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It's very helpful to frame the importance of an issue with numbers. If you're concerned about the climate, very good questions to ask include "What is the relationship between CO2 in the atmosphere and global temperature?" and then "How much CO2 is being emitted? By whom? And where?" If you're sounding the alarm about low growth, it's very helpful to measure that growth, and to do the same kind of attribution modeling—how much of it is driven by low investment (a problem in the UK), how much is low productivity growth (a problem just about everywhere since the early 1970s, albeit with some bright spots), and how much is from shifting demographics (from the start of the 1990s through last year, Japanese economic growth was precisely equal to US economic growth once both are adjusted for labor force size, hours worked, and price levels ($, Diff)).

Sticking numbers on claims is prestigious. "$11.23bn" sounds more authoritative than "a lot of money," even if, depending on the context, "a lot of money" or some other qualitative claim might be more descriptive. (If we're talking the cost of, say, building a new 3nm fab, $11.23bn is "surprisingly little" since the usual sticker price is $15-20bn.) The popularity of statistical arguments has led to an incredibly frustrating phenomenon that I like to think of as decorative statistics, where the point is to cite a number as an argument rather than to actually quantify the matter at hand.

Examples abound:

• The Verge once wrote a piece on the scourge of e-waste, which amounts to 9 million metric tons per year (Edit: originally this said “billion,” not “million,” though the rest of the math is correct. Poetic justice that I’d have an off-by-orders-of-magnitude error here). There are roughly 2.1bn households worldwide, so this is a bit less than three ounces per household per week, i.e. not something you'd ever actually notice when you're taking out the trash. Similarly, the article cites $9.5bn in potentially-recyclable materials that are discarded each year. So the financial burden is $4.52/household/year. Citing aggregate numbers does indicate the full scope of the problem, but the problem gets addressed at an individual level—even if there's a mandate to recycle, that mandate can only be implemented through the corvée labor of mildly inconveniencing everyone on earth. It seems more convenient and cost-effective to just mine a little bit more of these materials, and we'll know that isn't true when private companies are paying enough for used vapes that consumers recycle them on their own.

• The other day I had a layover in Phoenix, where a poster informed me that the amount of plastic waste dumped in the ocean each year is enough material "to build a sidewalk between Phoenix and the Grand Canyon 13,685 times." Which is a striking image, but if you try to visualize it you'll realize that you're being told one dimension of a three-dimensional object. Is "a sidewalk" four inches thick? Is it a millimeter thick? Is it a molecule wide? The phrasing is evocative, but anyone who feels more informed after reading that has made a mistake.

• It's sometimes popular to cite (generally stale) estimates of how much water a single interaction with an AI product consumes, like this piece pegging the number at as high as an ounce and a half per prompt. But all industrial water usage is about 1/8th the total amount used in irrigation, so this is a classic high-growth-off-a-low-base phenomenon. AI's water consumption might be material at some point, but if it's ever a big problem we can just tax almonds until they're a luxury product and end up ahead.

• Yesterday, Rep Ro Khanna claimed that health insurers made $1.39tr in profit last year, highlighting the need for Medicare for All. To his credit, he posted a correction a few hours later, noting that the actual number is about 5% of that. But he did not add that, as a consequence of this new information, the case for Medicare for All was now 95% weaker.

What all of these have in common is that the arguments don't really change much if the numbers are wildly different. Cut any of these problems by an order of magnitude, or increase them by that much, and you get basically the same emotional impact—and you get a quotable soundbite that gives the impression of being well-informed even if it doesn't actually contain useful information. Would anyone say "plastic waste has gotten so low that with the amount of plastic dumped in the ocean each year could only build a sidewalk between Phoenix and the Grand Canyon 1,369 times?" That would be a massive improvement, at least if the measurement standard were the same, but it doesn't sound any different.

And that provides a good pair of rules of thumb for these kinds of statistics. Any time someone cites a very impressive quantity like this, it's a good idea to ask questions like: what's the nearest relevant comparison? What else is true if that is true (for example, if health insurance really makes $1.4tr in profit, you can Google and find that health insurers tend to report single-digit profit margins, which implies that their revenue is about equal to total GDP). You can also ask how plausible it sounds to multiply the number by ten, or divide it by ten, or if that doesn't actually seem to change anything at all.

People decorate their claims with statistics for the same reason they apply any other kind of decoration: it looks nice, and it can make something otherwise plain feel evocative. But numbers are special: the viral-but-pointless ones are always in competition with the significant ones, and in the end policy still has to add up.

Read More in The Diff

The Diff aims to use numbers to discover the truth rather than to defend presumptions, but we’ve covered this kind of thing from a few directions:

• We’ve looked at a research report whose fundamental metrics don’t make much sense, but whose incentives certainly do ($).

• Are developing market conglomerates a form of measurement error ($)?

• Some companies can do very well by knowing exactly what to measure ($).

We’ve also looked at trades that perfectly versus imperfectly capture what they’re trying to bet on.

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1  The post does another nice rhetorical trick: "It is absurd that Big Insurance is raking in trillions while Americans are pinching pennies to afford treatment." A good way to distort scale is to compare the size of an aggregated unpopular group to the scope of problems that individuals face—the right-flavored version of this is to cite tiny research grants that are of a sufficiently small scope that people can compare them to their house or their annual salary. The relevant comparison is to take a per capita number and acknowledge that no amount of eliminating grants for studying the effects of narcotics on insects is actually going to affect the taxes people pay, but that doesn't play as well with the base.