Double Jeopardy: small brands lose twice

Origin

The name came first and the marketing came later. William McPhee, a sociologist at Columbia, coined “double jeopardy” in 1963 in a study of audiences for radio presenters and newspaper comic strips [3]. The less popular ones had fewer followers, and those followers also liked them less. McPhee thought it was a property of how attention works when choices are many and effort is low.

Andrew Ehrenberg saw the same shape in consumer purchase panels and spent the next thirty years documenting it. The paper that fixed it as a law of marketing is Ehrenberg, Goodhardt and Barwise, “Double Jeopardy Revisited”, in the Journal of Marketing in 1990 [1]. Their summary, which still stands: “small brands have far fewer buyers, and these buy them somewhat less often” [1].

The problem they were solving was that marketing had a theory of loyalty with no numbers in it. Loyalty was treated as something a brand earned by being good. The panel data said it was something a brand got by being bought.

What the evidence shows

The pattern is near universal in repeat-purchase markets. Ehrenberg’s panel work across grocery, personal care, and later services and durables showed that when brands in a category are ranked by penetration, their purchase frequency and share-of-category-requirements fall in step, with the smaller brands always a little lower on both [1][2]. The effect is modest in size and very consistent in direction.

It is predicted by the Dirichlet model. The NBD-Dirichlet, developed by Goodhardt, Ehrenberg and Chatfield, is a statistical model of how buyers in a category spread their purchases across brands [4]. Double Jeopardy is not an assumption of the model. It is an output. If buyers behave as the model describes, which they do with high fidelity across decades of panel data, then small brands must have slightly less loyal buyers. There is no separate loyalty mechanism to find.

It holds in B2B. The Ehrenberg-Bass Institute’s work on business markets found the same pattern among industrial and service buyers, which removes the objection that this is a soft drinks phenomenon [5].

The loyalty metrics move together. Repeat rate, share of requirements, purchase frequency and defection rate all track penetration. A brand that doubles its buyer base will see its loyalty metrics improve a little as a side effect. A brand that tries to improve loyalty metrics without growing its buyer base is working against the pattern.

The challenge

Two objections have standing in the literature.

The niche brand. Ehrenberg himself identified a small class of brands that sit above the Double Jeopardy line: fewer buyers than expected for their loyalty, or more loyalty than expected for their size [1]. They are usually brands with a functional restriction, a dietary product, a regional distribution, a professional tool. The honest reading is that these are exceptions that the model names, not refutations of it. Most brands that believe they are niche are simply small.

Loyalty programmes. The relationship marketing tradition holds that loyalty can be built directly, and the evidence for schemes doing so at scale is thin. Sharp’s reading of the data is that loyalty programmes mostly reward buyers who would have bought anyway, and shift the pattern very little [2]. Defenders of the schemes point to retention in contractual markets, where the Dirichlet fits less cleanly. That is a fair point about scope.

The literature is not split on whether Double Jeopardy exists. It is settled. The live disagreement is whether anything a brand does can move it from below the line to above it, and the honest answer is that the documented cases are few and have a structural explanation.

Where I see this go wrong

Loyalty targets set independently of penetration targets. A board asks for retention to rise from 70 to 75 per cent while market share stays flat. The pattern says this is asking for the brand to leave the Double Jeopardy line, which almost no brand does without changing its size. The target gets missed, the retention team gets blamed, and nobody checks the law.

The small brand studies the big brand’s loyalty. A challenger looks at the leader’s repeat rate and concludes the leader has a loyalty secret. It does not. It has a size. The challenger’s buyers would be exactly as loyal if there were as many of them.

Retention spend is funded by cutting acquisition. This is the one that costs real money. If loyalty follows penetration, then cutting the spend that brings in new buyers to fund the spend that keeps existing ones lowers both numbers on a delay. I have seen this argued as prudence in a downturn, and it is the opposite.

I taught this badly myself for a while, treating loyalty and acquisition as two levers with two budgets. The panel data does not support two levers. It supports one, called getting bought by more people, with loyalty as the dividend.

What to do with it

1. Plot your category. Penetration on one axis, a loyalty measure on the other, every brand you can get data for. If your brand sits on the line, which it almost certainly does, you have no loyalty problem. You have a size.
2. Set loyalty expectations from the line, not from aspiration. A brand of your penetration should expect roughly the repeat rate of other brands of your penetration. Anything above that is a bonus. Anything below it is a real problem worth diagnosing.
3. Fund acquisition first. Not because retention does not matter, but because it is mostly a function of the number you move with acquisition.
4. Audit the loyalty programme against the Dirichlet expectation. If your loyal buyers would have been that loyal anyway at your size, the programme is a cost of doing business, not a growth lever. Price it as one.
5. Treat “we are a niche brand” as a hypothesis with a test. Does your loyalty sit above the line for your penetration? If not, you are a small brand, and the strategy for a small brand is to get bigger.
6. Read Double Jeopardy alongside the 95-5 rule. Together they say most buyers are not buying, and the ones who are will spread their purchases roughly in proportion to how many brands they can think of. Both point at reach.

If you run the company rather than the marketing

You will at some point be shown a loyalty metric with a target attached and asked to fund a programme to move it.

Before approving, ask one question: where does our loyalty sit relative to brands of our size in this category? If the answer is “about where it should”, then the metric is not a problem, it is a description of how big you are, and the programme is being sold to you as a cure for a condition you do not have. If the answer is “below where it should”, you have something real to fix, and it is usually a product or service failure rather than a marketing one.

The broader point is worth holding onto because it is counter-intuitive and expensive to get wrong. Loyalty is mostly a result of size. The way to have more loyal customers is to have more customers. Any plan that funds retention by starving acquisition is spending the dividend to protect the capital, and it works for about a year.