Move one patient between two groups and both averages go up
Doctors reclassify a cancer patient from an earlier, healthier stage to a more advanced one, because a scan finally reveals metastases that were always there but previously invisible. That's the only change: one patient, one label. How can this single reclassification — with no one's actual health changing — raise the average survival rate of both stages at once?
Reveal the answer
The reclassified patient was below average for the healthier group but above average for the sicker one, so removing them lifts the first group's average and adding them lifts the second's — pure statistics, no one got healthier. Named the 'Will Rogers phenomenon' by physician Alvan Feinstein in 1985, after Will Rogers's joke that Okies moving to California raised the average intelligence of both states.