Scaling the 16-inch/50 into a 15-inch naval gun

What would the ballistics and penetration of a 15-inch/50 derived from a 16-inch/50 look like?

Probably not radically different, although retaining more barrel length as a 15-inch/51 or /53 could produce a more interesting performance change.

A 15-inch/50 scaled from a 16-inch/50 would have broadly similar ballistic and penetration behavior rather than a dramatic change. Keeping the same calibre ratio shortens the physical barrel, which opens the option of retaining more length and describing the weapon as a 15-inch/51 or 15-inch/53. That longer form could produce the more interesting ballistic difference the question is seeking. Elswick had explored an even larger 16.5-inch/48 concept around 1913-14, placing the thought experiment within real prewar gun experimentation.