Methodological Issues

Estimating ancient coin production

The main ambition of this website is to estimate the volume of ancient coin production allowing comparisons not only in recorded or original numbers of dies, but also in numbers of coins and even, for precious metals, in weights of silver. This is a topic which, once hotly debated 1 2 3 4, is now generally accepted as worth to be pursued5. However to be well understood, it requires a series of explanations or caveats.

The common strategy is a two-step process: first, to determine the number of original dies from the number of recorded dies in the sample. The second step is to multiply the original number of dies by what we think was the average production of a die. Another strategy developped by Warren Esty is to estimate the coverage, i.e. the relative part taken in the full production by the recorded dies6 7. Instead to give a value for the original number of dies, one can multiply afterwards by the average productivity per die to obtain a number of coins, it will offer a percentage (e.g.: the recorded dies are responsible for 90% of the full production).

Estimating the original number of dies

The first step is to estimate the original number of dies, more specifically the number of obverse dies (anvils) because they generally deteriorate slower than the reverse dies (on this issues, see 8 9). The three essential values are: 1) the number of observed dies in the sample ("o"), 2) the size of the sample (the number of coins: "n"), and 3) the number of singletons, i.e. the number of dies attested by only one coin ("f1"). More than 20 methods based on probability calculation were proposed in the 1970s and 1980s. Several contributions have demonstrated the similarities of results between these formulas, providing the ratio 'number of specimens divided by the number of obverse dies' is high enough 10. Let us say, roughly, that these calculations need some carefulness below a ratio of 3, are potentially dangerous below a ratio of 2 and must be avoided preferably below a ratio of 1.5. A majority of coinages fall well beyond that limit. With at least 600 coinages with a ratio "n/o" above 6 and even 45 above 30 [[1]]. Looking at the recent literature, it looks as though nobody is still frightened by that kind of calculations. In other words, the possibility to estimate the original number of dies has been accepted. It was first and for a long time opted for a binomial (i.e. Gaussian, or symmetric) distribution (Good, Carter), with no infantile mortality (A). This is clearly an unlikely model. In the 1980s, one moved to a Poisson distribution with a negative asymetric curve (B). Around the same time, looking at hundreds of real distributions, a combination of a negative distribution (for the infantile mortality) followed by a binomial distributon (for the surviving specimens) was first proposed 11.

Estimating the original number of coins

To estimate the average number of coins produced by each (obverse) die is a much more debatable issue. While it is easy to produce a long list of reasons for which this average should have varied depending of the metal, the denomination, the tools, the level of technical skills etc., it turns out that every time one may exercise some control, cheking through coin hoards, results are similar (as for the coinages in the name of Alexander the Great, the cistophoric tetradrachms in Asia Minor or the Roman Republican denarii).The reasons which allow the argument for such a figure are various and have been discussed several times. Much has been said about the accounts of the Amphictionic League, indeed a good starting point if only because it is the only (not exactly) straightforward evidence 12 13. Much has also been said about modern experimentations, even if I personally doubt that they could provide anything else than a minimal number 14 15. Much less has been said about the few cases for which we do have more than 1,000 coins struck with the same die, also as minimal figures (the Rhodian imitations in the name of Hermias struck by Perseus from the hoard of Larissa [IGCH 237] or the bronzes of Apamea from the hoard of Aphrodisias [the number of 6,000 has been reported]) or the few cases of extremely well dated instances of intensive production with realistic figures of c. 3,000 coins produced per day if using an average of 20,000 coins per die (Mithridates Eupator in 89 and 75 BCE, the joint reign of Justin and Justinian during 17 weeks [April 4th–August 1st, 527 CE]). And nearly nothing has been said about what could be deduced from survival ratios put in perspective, i.e., the fact that Greek coinages are considerably better documented today than medieval coinages and even modern coinages 16. Recent die studies often show an n/o ratio superior to ten (with 8.84, the Yehud coinage is close to that). Then, if we postulate an average output per die inferior to 10,000, we have to assume a survival ratio superior to 1 out 1,000 which is very high if put in perspective (c. 1 out of 5,000/10,000 for medieval coinages and c. 1 out of c. 2,000/3,000 for eighteenth century coinages).

Why an average of 20,000 coins per obverse die?

The average productivity for an obverse die has been uniformly fixed here to 20,000 coins. It is a stopgap measure that applies primarily to large silver denominations such as tetradrachms. It is an estimate which could be divided or multiplied by two (from 10,000 to 40,000 coins), but unlikely by three (from 6,666 to 60,000). Although remaining in the right order of magnitude for smaller silver denominations and other metals, this average of 20,000 coins per obverse die is likely to be adjusted depending of the kind of coinage.