From age 50 or so onward, statistics show, the risk of death increases year by year. In fact, the death rate rises exponentially over much of the adult life span. But after age 80 or so, the rate of mortality increase begins to slow down (an effect referred to as late-life mortality deceleration). Equations that quantify changes in the hazard function show that it levels off at some age between 105 and 110. That means equations derived from lower age groups are unreliable for estimating life span limits; proper analysis requires statistics derived from those aged 105 and up.

Analyses of those groups suggest that by age 110 or so, the rate of dying in each succeeding year is roughly 50 percent (about the same for men as for women). And the data so far do not rule out an even smaller annual chance of death after that.

Depending on the details of the dataset (such as what age ranges are included, and for what country), a possible longevity cap is estimated in the range of 130–180. But in some cases the statistics imply a cap of at least 130, with no upper limit. Mathematically, that means the highest ages in a big enough population would be infinite — implying immortality.