Is there a way to quantify the effects of luck versus skill in rubber bridge?
As Eric Murray famously said in the case of Crown vs St. Clair Bridge Club: 


  "The game [rubber bridge] is only one of luck when played as the
  justices of the Ontario Superior Court play it in closed chambers."


That is of course the same Eric Murray of the Canadian partnership Murray &amp; Kehela that was widely ranked the third best in the world during the 1960's and early 1970's.

Ironically, the luck element reduces as the overall quality of the players improves, yet increases in importance because the qualitative differences between the various players is reduced even more.

This question is difficult to address because of the above point. However, consider this advice to the budding "play for money" bridge player: 


  Choose Chicago against players who are a little bit weaker than you;
  but choose Rubber against players a lot weaker than you.


The reason is that when your skill advantage is small, you want lots of points in play, so that the luck evens out faster. When your skill advantage is larger, you want more opportunity for the opponent to make foolish decisions. A typical rubber-bridge strategy is to sit on a part-score and collect penalties for several hands before converting the game. Then repeat. even if the opponents get "lucky" and win the rubber, they will often have lost much more in penalties than the rubber bonus was worth.