A 5th cousin shares about 0.05% of your DNA. You might have 1,000 of them.
Every step out in the family tree, your genetic relatedness cuts in half — but the number of people standing at that distance does the opposite: it roughly triples. Two views of the same math.
50% → 0.05%
Siblings share half their DNA. By 5th cousins, that's fallen to about 1 part in 2,000 — less related than two random members of the same ethnic group tend to be by chance.
2 → ~1,000
Assuming roughly 3 children per family across the generations it takes to get there (a rough historical average, not a real prediction for any one family), the pool of people at each distance roughly triples every step out.
The two numbers move in opposite directions on purpose. "Relatedness" is exact: it's the standard coefficient-of-relationship formula geneticists and consumer DNA services use — (1/2)gA+gB-1, where gA and gB are how many generations back each of you sits from your shared ancestor. Full siblings (1,1) get 50%. First cousins (2,2) get 12.5%. It only depends on generations, not on any assumption about family size.
"Headcount" is different — it's an illustrative model, not a measurement. It assumes every generation averages about 3 children (in the U.S., actual total fertility ranged from lows near 2 in recent decades to a Baby Boom peak near 3.7, so 3 is a round mid-range stand-in spanning many generations of a real family tree) and multiplies outward from there. Real families vary enormously — the point isn't the exact number, it's that the crowd grows exponentially while the connection shrinks exponentially, at the same time.
Sources: coefficient-of-relationship formula per standard population genetics (as published in DNA-testing services' relationship-probability tables, e.g. AncestryDNA/23andMe support documentation); U.S. total fertility rate history, CDC National Center for Health Statistics.