WHAT FACTORS DETERMINE THE EXPECTED LIFETIME OF A GAS HOME WATER HEATER?
 It seems clear that more than age is involved. Surely the usage
volume must have an effect, and I would expect the number of on-off
cycles, as well as the brand or price  (inasmuch as it effects quality
of materials/workmanship/design) also plays a role. So... is there an
easily expressable algorythm or formula that we can plug these (or
other variables) into to generate the expected mean useful lifetime?

Most water heaters end their life when rust eats through the side of
the tank.  Typically a small leak appears near the bottom.  The rate
at which this happens is dependant on the nature of the water.  Most
well water has corrosive ability.  It would be impossible to project
the expected life of a water heater without a thorough enalysis of the
water fed to it.