The question of why some types of organic matter are more persistent while others decompose quickly in soils has motivated a large amount of research in recent years. Persistence is commonly characterized as turnover or mean residence time of soil organic matter (SOM). However, turnover and residence times are ambiguous measures of persistence, because they could represent the concept of either age or transit time. To disambiguate these concepts and propose a metric to assess SOM persistence, we calculated age and transit time distributions for a wide range of soil organic carbon models. Furthermore, we show how age and transit time distributions can be obtained from a stochastic approach that takes a deterministic model of mass transfers among different pools and creates an equivalent stochastic model at the level of atoms. Using this approach we show the following: (1) Age distributions have relatively old mean values and long tails in relation to transit time distributions, suggesting that carbon stored in soils is on average much older than carbon in the release flux. (2) The difference between mean ages and mean transit times is large, with estimates of soil organic carbon persistence on the order of centuries or millennia when assessed using ages and on the order of decades when using transit or turnover times. (3) The age distribution is an appropriate metric to characterize persistence of SOM. An important implication of our analysis is that random chance is a factor that helps to explain why some organic matter persists for millennia in soil.