U.S. equity markets made substantial gains last year. The Standard & Poor’s 500-stock index, the traditional benchmark for equities, was up 29.6 percent. Add in dividends, and it’s well over 30 percent. Technology and small-cap stocks did even better, with the Nasdaq Composite gaining 38.3 percent, and the Russell 2000 small-cap index up 37 percent.

You might think that after such a strong year, the markets might be due to “take a breather.” Perhaps a flat year is in order so last year’s gains can be “digested” — or so goes the popular assumption. And indeed, markets this year have ranged from flat to down a few percent.

Some would go further and, because of the “Gambler’s Fallacy,” assume that markets are bound to go the other way and sell off.

Those assumptions would be wrong. The data strongly suggest that very good years in the U.S. stock market are followed by more good years. When we review both the Dow Jones Industrial Average and the S&P 500, we learn that the years that follow a 20 percent gain (or greater) are typically stronger than average.

There have been 22 instances where the Dow has risen 20 percent or more. In the year after, returns average 8.4 percent, beating the average 7.8 percent of the 90 years from 1924-2013.

The results are even more dramatic in the S&P 500: Since 1954, the index was up 20 percent or more 14 years. Of those times, the average return the following year was 10.2 percent, more than 22 percent higher than the 8.3 percent average over the 59-year period.

A few caveats are in order. When looking at historical data, we do not know if the conditions that created these results exist currently. Remember, these are only probabilities based on past activities; they are not a guarantee.

Additionally, as I so frequently admonish, humans are terrible at predicting the future — especially when it comes to the economy or the stock market. Forecasting is simply not a strength of the species; we are much better with tools and narrative storytelling.

Analysis of historical data carries well-known statistical concerns. First, we might be fooled into thinking that a pattern of market behavior exists when we’re simply looking at random price fluctuations. Even if it seems as though we’ve discovered a pattern, we cannot assume it is real or know if it will continue. Even data highly correlated with one outcome does not mean that actual causation exists.

Second, assuming a causative relationship exists, we must still think of these “typical” outcomes as just one probability of many that could occur. An increased statistical possibility of a certain outcome means a higher likelihood of that outcome — but not a guarantee. Even a 75 percent probability results in one-in-four instances of the lower probability outcome winning out.

What about the contra arguments? What historical data suggest a less than average return? Consider two factors:

The data I used referenced market gains of more than 20 percent in a given year. But with 29.6 percent so tantalizingly close to 30 percent, might that make a difference?

Lance Roberts, chief executive at Streettalk Advisors, looked at what happens when markets were up 30 percent or better. He found the following year’s return was typically below average. In the 10 examples when markets were up more than 30 percent, the following year saw gains of only 6.12 percent; that’s below the long-term average. And, he notes, the following five years tend to be softer. While we usually prefer more samples for a complete statistical set, these 10 years do make the case that more than 30 percent is sufficiently different than more than 20 percent.

The second factor is the presidential cycle.

When we look at a composite of the average monthly returns of the Dow, starting with the first year of a president’s term and ending with the last over the past 125 years, we learn some interesting things: Markets seem to do significantly better in the second half of a president’s term than in the first half. Years three and four are very strong, while the first two years are weaker.

How to explain this? The party in power wants the electorate to feel good about itself in the fourth year of a presidency, i.e., election year. It spends lots of effort — and taxpayer dollars — trying to boost the economy that third year.

Analyses confirm these findings. Last year, S&P Capital IQ noted that “since 1945, the second year of a president’s term saw the S&P 500 gain 5.3 percent in price on average, versus 16.1 percent in the third.” In 1992, the Financial Analysts Journal compared the Dow and the cycle from 1901 through 1990. That data showed a similar relationship — mediocre second years and very strong third years.

The third year sees the index gain 88 percent of the time; the second year, only 59 percent. The second-year subpar performance is actually even worse for the first nine months of the year; losses average 0.5 percent.

This calendar year is just about one-third finished. So far, markets have been tumultuous, with the high-flying momentum winners from last year running into trouble. Netflix, Tesla, LinkedIn, SolarCity, Facebook and Twitter have all gotten shellacked, off as much as 40 percent from their highs. Meanwhile, the old-school tech companies — Microsoft, Cisco, Oracle, IBM, Hewlett-Packard — have held up surprisingly well.

This suggests a maturing market, moving its focus away from speculative names, toward more conservative names — more profitable, dividend-yielding firms. That implies to me that the bull market dating to March 2009 may not yet be over, but it is entering as different phase.

If we are lucky, it means more measured and sustainable gains. The key will be profit growth in the coming quarters.

Ritholtz is chief investment officer of Ritholtz Wealth Management. He is the author of “Bailout Nation” and runs a finance blog, the Big Picture. Twitter: @Ritholtz.