The statistics and probability are improperly applied to this situation, and fail to accurately model reality.

The numbers are taken as abstractions and untethered from the complex subsystems that generate the results. This decoupling eliminates any understanding of the underlying principles at work.

Human tissues are organized into organs that eventually fail. When you put the tables and figures away, and look at the actual centenarians themselves, there’s no expectation that those people’s organs will continue on an endless plateau of static operation without further incident, in an endless streak of winning coin flips.

The reality is that life at that age isn’t abstract coin flips, there’s definite decline lurking in the background. Externalities like microbial illness could be modeled as coin flips (does the individual catch the flu this year?), but internal deterioration is still a systemic function with a graded slope that varies from person to person.

That declining slope could be altered with transplants, but eventually the brain gets involved, and we lack the metaphysical and philosophical tools to argue about when a zombie robot brain transplant might mean animate brain death or the living exchange and passing of one distinct individual for wholly another living mind.

Good point. So the cause is more likely that the distribution of the underlying genetic code that determines max life span for an individual is what follows the Poisson distribution at the tail end, rather than any individual's own aging process (or apparent statistical lack thereof). That makes more sense.

Granted it appears the number of people to live so long is only a few hundred. And if halving each subsequent year, not a huge sample size.