When adjusting a string saddle and moving it back, making the string effectively longer, does that decrease the sharpness or increase it??
I assume you're talking about adjusting a guitar's intonation. You need to compare the pitch of the fretted note on the 12th fret with the harmonic on the 12th fret. If the fretted note is higher than the harmonic, this means that the distance between the saddle and the 12th fret of that string is too short, i.e. you need to move the saddle back such that that distance is increased. If the fretted note is too low, you obviously do the opposite.
For a given tension and thickness of string, making the string longer lowers the pitch. If your open string was in tune, but your 12th fret was flat, you would want to shorten the string or lengthen if the 12th fret was sharp.