Moving the below-average cases out of your group and into the comparison group improves both averages simultaneously. Nothing got better.

The Will Rogers phenomenon (also called stage migration) occurs when moving an element from one group to another raises the average of both groups, even though no actual change in the underlying values has taken place.

A Scene Worth Recognising

At a local high school, the math department splits students into an honors class and a standard class. The honors class average score is 85, while the standard class average is 70. A student who scored 78 is moved from the honors class to the standard class. Because 78 is above the standard class average, the standard class mean rises. Removing the 78-score student from the honors class eliminates a score below the honors average, which also lifts the honors mean. No new points are added; only the grouping changed.

What it means and how it works

Let Group A have average μ_A and Group B have average μ_B with μ_A > μ_B. Select an item x such that μ_B < x < μ_A. Removing x from A reduces A's sum by x but also removes a value below μ_A, which can increase μ_A if x was pulling the average down. Adding x to B increases B's sum by x and adds a value above μ_B, which can increase μ_B. The net effect is higher averages for both groups while the combined total stays the same.

Because averages are sensitive to the distribution of values, transferring an item whose value lies between the averages of two groups can increase the mean of each group. The item is above the lower group's average (raising that group's mean) and below the higher group's average (also raising that group's mean when the item is removed). The total sum of all values remains unchanged, so the improvement is purely statistical.

Why it matters

The phenomenon can create illusory improvements in fields that rely on group averages, such as medicine (survival rates after stage migration), finance (fund performance metrics), education (test score averages), and public policy. Misinterpreting these shifts as genuine progress may lead to flawed decisions, resource allocation, or overconfidence in ineffective interventions.

The verified research on this pattern supports the following:

  • The Will Rogers phenomenon was first described in a 1985 New England Journal of Medicine article by Alvan Feinstein and colleagues.
  • Moving a moderately performing asset from a high-average fund to a lower-average fund can raise the reported average returns of both funds while the combined portfolio value stays unchanged.

Common misunderstandings

Misunderstanding 1: Believing the rise in averages reflects a real increase in underlying value or performance.

Misunderstanding 2: Confusing the Will Rogers phenomenon with Simpson's paradox, which involves reversal of trends when groups are combined.

Misunderstanding 3: Assuming the effect only occurs in small samples or artificial examples.

Real-Life Contexts

See Will Rogers Phenomenon in everyday decisions

Pick a life context to see how this bias can show up outside the textbook.

Shifting a Moderately Performing Stock Between Two Funds

Moving a stock with moderate returns from a higher-average fund to a lower-average fund raises both funds' reported average returns while the combined portfolio value stays unchanged.

Approved

Scenario

Maria holds two mutual funds. Fund A tends to deliver higher-than-average returns, while Fund B delivers lower-than-average returns. She owns a stock that has delivered moderate returns over the past year. She decides to move that stock from Fund A to Fund B. After the move, the average return of Fund A rises because the stock's return was below Fund A's average, removing a below-average pull. The average return of Fund B rises because the stock's return is above Fund B's average, adding an above-average boost. The total value of Maria's combined holdings has not changed; only the grouping of the stock changed. This shift can fool even experienced investors who glance only at average returns.

Where The Bias Enters

The Will Rogers phenomenon occurs because moving a value that lies between the two group averages raises each group's mean. The stock's moderate return is above Fund B's average and below Fund A's average, so removing it from Fund A increases that fund's mean and adding it to Fund B increases that fund's mean, while the sum of all returns stays unchanged.

Decision Check

Before judging a fund's improved average return, ask whether any assets were moved between funds and examine the underlying returns or median rather than relying solely on the mean.

This pilot example is illustrative and review-gated. It is designed to explain the pattern, not to claim a documented public case.

Sources

  • Niroula, Rishab. REV 2.0 Topic Catalog. Hello to Halo.
  • Kahneman, Daniel. Thinking, Fast and Slow. Farrar, Straus and Giroux, 2011.
  • Taleb, Nassim Nicholas. The Black Swan: The Impact of the Highly Improbable. Random House, 2007.

The next time this pattern surfaces, the move is not to fight it - it is to notice it. Naming Will Rogers Phenomenon creates a moment of pause before the decision. That moment is usually enough.