I came across this article on a website created by two US academics who teach a course on spotting fake news. No one is suggesting that Nestle is lying on the package – the statistic used is true, but it is also meaningless.

"99.9% caffeine-free," the packaging boasts. That night at the hotel, a 99.9% caffeine-free drink seemed like a good idea to me, a prudent alternative to an evening cup of coffee given that I was already chronologically disposed to stay up until bedtime three time zones to the west.

But pause and think about it for a minute. Caffeine is a really strong drug, after all. And there's a lot of mass in a cup of cocoa. Caffeine in coffee is not like sugar in coke, for example. So is a 99.9% caffeine-free drink really something you want to drink right before bed?

Let's figure it out. How much caffeine is in a cup of coffee? According to the Center for Science in the Public Interest, there are 415 milligrams of caffeine in a 20oz Starbucks coffee. (This turns out to be on the strong side relative to other drip coffees or milk-based espresso drinks.) That corresponds to about 21 mg of caffeine per ounce. An ounce of water weighs about 28 grams. Thus a Starbucks drip coffee is about 0.075% caffeine by weight. In other words, strong coffee is also 99.9% caffeine free!

While I don't have an exact figure for this brand of cocoa, most cocoas have about 20mg of caffeine in a 8 ounce cup, i.e., they're about 0.009% caffeine by weight. At first I thought that perhaps the 99.9% figure referred to the powder, not the finished drink. Given the figures about, the powder probably is close to 0.1% caffeine by weight. But Nestle's website makes it clear that they are referring to the prepared drink, not the powder: "With rich chocolate flavor and only 20 calories per single-serve packet, this cocoa makes a 99.9% caffeine-free, 8 fl oz serving."

Thus it seems to me that Nestle's packaging could list an extra decimal place: 99.99% caffeine free. So while there's nothing inaccurate or dangerous about the 99.9% assertion, it's a kind of silly thing to say and an even sillier thing for us to be reassured by. Most regular coffees could be labeled in the exact same way.

This blog is an edited extract of an article written by Carl Bergstrom and Jevin West from the University of Washington in Seattle: find the original article