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Can I run a 30t cassette on a short cage 6770 derailleur?
Not officially, but in practice you often can. The specification is based on the worst case (smallest) separation of the dérailleur mounting hole from the axle and mounting face offset from the inside face of the dropout. It doesn't take much extra on either or both dimensions to make room for the upper pulley to be an extra 4mm away from the axle centre, which is all that's needed to clear the extra two teeth on the big sprocket.
You might have an issue with total capacity to take up chain slack if you also have the full 16T difference between chainrings.
gbj_tester
Thrasher
Can I run a 30t cassette on a short cage 6770 derailleur?