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.
Contributions
Comment feed for ongoing:
From: Paul Clapham (May 30 2025, at 16:43)
My Grade 6 teacher, many decades ago, impressed upon me that "two times as much as ..." meant multiplying the original value by 2, but "two times more than ..." meant multiplying by 3. Which made total sense to me as his best math student.
But nobody has paid any attention to that rule for decades either. Basically the two versions are synonyms now for most cases. Except for percentages less than 100; "10% as much" still means a much smaller number whereas "10% more than" means a little bit larger number.
So yeah, if you ignore my Grade 6 teacher's rule (which everybody does these days) then it makes percentages over 100 look confusing because you don't ignore his rule when you're talking about percentages.
In other words I don't feel that it is much easier to understand “3.5 times” than 250%. Instead, I have to remind myself that "increasing by 3.5 times" actually means "increasing by 2.5 times" to everybody these days.
So I agree with you that it's confusing. I just have a different reason why it's confusing.
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From: Ed Davies (May 31 2025, at 01:48)
Then there're “exponential” increases. Yes, an increase of 0.000001%/year, assuming the percentage is of the value that year, is an exponential increase but probably not what people usually mean.
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From: Robert Sayre (May 31 2025, at 10:05)
None other than Brian W. Kernighan wrote a book on this one.
"Millions, Billions, Zillions: Defending Yourself in a World of Too Many Numbers"
Subtitle: An essential guide to recognizing bogus numbers and misleading data
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From: sean (May 31 2025, at 11:51)
Preach!
Orders of magnitude are useful in the right context -- usually when someone would otherwise say "a factor of ten to the nth" -- but general writers shouldn't be allowed anywhere near them. I'm with you on percentages for differences less than 100%, and factors otherwise.
The one that really gets me is using relative versus absolute values in misleading ways. "Elon Musk slashed $100 MILLION from the federal budget" sounds like a lot, until you put it in context and see that it's basically nothing compared to the budget or GDP. "MumbleAI's" profits grew by a factor of five" sounds really good until you see that they went from making $1 to $5 on $400m revenue. When in doubt, include both, e.g. "quarterly revenue grew by $15m (or 3%) year-over-year."
PS- A personal pet peeve is using "decimate" to mean "utterly destroy," when it originally meant "reduce by a tenth." But that's just pedantry...
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