Nebulous Percentage Shenanigans

Posted on Sat 15 October 2022 in blog • 8 min read

Surely you’ve seen a question similar to the following in a survey or request for feedback.

How likely is it that you’ll recommend X to a colleague or friend?

In this question, X is either a product or service, or a brand, or all of a company’s products or services. Answers are given on a scale of 0 to 10, with 0 being “not at all likely” and 10 being “extremely likely”. It is frequently the last question in a survey, or even the only one.

The reason this question is so frequent is that it drives a metric that is popular with marketingfolk and management: the net promoter score, or NPS.

To work out the NPS, what you do is deduct the percentage of “detractors” of your product from that of the “promoters”. If the net result is above zero, per the lore, you are generally doing well. If you hit above 30, your product or service or brand or company is allegedly performing excellently.

What’s a promoter? What’s a detractor?

Now, what defines your promoters and detractors, according to the NPS metric? Clearly we’ll have to slot the possible responses into categories.

And here’s where you’ll notice something peculiar about the scale. It consists of discrete values going from 0 to 10 inclusive, not from 0 to 9 or 1 to 10. That means it’s an 11-point scale. What do we notice about the number 11? Exactly, it’s prime. It’s thus impossible to sort the scale items into evenly sized categories, no matter how many or few.

But okay, let’s say it’s not a law that the categories need to be evenly sized. So you might think that answering anything from 0 to 3 makes someone a “detractor”, and anything between 7 and 10 a “promoter”, with the middle ground (4 to 6) being somewhat neutral.

But that’s not what NPS uses. The actual NPS scale looks like this:

  • 0 to 6: detractor
  • 7 to 8: “passive”
  • 9 to 10: promoter

Now, recall that NPS ignores the “passive” respondents altogether, and only looks at the percentage of “promoters” minus that of “detractors”. If a majority of respondents answer 7 or 8 (intuitively a solidly positive score, if you ask me), those do not factor into the result at all. Only being inclined to rather enthusiasically recommend a product or service makes you a promoter. And answering 6, clearly north of the scale’s middle mark, makes you a detractor.

Obviously, this oddly warped scale in combination with ignoring part of the sample altogether makes the deduction of one percentage from another rather agony-inducing for any secondary school maths teacher. That’s eminently not how these things work; on its face it’s one of those results that Wolfgang Pauli would have called “not only not right, but not even wrong.”

Would you recommend a rental car company to someone who doesn’t need a rental car?

But in addition to a warped scale and off-label use of percentages, NPS also uses an inherently biased premise.

Suppose I rent a car from a fictitious company we’ll call My Local Public Transit Sucks, or MyLoPTS. And after I return my vehicle, I am asked how likely I am to recommend renting a car from MyLoPTS to “a friend,” which I would presume to mean any randomly selected one of my friends.

Now I would not recommend any rental car company to someone I know to not be in need of a rental car. And I would assume that a maximum of 10% of my friends, acquaintances, and colleagues are in need of a rental car at any one time (considering that my locally available public transport very much does not suck, so the demand for rental cars is quite low). So even if I was certain to recommend MyLoPTS to anyone needing a rental car, the correct answer for the question as asked — the likelihood of recommending MyLoPTS to a friend, regardless of circumstances — on a scale of 1 to 10 would be 1. My answer to the question as stated thus has little to no relation to how happy I am with MyLoPTS’ service.

So, it’s a misguided question with a warped scale that makes implicit assumptions and then does creative maths with the result. Why do so many people believe that this makes any sense?

Greetings from Harvard

The answer, apparently, is in a single article in the Harvard Business Review. That article will be old enough to drink in two years’ time in its USian habitat, so whether its 2003 findings are still valid in 2022 is debatable. But let’s assume for the time being that they are.

On the subject of the scale in question, here’s a quote from that article:

[We] settled on a scale where ten means “extremely likely” to recommend, five means neutral, and zero means “not at all likely.” When we examined customer referral and repurchase behaviors along this scale, we found three logical clusters. “Promoters,” the customers with the highest rates of repurchase and referral, gave ratings of nine or ten to the question. The “passively satisfied” logged a seven or an eight, and “detractors” scored from zero to six.

