I really wish people would stop saying N times smaller than something when making a comparison; that makes no sense - it's 1/9th (11.11%) the size. You don't get a smaller quantity by multiplying by a number greater than 1.0. You could instead reverse the subjects being compared - "the original model is 9x bigger than this new smaller, efficient model" or some such. That makes sense.

I keep seeing this being used when people talk about efficiency or performance gains and it's just very unintuitive language.

I agree it makes little sense in a literal mathematical take but "it's 9x smaller" or is too much of linguistic advantage compared to "the original is 9x larger" or "it's 1/9th as large" to expect a change with. You don't have to invoke fractions, it keeps the thing in focus as the first subject, it matches the pattern of the inverse statement, and it's just plain short... so that's what people will adapt and interpret the meaning to be.

One other way to map both types of linguistic statement consistently to math is to interpret "9x" as "there is a 9 times difference between these two things" and then "smaller"/"larger" tells you which end of that separation the subject is (rather than specifying whether the multiplication builds up or down).

If we were talking about speed instead of size, i think it would be perfectly reasonable to say 9x faster. I'm not sure I agree that 9x smaller is unintuitive. It makes sense to me.

Eh, when I read smaller with an integer multiplier, I mentally switch to the reciprocal. Easier than convincing the world not to use "9x smaller". Do you feel the same way about "9x faster"? What you're actually measuring is time, and "faster" is the reciprocal of time, similarly to "smaller" being the reciprocal of size.

Me too!! It's a huge pet peeve. And it's so hard to get people to see how it's linguistically AND mathematically WRONG.