The Dow missed its 14th straight gain — coin flip could have done that

The Dow Jones Industrial Average closed negative Thursday, breaking a 13-day win streak in which the blue-chip index gained 5.3%. It also missed the opportunity to tie its longest rally on record: a 14-session run in 1987.

But here’s the thing: Regardless of whether the Dow made that 14th straight gain, basic probability tells us that we will get this kind of streak every once in a while naturally. It’s sort of like a version of the famous “Gambler’s Fallacy” in which people erroneously believe an unusual streak in a roulette wheel means something for future outcomes, when you’d actually expect long streaks to happen on occasion.

related investing news

We can even show that these streaks aren’t that different from a result of a coin flip.

CNBC ran a simulated coin flip thousands of times and counted the number of times “heads” came up in a row. Treat those like daily gains in the stock market. Remember, these are totally independent events where the outcome is not affected by the prior simulation.

Since the Dow’s inception in 1897, there have been nearly 33,000 trading days. In that time, we’ve seen a single 14-day streak of gains and two streaks that ended at 13 positive sessions in a row. Prior to this week, the last 13-day rally was in January 1987.

In our simulation of flipping a fair coin 33,000 times and recording the number and length of “heads” streaks, we actually got exactly the same as the real Dow: a single 14-day rally. With a coin slightly biased toward “heads” (in this case, giving the results of each flip a 0.523 chance of being heads), our simulation turned up two rallies of 14 days and three streaks that ended at 13 days.

In the world of stock market speculation, pundits like to attribute explanations for every twist and turn. But just by using the 50-50 assumption of our theoretical coin, we can show that long streaks are not as extraordinary as they may seem.

— CNBC’s Gabriel Cortes contributed to this report.