Honestly, I think rust actually prevents a lot of logic problems, but it's hard to quantify and a subjective feeling that I'm not sure how I'd even go about trying to "prove". Order of magnitude I'd say 50% less logic bugs than a language like Java.

Why? Just good language design. Things like "enums" (algebraic data types, not C-enums) making for type checked state machines, really strict typing, immutability by default, simple language semantics, good linters that people actually use, the borrow checker actually does usually lend itself to good design too, and so on.