels counter-intuitive as there is no "reward" from the more difficult tee...
However, as everyone explained above, it's the course differential that matters (though see below, matters for what? for the handicap index?). The formulae for which is (113/SR)*(Adj Gross - CR), which in the case of the above player scoring 93 from both of these tees, the differentials will be respectively:
(113/139)*(93-73) = 16.3
(113/135)*(93-69.8) = 19.4
Hence, the player certainly played better from the white tees 
The only question I then have left, what was the relevance of the course handicap for the player? Is it for the purposes of the competition only(ignoring the playing handicap for the moment)?
From the competition point of view, the player receiving 20 shots would benefit from playing from the yellow tee, as they would've scored:
white: 93-20 = 73 which equals the course rating?
yellow: 93-20 =73 which is 3 shots above the course rating?
Or should I be comparing this to Par which is 72 from both tees and therefore the player scored the same for the purpose of the competition?
Would the following be a reasonable conclusion:
-- If given the same number of shots from the longer/shorter tees, for the handicap index purposes it's better play the longer tees (higher course rating)
-- If playing in a competition, provided the par is the same from both tees, it's better to play from the shorter (easier) tee?
PS While I like computers doing the job of all these calculations and being able to submit a round from anywhere and get the immediate hcp index update, it does look soooo complicated compared to the good old hcp/CSS/buffer...
