The main ambition of this website is to estimate the volume of ancient coin production. This is a topic which, once hotly debated 1 2 3 4, is now generally accepted as worth to be pursued 5.
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. Two dozens of statistical methods have been proposed for this task whose results are generally considered as unproblematic as long as the ratio number of cois/number of dies is superior to 3 (which is the case for most ancient coinages) [[1]]. The second step is to multiply the original number of dies by what we think was the average production of a die. This is much more debatable. While it is not uneasy to produce a long list of reasons for which this average should have varied giving the illusion of a desperate level of uncertainties, things are hopefully less unsecure looking at coins. The nature of the metal and the size of the coins make indeed significant differences (but keeping inside the same level of magnitude), but 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 first step is to estimate the original number of obverse dies, because they generally deteriorate slower than the reverse dies (on this issues, see 6). 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 7. 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. With ratios regularly as high as 6, a vast majority of Hellenistic coinages fall well beyond that limit. 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 8.
The average productivity for an obverse die has been uniformly fixed here to 20,000 coins. Not that this number could be presented as secured (it is not) but because this is an estimate which, at the very most, could be divided or multiplied by two (from 10,000 to 40,000 coins), but very unlikely by three (from 6,666 to 60,000). 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 9 10. Much has also been said about modern experimentations, even if I personally doubt that they could provide anything else than a minimal number. 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 11. 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).
References
- ^ Buttrey, Theodore V. (1993), "Calculating ancient coin production : facts and fantasies," Numismatic Chronicle, 153, p. 335-351
- ^ Buttrey, Theodore V. - Cooper, Denis (1994), "Calculating ancient coin production II : Why it cannot be done," Numismatic Chronicle, 154, p. 341-352.
- ^ Callataÿ, François de (1995), "Calculating ancient coin production : Seeking a balance," Numismatic Chronicle, 155, p. 40-54.
- ^ Buttrey, S. E. - Buttrey, Theodore V. (1997), "Calculating ancient coin production, again," American Journal of Numismatics, 2nd ser., 9, p. 113-135.
- ^ Callataÿ, François de (2005), “A quantitative survey of Hellenistic coinages: recent achievements”, in Zosia H. Archibald, John K. Davies and Vincent Gabrielsen (eds.), Making, Moving and Managing. The New World of Ancient Economies, 323-31BC, Oxford, Oxbow, p. 73-91.
- ^ Callataÿ, François de (1999), “Étude de technique monétaire : le rapport ‘nombre de coins de revers/nombre de coins de droit’ à l'époque hellénistique”, Revue des Archéologues et Historiens de l’Art de Louvain, 32, p. 91-102.
- ^ Callataÿ, François de (193), “Estimation du nombre originel de coins : en augmentant l'échantillon...”, Acta Numismatica, 21-23 (Essays in honour of L. Villaronga), p. 31-48.
- ^ Callataÿ, François de (1987), “Statistique et Numismatique : les limites d'un apport”, Revue des Archéologues et Historiens d'Art de Louvain, 20 (Mélanges J. Trizna), p. 76-95.
- ^ Kinns, Philip (1983), "The Amphictionic Coinage Reconsidered", The Numismatic Chronicle 143, p. 1-22, pl. 1-4.
- ^ Marchetti, Patrick (1999), "Autour de la frappe du nouvel amphictionique," Revue belge de Numismatique, 145, p. 199-113.
- ^ Callataÿ, François de (2000), "Les taux de survie des émissions monétaires antiques, médiévales et modernes. Essai de mise en perspective et conséquence quant à la productivité des coins dans l’Antiquité," Revue Numismatique, 155, p. 87-109.