— Frederick F. Reichheld, The One Number You Need to Grow, Harvard Business Review (2003)

So, this confirms that the scale itself isn’t meant to be warped by default. Anything under 5 means unlikely to recommend, 5 is neutral, and anything above 5 is likely to recommend. (Since the respondents would presumably be required to select discrete values, that fact still warps the scale and places the “neutral” value off-centre — but let’s assume the creators of the scale did think of it as a continuum, which does not have this problem.)

Rather than being baked into the scale from the get-go, the categorization into “promoters” comes from an actual correlation of responses to repurchase and referral behavior. Or at least the article claims so — the research data it’s based on does not appear to be publicly available. We can only assume that similar correlations with actual customer behavior were drawn for the “passively satisfied” and “detractor” categories, though I am not quite sure how they would have identified the former, separating them from promoters. I suppose a “passively satisfied” person could perhaps have been one that did come back to make another purchase, but never made a referral? It would be interesting to see how they tracked that in 2003.

At any rate, the HBR article then asserts that NPS was a predictor of company growth when comparing to its competition: in other words, that companies with a higher NPS than their competitors also experienced higher revenue growth than them — across multiple industries (the article specifically mentions airlines, ISPs, and rental car companies).

The article also says this:

The “would recommend” question wasn’t the best predictor of growth in every case. In a few situations, it was simply irrelevant. In database software or computer systems, for instance, senior executives select vendors, and top managers typically didn’t appear on the public e-mail lists we used to sample customers. Asking users of the system whether they would recommend the system to a friend or colleague seemed a little abstract, as they had no choice in the matter. […]

Not surprisingly, “would recommend” also didn’t predict relative growth in industries dominated by monopolies and near monopolies, where consumers have little choice. For example, in the local telephone and cable TV businesses, population growth and economic expansion in the region determine growth rates, not how well customers are treated by their suppliers.

— Frederick F. Reichheld, The One Number You Need to Grow, Harvard Business Review (2003)

That sounds quite reasonable. Obviously, recommending a product to a friend or colleague doesn’t help the company selling it, if the friend or colleague has no say in the purchase decision.

Cultural bias, and Goodhart et al.

But there’s another thing that the article doesn’t say, apparently because it’s obviously implied: all companies covered in the research, and presumably the vast majority of the customers surveyed, were from the United States.

It’s rather well understood that scales are read differently by people from different cultures. So while the correlation of a certain response score with a certain behaviour is likely to work fine when you’re surveying U.S. customers of U.S. companies, it’s likely to fall apart when you’re trying to make similar predictions from answers from non-U.S. respondents, or to compare responses internationally.

Note further that the article describes NPS as a predictor of growth, meaning the underlying conditions that cause a company to have a high NPS also give it a competitive advantage and thus facilitate growth. Trying to tweak the measure itself — for example, by coaching people to respond 9 or 10 when they would intuitively select 7 or 8 — is a great example of collapsing a statistical regularity by placing pressure on it for control purposes, i.e. Goodhart’s Law.

And, of course, NPS is subject to Campbell’s Law as much as any other metric. When a score becomes the goal of a process, it both loses its value as an indicator, and distorts the process itself in undesirable ways. You could argue that this effect of NPS is a regrettable, but natural aftereffect of its enduring popularity over nearly 20 years — but no, it’s right there in the same HBR article:

Branch scores were not improving quickly enough, and a big gap continued to separate the worst- and best-performing regions. […] So the management team decided that field managers would not be eligible for promotion unless their branch or group of branches matched or exceeded the company’s average scores. That’s a pretty radical idea when you think about it: giving customers, in effect, veto power over managerial pay raises and promotions.

— Frederick F. Reichheld, The One Number You Need to Grow, Harvard Business Review (2003)

“Radical” strikes me as a rather charitable assessment for what Goodhart and Campbell (and Marilyn Strathern) would call completely messing up the measure, by making it a career-defining target.

In summary

NPS strikes me as Not Particularly Sensible.

Further reading

These are provided for additional reference only; I do not necessarily agree with all their findings and suggestions.

I should mention that I particularly disagree with the notion of “replacing” the NPS with something else. See my thoughts on metrics for background.