This is just a gripe about two differently bad ways to compare numbers. They share a good alternative.

“Order of magnitude” · Typically sloppy usages: “AI increases productivity by an order of magnitude”, “Revenue from recorded music is orders of magnitude smaller than back in the Eighties”.

Everyone reading this probably already knows that “order of magnitude” has a precise meeting: Multiply or divide by ten. But clearly, the people who write news stories and marketing spiels either don’t, or are consciously using the idioms to lie. In particular, they are trying to say “more than” or “less than” in a dramatic and impressive-sounding way.

Consider that first example. It is saying that AI delivers a ten-times gain in productivity. If they’d actually said “ten times” people would be more inclined to ask “What units?” and “How did you measure?” This phrase makes me think that its author is probably lying.

The second example is even more pernicious. Since “orders” is plural, they are claiming at least two orders of magnitude, i.e. that revenue is down by at least a factor of a hundred. The difference between two, three, and four orders of magnitude is huge! I’d probably argue that the phrase “orders of magnitude” should probably never be used. In this case, I highly doubt that the speaker has any data, and that they’re just trying to say that the revenue is down really a lot.

The solution is simple: Say “by a factor of ten” or “ten times as high” or “at least 100 times less.” Assuming your claim is valid, it will be easily understood; Almost everyone has a decent intuitive understanding of what a ten-times or hundred-times difference feels like.

“Percent” · What actually got me started reading this was reading a claim that some business’s “revenue increased by 250%.” Let’s see. If the revenue were one million and it increased by 10%, it’d be 1.1 million. If it increased by 100% it’d be two million. 200% is three million. So what they meant by 250% is that the revenue increased by a factor of 3.5. It is so much easier to understand “3.5 times” than 250%. Furthermore, I bet a lot of people intuitively feel that 250% means “2.5 times”, which is just wrong.

I think quoting percentages is clear and useful for values less than 100. There is nothing wrong with talking about a 20% increase or 75% decrease.

So, same solution: For percentages past 100, don’t use them, just say “by a factor of X”. Once again, people have an instant (and usually correct) gut feel for what a 3.5-times increase feels like.

“But English is a living language!” · Not just living, but also squirmy and slutty, open to both one-night stands and permanent relationships with neologisms no matter how ugly and imports from other dialects no matter how sketchy. Which is to say, there’s nothing I can do to keep “orders of magnitude” from being used to mean “really a lot”.

In fact, it’s only a problem when you’re trying to communicate a numeric difference. But that’s an important application of human language.

Perversely, I guess you could argue that these bad idioms are useful in helping you detect statements that are probably either ignorant or just lies. Anyhow, now you know that when I hear them, I hear patterns that make me inclined to disbelieve. And I bet I’m not the only one.