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 CiteRef::Buttrey 1993 CiteRef::Buttrey - Cooper 1994 CiteRef::Callataÿ 1995b CiteRef::Buttrey - Buttrey 1997, is now generally accepted as worth to be pursuedCiteRef::Callataÿ 2005b. It requires a series of explanations and 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 diesCiteRef::Esty 1984 CiteRef::Esty 2006. 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 CiteRef::Callataÿ 1999 CiteRef::Faucher 2011). 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" CiteRef::Callataÿ 1993c. "High enough" means a ratio "n/o" of at least 3. Below 3, these calculations need some carefulness and are potentially dangerous below 2. They should preferably be avoided below a ratio of 1.5. Fortunately, a majority of coinages fall well above that limit, with 600 coinages showing a "n/o" ratio above 6 and even 45 above 30 [].

All these methods use a theoretical form of distribution. It was first and for a long time opted for a binomial (i.e. Gaussian, or symmetric) distribution (Good, Carter). This is clearly an unlikely model. In the 1980s, one moved to a Poisson distribution with a negative asymetric curve. At the end of the 2000s, it was argued that the most realistic model was simply the negative distribution CiteRef::Esty 2011. Following an intuition already expressed in 1987 CiteRef::Callataÿ 1987 and looking at hundreds of real distributions including the best attested ones for the Greek world providing a much better support than the Roman Republican ones mostly used so far, it has been recently argued that the most realistic distribution is likley to be a combination of a negative distribution (for the infantile mortality) followed by a binomial distributon (for the surviving specimens) CiteRef::Albarède et al. 2021. 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 they are for the coinages in the name of Alexander the Great, the cistophoric tetradrachms in Asia Minor or the Roman Republican denarii).

Much has been said about the accounts of the Amphictionic League, our only straightforward evidence. One can discuss about how to precisely interpret the epigraphic evidence but it gives in any case an average superior to 10,000 coins per obverse, far superior to the values proposed until then CiteRef::Kinns 1983 CiteRef::Marchetti 1999. Much has also been said about modern experimentations, even if I personally doubt that they could provide anything else than a minimal number CiteRef::Sellwood 1963 CiteRef::Faucher et al. 2009. 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 CiteRef::Callataÿ 2000c. 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.