What Chicago piano tuners have in common with Canadian weed dealers.

Statistics Canada has tackled a tricky but important question: how much marijuana have Canadians been consuming in the years leading up to 2018’s intended legalization of the stuff? This is the kind of thing that hard scientists and engineers call a “Fermi problem,” named in honour of the Italian-American nuclear pioneer Enrico Fermi.

Our data on the collective consumption of marijuana are pretty sparse. We don’t have an easy way to infer the total volume of consumption for the whole country. But as a practical matter we need some estimate, even if we think consumption will double, or halve, when pot is legalized. Investors are gambling on the existence of a marijuana market, measured in dollars, and on some figure for total national demand, measured in tonnes.

Hence the Fermi approach: we break the big problem down into individual pieces, take stabs at each one, and hope for a final answer that looks like it is more or less on the right order of magnitude.

The canonical example of a Fermi problem is guessing how many piano tuners live in Chicago. You work from the population of the city, to the total number of households, to the likely number of regularly-used pianos, to the number of likely piano tunings...

Some of your guesses might be off, but most of the coefficients won’t be absurdly far off, and perhaps the errors will cancel out. You can thus get a final answer that is useful, assuming it is acceptable for that answer to be off by 50 per cent rather than 5,000 per cent. The Fermi style of estimation was useful in early nuclear research, where scientists, having little data on fission and no electronic computers, were concerned with order-of-magnitude questions like, “Will we set Earth’s atmosphere on fire?” Fermi problems are sometimes said to still be favourites in tech-industry job interviews: business startups are full of decisions that must be made on the basis of slender data and rough calculation.

That’s what legal marijuana is, sort of: one big business startup, with a myriad of retail competitors and Canadian governments having a piece of the action. Statcan’s Fermi-like effort to guess at total historical consumption in the black market is explicitly described as “experimental,” an important qualifier that is not finding its way into the quickie news summaries of the findings.

They estimate, for example, that Canadians probably smoked 700 metric tonnes of weed in 2015. But when you add up all the sources of uncertainty in the chained calculation by economic analysts Ryan Macdonald and Michelle Rotermann, the actual quantity might be double that. Or it might, as they admit, be half. That’s still very useful information: we know the real number probably isn’t 70 tonnes, or 7,000.

The point is to have some estimate, and a reasonably transparent process for generating that estimate — a picture of the chain of calculations, along with the uncertainty associated with each one. The name “Fermi” does not appear in the MacdonaldRotermann paper, but if you know the famous piano-tuner example, you can only laugh at how close the structure of Statcan’s analysis comes to it.

The best data on historical cannabis use in Canada is data from surveys — and so surveys are what Macdonald and Rotermann use: their approach, they write, “first multiplies the population by the prevalence of cannabis use to estimate the number of consumers, and then multiplies the number of cannabis consumers by the number of days of consumption and their dosage per day.”

StatCan’s own data is the strongest, despite being spotty time-wise and coming from many different survey products, but there are other surveys available to provide a sanity check on prevalence numbers, including material from the Le Dain Commission on drugs from 1972 and numbers from Toronto’s Centre for Addiction and Mental Health. One goal of the StatCan paper is to create backward-looking estimates of gross marijuana consumption for use in national accounts — from which illicit drugs are artificially excluded as a sort of pious sanitation measure, as long as they stay illicit.

But the emphasis in the news will inevitably be on that 700-tonne guess at the total consumption in the last year of the series, 2015. Others who have tried to guess at marijuana market size have come up with similar figures. One marijuana CEO pegged demand for the first crop of legal weed at “a thousand metric tons.” The federal Parliamentary Budget Office, using a Fermian approach quite like Statcan’s, forecast a demand of 655 metric tonnes in 2018.

It’s perhaps not the physical volume of marijuana that is the most interesting measurement here anyway: it’s the cash value. As Macdonald and Rotermann point out, it looks as though the Canadian cannabis market is already at least half the size of the market for beer and 70 — 90 per cent as large as that of wine.

This is something to keep in mind every time a policymaker or do-gooder behaves as though the federal government were — in the words of my colleague Chris Selley — inventing marijuana rather than legalizing it. The endless “new” social and legal problems that are supposed to sprout up this summer? They’re not new. Don’t kid yourself (and if you are kidding the rest of us, please stop).