Exactly

Probably some US colloquialism? Doesn't make sense to me either, except in the sense "went down 300%" which obviously wasn't the purpose here.

I dislike this common usage as well because of the weird properties it has too (if "decrease by two thirds" and "decrease by three" is the same, the "decrease by" function has a rather weird shape, also, 66% faster = 200% faster?), but at this point, seeing someone use the term the way I think is "correct" is the exception that I notice rather than the rule. This fight is lost. When speaking myself I tend to just use an unambiguous construct (e.g., "the code takes only 1/3rd as long to run") and let everybody else do their own thing. It's rare for it to be a real problem.

Honestly, doing any sort of math with percentages in particular is just silly and should be avoided. Schools try to teach an official interpretation of "56 + 34%", but it's clear it doesn't stick and the adult world uses it fairly inconsistently in general. (In specific cases it is used unambiguously, for example, the accounting world, but in general, it's very sloppy.)

Decreasing or increasing by a factor is mathematically cleaner than decreasing or increasing by a percent. To decrease by a percent the formula is (1 - 66/100)*x, to decrease by a factor of three the formula is x/3. It might not seem like a big difference, but the latter can make things a lot cleaner in long finance formulas.

no, decreasing by 3 is `a - 3`

decreasing by factor of 3 is `a / 3` or `a * 0.(3)` or `a * 33.(3)%` or `a - a * 66.6%`

edit: math is hard!

Do you have similar issues with the phrase "increased by 2x"?

Why the need to convert to percent?

Well, when you fold something you don't necessarily have to fold it in half.