Percentage gotchas

I’ve been thinking a surprising amount about percentages recently. Bear with me. It’s more interesting than you might think.

Our work at SearchPilot requires a lot of discussions of percentages - not only measuring them, but also communicating them well, making our points clearly, and being easily understood.

It’s surprisingly hard.

Now, this is coming from a company who’s longest-ever slack thread was about how many significant figures to use in displaying dashboard data, so we may over-index on the geekiness factor, but I hope there is something of general interest. Because while our high school teachers were spectacularly wrong when they said “it’s not like you’re always going to be carrying a calculator in your pocket”, it’s nevertheless true that certain kinds of numeracy are critical to navigating and understanding the modern world.

I’d argue that comfort with percentages is a key part of that.

Here are some common mistakes and misconceptions that I see a lot:

1. A 10% decrease followed by a 10% increase doesn’t get you back to where you started. The easiest way to see this is that a 100% decrease means “decrease to zero” and no % increase from zero gets you back away from zero again. The wonkier version is that after you’ve decreased, you’ve got a smaller base, so the same percentage increase adds a smaller amount back on.

Real world impact: if you’ve seen a 10% drop, you need to more than 10% growth to get back to baseline.

2. You can’t average percentages. It’s essentially averaging averages, which you might remember is a big no-no. The easiest way to remember this is that the number of attempts really matters. If your blog gets 1m visits and converts at 0.1% (1,000 conversions) and your homepage gets 10,000 visits and a 5% conversion rate (500 conversions), the overall conversion rate is not 2.55% (the average of 5 and 0.1) but rather 0.15% (1,500/1,000,000)

Real world impact: always remember when you’re combining percentages to go back to the real numbers of things and re-run the percentage calculation.

3. The difference between “percentage change” and “percentage point change” is critical for communicating well. A percentage change is a change in a real world number while a percentage point change is a change in a percentage. For example, if you increased your homepage conversion rate in the previous example from 5% to 6% that’s a 1% PERCENTAGE POINT change in conversion rate, but a 20% increase in the percentage of visitors who convert. It is most likely that you want to talk about percentage point changes whenever you are talking about changes in rates - it gets confusing quickly to talk about the % change of a %. If you must do so, consider changing the sentence to talk about the % change to the underlying number.

Real world impact: really this is as simple as remembering to take great care whenever you are trying to communicate a change in a percentage.

4. Many people struggle to remember the formula - if something goes from 8 to 10, is that a 20% increase or a 25% increase? The way to remember this is that you’re talking about a CHANGE, and you always measure changes from the starting baseline. So in this example, it would be an increase of 2 compared to a starting point of 8. In other words this is a 25% increase.

5. It’s easy to get confused about large percentage changes: it’s not possible to decrease a number by more than 100%, and a 100% increase is a doubling. It’s tempting to think that a 200% increase means “doubled” but actually it’s 3x! The way to remember this is to think about the 100% example: I always find it reasonably easy to remember that a 100% increase is “add all of what we have on again” i.e. “double” and that leads quickly to remembering that a 200% increase is “adding on twice what we already have” — in other words “triple”

6. Finally — and this one is less common outside finance, but I thought it was worth mentioning because I don’t remember being taught it at school — is the definition of “basis point”. I would advise not using basis points unless writing for a highly-sophisticated financial audience - but you might come across them in financial journalism. There is a common misconception that a basis point is the same as a percentage point, but it’s not - it’s actually 100th of a percentage point. So, when you are talking about changes in percentages (see #3 above), a 100 basis point increase in a 5% figure is an increase of 1 percentage point (i.e. 5% —> 6%). You can describe this as a 1 percentage point increase, or a 20% increase in the percentage, or an increase of 100 basis points. You’ll commonly see this in changes in interest rates, where the central bank might increase rates by 0.25 percentage points or 25 basis points.

I think if I were to try to leave you with one mental trigger on how to communicate well with percentages, it would be: remember any time you are about to talk about a percentage change, or a change in a percentage, to think very carefully if you mean percent change, or percentage point change, and to sense-check back to the underlying whole numbers.

What other common misconceptions have you come across? How do you remember key facts?