After I wrote about being struck by a car last week, I was heartened by the many emails wishing me a speedy recovery. A handful tried to cheer me up by saying that I was now due for bountiful good luck. That expectation is a good example of the difference between the (fallacious) law of averages and the (correct) principle of regression toward the mean.

A coin that lands heads does not increase the chances of tails on the next flip. Coins are inanimate objects with no memories of the past or control over the future. Each flip has a rock-steady 50% chance of landing heads. Nonetheless, some people looking to win games of chance count on the “law of averages” to reward them. That is an unfounded optimism also known as the “gambler’s fallacy.”

The fallacious law of averages

Many also embrace the fallacious law of averages in their daily lives—particularly after setbacks like my bicycle accident. Some baseball players who have experienced “out” after “out” think they are “due for a hit.” Likewise, some managers of teams that have been losing game after game think they are due for a win.

Recently, the CEO of an AI-powered mutual fund was compelled to acknowledge that the fund’s performance had been a “complete disappointment.” But he spun that failure into good news by asserting that, “To the extent that they may have underperformed today, there is a strong possibility that they can outperform in the future.”

Jay Cordes, a friend and co-author, told me about a team leader who tried to cheer up his sales team by telling them that every cold call that ends with a no brings them closer to a yes. Because 1 out of every 100 calls results in a sale, they just had to cold call their way through 99 nos. Jay protested “No, the calls are independent. You’re not getting any closer to anything when someone says no.” I would go further. If a salesperson is getting no after no after no, maybe something is wrong with the sales pitch.

In the same way, a baseball player who makes out after out might consider practicing more, or choosing a new profession. A team that has been losing game after game might consider some personnel changes. A mutual fund that has been a complete disappointment might consider a new investment strategy.

Regression toward the mean

The regression toward the mean principle is superficially similar but it is correct and useful. Every semester, in every class I teach, I see that the top scorers on one test usually do not do as well on a second test. A “coasting” explanation is unconvincing because I see the same pattern whether I look forward or backward in time. Test scores are affected by student abilities but also by luck; for example, the questions I choose to ask and the guesses that students make when they are unsure of the answer.

The top scorers on any single test most likely benefitted more from good luck than bad, which means that their high scores overstate their ability. Their scores on a second test are likely to be somewhat lower—closer to the mean—no matter whether the second test is taken before or after the first test.

This regression toward the mean happens whenever “performances” are affected by luck. The baseball player with the highest batting average in any season generally does not do as well the season before or the season after. The best-performing stock in any year generally does not do as well the year before or the year after. The tallest people usually have somewhat shorter parents and children.

Jay shared a wonderful example. A company that manages millions of websites gave one of its employees (“George”) a list of sites with the largest drop in revenue over the previous three months. George was asked to tinker with the layouts in order to boost revenue. He fiddled and faddled and revenue generally popped 20 percent or more the very next day. George was a website wizard!

Then, one day, the curtain was pulled back. George had been too busy to make any changes and, yet, revenue jumped like it always did. Yep, regression toward the mean.

The worst-performing sites had no doubt experienced more bad luck than good luck in the volume and type of visitors and were consequently very likely to do better in the future even if George did nothing at all.

Illusory problems and solutions

I was reminded of George when I read recently that “a survey of 702 executive staff and project managers found that of those who worked with the three biggest consultancies in corporate transformation projects, 84 per cent felt they ‘were no help at all’.”

A company that experiences a sharp downturn in revenue or profits might bring in highly-paid consultants to turn things around. The consultants poke around, make some recommendations, and the company miraculously improves.

That could be a team of richly compensated Georges. A company doing poorly is more likely to have experienced bad luck than good luck and is consequently likely to do better in the future, whether or not the consultant’s recommendations have any merit or, indeed, whether a consultant is even hired.

I don’t know how helpful consultants are. It surely depends on the consultants and the situation. I do know that inevitable fluctuations in business performance can create the illusion of a problem and a cure when there is neither. In medicine, randomized controlled trials can be used to evaluate treatments, while taking regression into account. We can’t do that with consulting but we can remember that the effectiveness of a treatment in medicine, business, or anything else cannot be assessed without considering regression to the mean.

Personally, I am optimistic about the future but not because I was struck by a car. Terrible bad luck does ensure an equal amount of good luck but I am confident that my life will soon return to normal.