[srgseg]

A way of explaining it that (hopefully) makes it clearer:

Let's say you have just invented the concept of prison, and let's say 50% of people come back every year after going to prison for the first time, and 50% never come back again.

In year 2, you'd observe that of the year 1 population, 50% returned, and 50% didn't.

In year 2, you'd also add a new influx of prisoners.

Therefore, in year 3, you'd observe that of the year 2 population, 75% returned and 25% didn't.

But, the real underlying recidivism rate is still 50%, not 75%.

[srgseg]

To expand on their mall analogy: There is a big difference between asking "what percentage of this week's mall visitors will return next week", and asking "when people visit this mall for the first time, what percentage of them will return the following week".

[gsibble]

So the difference in their studies is what percentage of first time offenders will return to prison vs. what percentage of overall prisoners will return to prison?

[Abraln]

Seems more like one counts (Number of prison stays)/(people who have gone to prison), while the other counts (people who have gone to prison more than once)/(The number of people who have gone to prison in total)