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The true madness of a viral wing pricing scheme

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The ‘Wing Bowl’ Buffalo Wing Eating Contest Is Held In Philadelphia Photo by Jeff Fusco/Getty Images

If you’ve been on Twitter in the past week, you may have seen this bewildering wing menu. I saw it a few days ago, and it has consumed my thoughts in every unoccupied moment since. We know nothing of where it came from or why, although it’s probably safe to assume it’s a wing place.

It’s weird, of course — just set a price per wing! — but as I pondered the numbers, more and more strangeness revealed itself. Like a fractal curve, it failed to cohere on closer inspection, producing only deeper challenges and further unknowns.

To begin, here is a chart of the price of the various quantities of wing, the beginning of our journey. It may seem simple, but I promise you, it is maddeningly complex.

There is a certain logic to it: more wings, more money. This is how these things usually work! If there were a single price per wing, this would be a straight line, with each wing increment corresponding to a stable and predictable price increment. And it almost looks like one! (It curves up at the end because of the higher increments, but let’s put that aside for the moment.) In fact, that straight line conceals seemingly random variations in the price per wing, which changes according to no discernible logic.

Below is a chart of the average wing price at each wing quantity:

The first thing to notice here is that it doesn’t change that much. We’re staying roughly between $1.11 and $1.14 per wing, and an extra three cents per wing isn’t going to break the bank for anyone. It also gets lower as you buy more wings, which is common in commercial enterprises: you want to sell more stuff, so you take a smaller margin on higher-volume purchases. But the variation is so small and so haphazard that there doesn’t seem to be any real intention behind it. Why such a steep drop at 25? Why does it bounce up and down after that? It’s as if they were just picking numbers for the sound of them.

But even that conceals the true madness of the pricing scheme, the genuine anarchy at the heart of this bewildering chart.

If you really want to incentivize wing purchases, you don’t care about the average wing price so much as the incremental wing price. That’s the first derivative of the initial graph: what does it cost to buy another wing? But when you chart that marginal change, the logic breaks down entirely.

In general, another wing will cost you between $1.10 and $1.15 per wing — a reasonable but not remarkable price. But for some reason, the 25th wing (hereafter, The Phantom Wing) costs only 55 cents. You can verify this if you look back to the original chart: 24 wings cost $27.25, and 25 wings cost $27.80, a difference of 55 cents. The following, non-Phantom Wing bumps the price to $28.95, a difference of $1.15 cents.

Most of the wings cost either $1.10 or $1.15 (although the jump from 40 to 50 is also a notably good deal), but for some reason, the Phantom Wing is half price. This might even be conceivable as a marketing strategy — 25 wings is a lot, but maybe the price makes it worth it? — except that the information is buried so deep, accessible only to those mad enough to stare into the eyes of the beast and risk the knowledge of its true nature.

Even now, at the end, it eludes me. What are we to do with this knowledge? What is the true nature of the Phantom Wing? I cannot say.