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This is a feature request. Feature requests can be voted up by supporters.
Current Priority: +0
The letter rank next to a song name on the map selection screen is the letter rank of the highest-scoring play, not the highest letter rank obtained. Since letter ranks are not an increasing function of score, this can lead to strange behaviour. For example:

Here I have two As, but since the B has a higher score, the rank displayed over at the right shows B.

This might be intended behaviour, but I don't see how it's desirable. For instance, it's possible to decrease the displayed rank by beating your highest score while getting a lower rank.
http://i.imgur.com/EUvzTMx.jpg Put this into your [img] tag
Anyway, was reading what you wrote - The rank showing on song select, is ONLINE RANK achieved on that song, AND THE HIGHEST score. So for example:
You have made S offline, but you had B rank before - B rank will remain on difficulty select.
You made A rank with 128 combo, but B rank with 500 combo, - B rank will remain, because A rank had less score.
I understand that, but I think that behaviour is silly. (I can understand wanting to limit it to online scores, though.)
Why is it silly? It displays what your current online score is. I wouldn't want it to show an S when my online score is an A etc.
Online score: Obviously display the online rank. You will just confuse yourself when you see you get A online (in your Personal Best score) but S in the difficulty selection. (I also see that you agree with this.)

Local score: Try getting SS with some easy mod on. Now get S (or even A, if you have sufficiently high combo) without that easy mod. Which one do you prefer to be displayed? Although for same mod selections, I do agree that the better rank should be displayed.
Actually, at one time it was showing your highest rank letter, but that was apparently silly and it went away.

Letter grades really don't mean that much, it's easy to have a soft-S, where the play is so filled with slider breaks that a B or even C could beat it. If an S isn't good enough to stand up against a B play, then it really isn't worth more than one anyway... it's better that that S does get buried until a real S comes along. The local scoreboard is always there if you want a more complete view anyways.
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