In chemistry, turnover number (TON) refers to the average number of
cycles a catalyst can perform before decomposition. TON is inversely
proportional to catalyst loading; lower TON means more catalyst is
required to transform a given amount of substrate.

For fans of statistics and probability, determining the
distribution of molecular turnover numbers among the entire ensemble
of catalyst molecules is an interesting and non-trivial problem. An
average over all the molecular TONs must give the macroscopically
observed TON, but it's extremely unlikely that every single catalyst
molecule performs exactly the macroscopically observed number of
turnovers then just dies. There is some distribution of molecular
turnovers with its mean at the macroscopically observed TON. But what
is the shape of this distribution? Is it time-dependent? What factors
govern its shape? Questions abound.

To the crudest approximation, the macroscopic TON depends in some
way on the relative rates of catalyst decomposition and turnover.
Catalysts that have extremely low rates of decomposition, like enzymes,
have massive turnover numbers. Similarly, catalysts that perform their
cycles quickly (relative to the rates of any decomposition pathways)
also have large TONs. Catalysts with multiple decomposition pathways,
on the other hand, often have low turnover numbers. Transitional metal
catalysts exhibit a range of TONs that extends over multiple orders of
magnitude: numbers from 20 to 2,000,000 and beyond have been reported.