Is there a way to use handicaps in chess to bridge the gap between players of different skill levels? Handicapping is routine in the Japanese game Go (my best game). The basic strength unit is one stone, and a one-stone difference represents a full level of difference in strength.

I (about a 1500 player) once asked a 2100 player how much of a handicap she would need to give me so that we would have an equal chance to win. "Probably a knight, maybe more," she answered. I once took a knight handicap against a 2200 player and lost, but it was a much tighter, closer game than one with no handicap.

That might suggest that a pawn is equivalent to about 200 points of rating. Apparently handicapping doesn't do much for say, a 50 point difference in strength (you just play and take your chances). But above that, there might be ways to use handicaps. Even giving someone the first move two times out of three (as was earlier done in professional Go) might do something.

Or would it? Why hasn't handicapping been done much formally in chess, as in Go?
Handicapping changes chess in a fundamental way that stones in go do not.  

In go, getting an extra stone is roughly equivalent to having an extra move.  In chess, losing a piece is catastrophic, and in a game between two players that are within ~300 rating points, losing a piece means loss of the game.  

One other reason that handicapping is not done this way is that while you (1500 player) might lose to a 2200 player (barely) without a knight, it is highly unlikely that a 2000 player would lose to a 2700 player at a tournament time control.  

Handicapping was done before rating systems became so prevalent.  In clubs, players would be said to be "knight players" meaning that they needed odds of a knight in order to give a stronger opponent a good game.  Similarly there were "pawn" players and "rook" players.

An easier handicap between two roughly equal opponents would be to give the weaker player white.  This is roughly equal to 25-40 rating points [1].  Another common handicap is for the stronger player to play "blindfolded", meaning that he or she cannot look at the board, but has to call out the moves in order to play.