Each time the Romans debased their currency, they could be fairly confident that previous more valuable issues had a tendency to be hoarded if possible from that point on, and with a precise measure of the exact amount leaving the treasury could get a reasonably good estimate of how much was actually needed to be in general circulation. Perhaps the minimal amount to get by, perhaps not, maybe just depending on how generous Caesar felt at the time. And by offering a slightly more-than-fair exchange for the silver content, when issued, the amount that can afford to be hoarded can be deduced. While still turning a little bit of a "profit" from fractional percentages of silver that the general public can not measure accurately. Their central bankers were as shrewd as any existing today, equally as gifted mathematically as modern man can be.
Further inference can also be made about the resulting state of affairs by later following the private trading of recalled issues at "inflated" (previous) values.
If you were the one setting monetary policy risky enough that the chance for collapse was not as slim as it could be, you would want to know how close you were cutting it and the best way would probably be to get as good a handle on the money supply as you could, even if you could not gain full control. Nobody can anyway. But all effort always will be toward gaining more control.
This is basically the variable you could call _value of money_.
Not exactly the same as _price of money_, which is manipulable somewhat differently, but directly related to it in terms of _prices of goods_.
Which seems to be directly related to any type of inflation you can imagine :\
[0] Like the 1960's.