The odds the Dow Jones Industrial Average will finish this year with a double-digit gain are no worse just because it did so in the last three calendar years.

I point this out to counter an emerging narrative on Wall Street that the stock market’s odds in a given year are dependent on how it performed in prior years. That narrative betrays a rookie mistake that’s known among statisticians as the “gambler’s fallacy.”

This fallacy is perhaps best understood in the context of flipping a coin. It’s the mistaken belief that, after a coin comes up heads several times in a row, the chances of it coming up heads on the next flip are particularly low. In fact, of course, the chances of a coin coming up heads are 50% with each flip, and they have nothing to do with how many heads or tails came in prior flips.

The stock market’s succession of calendar-year gains and losses is not completely identical to a series of coin flips, of course. But the two are quite similar. The stock market is forward looking, discounting the future, and therefore doesn’t take history into account. That’s why the market’s gains in each given year are, like a coin flip, largely independent of the gains in other years.

This is the theory the finance textbooks teach us, and it’s borne out in practice — as illustrated by the accompanying chart of calendar-year gains since the creation of the Dow Jones Industrial Average in the late 1890s. The baseline probability of a double-digit gain in any given year is 49%, based on the Dow’s 129 calendar years. As you can see, this probability doesn’t significantly change regardless of the number of prior successive years in which the Dow also produced double-digit gains.

Notice that, in some cases, the chances of a double-digit gain are even higher than the baseline average after several years in a row of such gains — just the opposite of what the emerging Wall Street narrative would have us believe. But this is based on a small number of cases, so don’t read much into it. None of the differences between the chart’s various columns is statistically significant.

Odds of a crash

A closely related worry is that a crash may be imminent, given that the stock market has been performing so well and for so long. But once again, the evidence doesn’t support this worry.

That doesn’t mean the market won’t crash, I hasten to add. But if it does, it won’t be because of how well it has performed in recent years.

That’s the conclusion of research conducted by Robin Greenwood and Andrei Shleifer of Harvard University and Yang You of the University of Hong Kong. In their study entitled “Bubbles for Fama,” they used prior two-year returns to calculate the odds of a crash — defined as a drop of at least 40% over the subsequent two years. Based on their results, the probability of such a crash currently is actually below average.

That’s according to the “U.S. froth forecasts” created by State Street Markets in consultation with Greenwood. According to the latest update of those forecasts, reflecting trailing two-year returns as of Jul. 31, there is just a 19% probability that the U.S. stock market would fall at least 40% over the next two years. Although you might find even that high a probability to be alarming, you should know that the average of those probabilities over the last five years has been 26%. So the chances of a current crash are well below average.

To repeat what I emphasized above, however, these below-average chances derive solely from the stock market’s trailing two-year returns. There are other reasons to worry about a crash, such as the stock market’s extreme overvaluation.

The bottom line? Your best bet, based on the stock market’s recent returns, is that the probability the market will finish 2026 with a double-digit gain is the same as it would be in any other year — 49%.