In 1886 Francis Galton published the heights of 928 adult children of 205 pairs of parents. Tall parents had tall children, but less tall than themselves: on average, a child’s height stood about two-thirds as far from the average as the parents’ did Published. He called it regression towards mediocrity. We call it regression to the mean, and it applies to every number that mixes something real with something random.

The flight instructors

Daniel Kahneman called it “the most satisfying Eureka experience” of his career. He was teaching Israeli Air Force flight instructors that praise works better than punishment for learning a skill, when a senior instructor objected. In his experience, cadets he praised for a clean maneuver usually did worse on the next try, and cadets he screamed at usually did better Published.

The instructor’s observation was right and his explanation was wrong. He praised after unusually good flights and screamed after unusually bad ones, and unusual flights are followed by more ordinary ones whatever the instructor says. Kahneman’s conclusion: because we reward others when they do well and punish them when they do badly, “we are statistically punished for rewarding others and rewarded for punishing them.” He then had the instructors toss two coins each at a target behind their backs, without feedback, to show the same pattern appearing with no instruction at all Published.

Praise follows a lucky week. So does disappointment.

Where it shows up in a store

• The winning campaign. Last quarter’s best email, resent to a similar audience, does worse. The copy didn’t wear out. Part of the first result was luck.
• The breakout SKU. The product that doubled in its second month gets a deep reorder, and month three is merely good. Now there’s a warehouse problem.
• The hot channel. The ad set, influencer or channel with the best return last month gets the budget, and returns less.
• The fix that “worked.” The worst flow, page or rep gets attention after its worst month, and improves. Some of that would have happened anyway, which is why a fix needs a comparison, not a before-and-after.

How much falls back

Kahneman’s rule: “Whenever the correlation between two scores is imperfect, there will be regression to the mean” Published. How far a result falls back depends on how much of the spread between results is real. If your campaigns differ a lot in true quality and each is sent to a big audience, a winner keeps most of its lead. If they’re similar in quality and the audiences are small, most of the lead is noise and goes away.

You can estimate the split from your own history. The spread of past campaigns’ results is real differences plus chance. Chance you can compute from the audience size. Take it away, and what’s left is the real spread. The share of a winner’s lead you should expect to keep is the real spread divided by the real spread plus the chance in that one result Derived. The tool does it for you.

With the defaults, a campaign to 12,000 people that produced 30 orders, a 0.25% order rate against a usual 0.15%, should be expected to do about 0.20% next time: half its lead is likely real and half was luck. That’s 24 orders, not 30. Double the audience of the winner to 24,000 with 60 orders and about two-thirds of the lead holds, because a bigger audience carries less chance.

DerivedExpected = 0.15% + 0.5 × (observed − 0.15%), where 0.5 is the share of the lead that holds with the default inputs. Bars scaled to 0.30%.

The winners are still winners. They’re just closer to the pack than the dashboard says, and the gap between them mostly disappears.

Do this

• Before any winner gets more budget, inventory or a slot in the calendar, run it through the tool and plan on the expected figure. For SKUs, use weekly units against the category’s weekly units and treat the output as the reorder forecast.