zermelo wrote:when you approach perfect play, ratio (difference in winning %) / (difference measured as handicap stones) goes to infinity
Actually I think there is more to this. We like to measure strength with a single number for simplicity. But instead of "- stones" (extra stones needed for 50% winrate against perfect play) let's use "- points" (points dropped on average during a game, roughly the extra komi needed for 50% winrate - may loosely correspond to stones when divided by ~14).
And add a variance/deviation factor. So perfect play is "0,0" (drops 0 points with no variance). The "-1 stones" player is, say "-15,10". So he sometimes drops only 5 points instead of 15, which would increase his winrate elsewhere. But against perfect play -5 is still loss. He also loses the chance to play significantly above his average. However, a similar thing can happen at much weaker levels, if we imagine an opponent with no variance, such as "-100,0" (a very special amateur dan?

).
Half joke OC, although variance can explain some subtleties, there are limits for how well results in even games can be translated to handicap stones. Also points dropped against perfect play may not correspond well to points dropped against weaker opponents.