I feel that the metric to measure "rank" and "tsumego rank" is not derived in the same way, so it's kind of difficult to compare.
Your "rank" in go is based on when you win games. Various ways are proposed to do this, but if you have a consistent mechanism, you can have some accurate predictions on who will win what games.
Problems feel different to me. I think problem "ranks" are given based on a pre-existing go rank. So if you are 1d because you win against 1ds, then you solve this problem that another 1k can't solve and a 2d can solve... maybe someone will call that problem a 1d problem.
But it's not really a fair way to measure problems:
1.) There may be a certain shape a 5k has seen that a 1d has not seen, and the 5k happens to know the correct answer.
2.) Less directly, a given 5k may be more familiar with a certain type of problem that another 1d is not.
3.) If you have someone that is 1d in go... maybe he's 1d because he is good at fighting and he can out-read others. Another 1d in go may suck at fighting but may be pretty good at positional judgment. It'd be likely that a more difficult reading problem can be solved by the first person than the second. So in that case... What's the rank of the problem?
I feel that the "rank" for a problem is simply a reflection of the ranks of the players that solve those problems. So you could say that your tsumego rank is a function F where F(X, Y, Z, ...) takes, as input, the ability for player X, player Y, player Z, ..., to solve the problem in a given amount of time. How else do you get a "grade" for the problem?
With this mindset, I think that it comes down to this:
Given that I am rank X in go based on my ability to beat other players of various ranks, my strength in reading localized problems is greater/lesser than average.
To give an analogy, let's say you are filling a cup with 100mL of liquids. You could fill it with water or with milk or with coffee. Maybe some person fills their cup entirely with water, and another fills 43% water, 17% milk, and 40% coffee. Both people have 100mL of liquid, but one guy has more coffee. Either way, it all contributes to your volume of liquid. To bring it back to go, maybe some 1d have that skill based 30% on reading, 20% on joseki, and 50% on good looks that psych out the opponent. And maybe others are more like 80% reading and 20% fuseki. Both 1d are still 1d.
This is all theoretically speaking now. Practically speaking, how do we measure that someone has a skill of 30% reading vs. 50% reading? I don't think it's possible. The only measurement we have is the ability to win games. And how you do that... Well, that's complicated.
