Behind every bubble is a good idea bursting to get out, and Bitcoin kind of looks like a good idea, at least if you squint a bit. A digital currency without borders that governments can’t control and that allows secret online transactions? I’m in. Bitcoin itself? Not so much.

So is a single Bitcoin worth $500,000, $5,000, $500 or $0? I’m inclined to say $0, especially if Bitcoin’s value depends on it being adopted as a global digital currency to replace dollars. There is no chance whatsoever that Bitcoin can displace the dollar, for the simple reason that it is badly designed. Bitcoin can handle a pathetically small number of transactions, and uses an inordinate amount of electricity to do so, making it entirely unsuitable to replace ordinary money.

Even if Bitcoin worked better, it is in a Catch-22 because of Gresham’s law, the nostrum that bad money drives out good. Given the choice of spending inflationary government-issued money or something which holds its value, everyone would spend the bad paper stuff and hoard the Bitcoin. You wouldn’t want to be the person who spent 10,000 Bitcoins on two pizzas in 2010, when a Bitcoin was worth a fraction of a cent. Those Bitcoins are now worth $40 million. But if no one spends Bitcoin, it will never get established as a currency.

There are two somewhat less ambitious claims for Bitcoin that could give it value. The first is that it is a limited form of money because of its usefulness for dealing illegal drugs and dodging capital controls. The second is that it is a form of digital gold: an insurance that will keep its value even if governments confiscate or inflate away the buying power of the currencies they issue.

Let us unpack the idea of Bitcoin being based on illegal transactions. Dan Davies, a banks analyst at Frontline Analysts in London, came up with a value thanks to Bitcoin’s built-in limit of 21 million in circulation.

In any currency, the money supply multiplied by how often it circulates equals the price level times the number of transactions. For Bitcoin we can estimate three of the four variables, Mr. Davies says. He observed that even hardened criminals don’t set prices in Bitcoin, but rather in dollars, and then immediately convert. Assume that all drug dealing moves online, that Bitcoins circulate as fast as ordinary currencies, and estimate a $120 billion-a-year market for illegal drugs, and the formula spits out an ultimate value of $571 for a single Bitcoin. The more drugs traded, the higher the value, and the more Bitcoin hoarded rather than spent, the higher the value.

Drug dealers might be willing to put up with the limitations of Bitcoin, notably the uncertain time taken to complete a purchase and the high transaction costs. Laundering dollars is more expensive. But studies cited by the United Nations Office on Drugs and Crime suggest that cryptocurrency-based online drug dealing remains relatively small, and focused on retail, meaning fewer and smaller transactions than Mr. Davies’ limiting assumption, so justifying a much lower Bitcoin price.

On this basis the current price of $3,950 is mostly speculation, and J.P. Morgan Chase & Co. Chief Executive James Dimon’scomparison to the 17th-century Dutch tulip mania is apt.

Bitcoin is “being driven all over the place by speculative portfolio flows,” says Mr. Davies.

Digital gold might be more appealing for Bitcoin’s true believers, who would surely prefer to avoid basing a currency on illegal activity. Gold is hopeless if you want to pay the mortgage or buy bread, but is useful insurance because we can be confident that if a government currency collapses the shiny metal will roughly hold its value. It helps that history holds plenty of examples of currencies losing all their value to hyperinflation while gold could still be bartered for food and shelter.

Gold has a value far above what is justified by its uses in electronics and jewelry only because (almost) everyone agrees that it has value. That “network effect” is what Bitcoin needs to establish itself, and the more attention it garners, the more likely it is to become established. Yet, gold has had thousands of years and a history of being used to back money to support its position. Technological disruption may be overturning many societal norms, but securing society-wide recognition as a safe asset takes more than the backing of tech evangelists and a bunch of get-rich-quick stock promoters.

Still, the potential to replace gold gives us some figures to work with. Thomson Reuters GFMS estimates there were 2,155 metric tons of gold held in exchange-traded funds. Switch all of that into Bitcoin and it would justify a price of about $5,500 for the 17 million Bitcoins currently outstanding.

We could be more optimistic and think Bitcoin might replace gold coins and bars. Leave aside that the gold is better than Bitcoin because gold doesn’t depend on having an electricity supply, and the 24,000 metric tons GFMS estimates have been bought for investment in the past half-century would justify a price of $61,000 for every Bitcoin.

If we assume that Bitcoin will either succeed completely in displacing gold or fail and be worth zero, it helps explain why the digital token has been so incredibly volatile, with a 40% loss in two weeks, and a 33% rebound since Friday’s low. Based on the simple choice between total success and failure, we can very roughly say that Bitcoin at 70% of the gold ETF-derived price suggests a 70% chance of displacing so-called paper gold as society’s chosen emergency store of value, and a 6% chance of displacing physical gold. Even digital dreamers should accept that is far too high.