First, we need to define what we mean by "this go problem is rated X." For this, I propose the following:
For a given threshold H% and number of seconds S, a go problem's level is the lowest (weakest) N for which H% of players rated N will recognize it and play the correct solution in their own games using time controls of zero main time and one period byo-yomi of S seconds (without playing tenuki forcing moves to gain thinking time).
For example, if we set H%=95% and and time controls to 10 secs/move blitz, then we get a definition of go problem levels more or less according to "internalized knowledge" -- for a problem to be rated 5-kyu, it would mean that 95% or more of all 5-kyu players will have internalized this pattern to such a degree they could immediately recognize and solve it within 10 seconds in their own game. Likewise, if we relax H% a bit and also set S to a more relaxed 2 minutes/move scheme, we'll get levels which correspond more to "patterns which a N-rated player will recognize as fishy and, in more cases than not, be able to find the correct play within 2 minutes."
Now, a rough sketch of what confidence means:
We all(?) have experience with being able to solve go problems that we would never be able to recognize or solve in a real game, simply because we wouldn't think to look for the solution. The case of having absolute confidence in your own ability to win is, I think, similar to the mindset when solving go problems: you know you can win and you know (feel) there is a "solution" to the current state of the game that gives you that win. That is, your mind is treating it basically as a life & death, tesuji, fuseki, yose, or generally just a whole-board middle-game problem. In this mindset you will use your time expediently until you find the solution and play it. You do not get intimidated and you reflect calmly on each new turn of the game. (Of course, if you repeatedly do not find the solution or play the wrong moves so you're put at a disadvantage, your confidence will of course drop and your confidence-boosted playing level drops with it.)
So, my rough proposal to how much can be gained from confidence:
A player's absolute confidence in her own ability in a game with time controls set to S secs/move can be estimated to a rating C, where C the highest (strongest) rating N of go problems (presented to her as go problems; e.g. in a book or on an internet site) that she is able to solve H% of the time within S seconds. (Perhaps given a deterrent for answering wrong, like being subtracted H for each wrong answer, while gaining 1 for each correct answer.)
For example, let's assume for a minute that 75% of all KGS-rated 1-dans would be able to "solve" a given set of patterns (go problems) with the correct play occuring in their own games with S secs/move. (And that less than 75% of the kyus on the same server could find the correct play given the same S.) Now, we take these patterns and present them as go problems in a book and give it to a person rated 3-kyu on KGS. Let her sit down and study them given S seconds per problem at which point she must answer immediately. If she is able to solve 75% or more of these problems, you could say her confidence is worth at least three stones.
The weaker the players the bigger the gap tends to be between go problems they are able to solve in a book and in their own games. These are also the players who tend to gain the most stones from confidence, as a player with confidence does not panic, does not get emotional (mad), and will refuse to be unduly submissive. Aggressiveness in such a player will also tend to be reasonable and not just wild blood thirst.
 I think it might be in the user info of someone on KGS actually. Can't remember who (anyone know?). It also sounds very much like a (Occidental) proverb to me, though I haven't seen it listed anywhere (should it be?).
 Or was it three?
 Can there be agreement on this definition? Should this be on a separate page? Is it already presented elsewhere?
 Assumption: all players are rated according to the same ladder.
 A.k.a the feeling of "I think Black can do something here....hmmmm"
 Of course, absolute confidence is probably never attained, but it could work as a statistical upper bound.