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. 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 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 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. "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 [[1]].

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 geometric model (i.e. a negative distribution) 11. Following an intuition already expressed in 1987 12 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 likely to be a combination of a negative distribution (taking into account the infantile mortality) followed by a binomial distribution (for the surviving specimens) 13. This explains why we still find new dies even with very well documented samples. And this is the reason why, similarly, we may observe a large percentage of singletons even with these well documented samples (on this, see 14).

Estimating 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 proves to be strikingly coherent (as they are for the coinages in the name of Alexander the Great, the cistophoric tetradrachms in Asia Minor or the Roman Republican denarii). And the same is true when looking at the largest issues in terms of monetary mass with Athens, the Alexanders, Rome, and the Parthians coming first, followed by the Ptolemies and the other Hellenistic kings, meanwhile civic coinages are (with a few exception such as Rhodes at the peak of its power) relegated well after [[2]].

But how to get a number for the average productivity of each die?

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 15 16.

Much has also been said about modern experimentations. They are of great interest but have not provide anything else than a minimal average number 17 18. Their results may be combined with the few attested 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] 19 or the bronzes of Apamea from the hoard of Aphrodisias [the number of 6,000 has been reported]).

There are also a few cases of extremely well dated instances of intensive production for which one can deduce a figure of c. 3,000 coins produced per day and per working unit if using an average of 20,000 coins per die (Mithridates Eupator in 89 and 75 BCE 20, the joint reign of Justin and Justinian during 17 weeks [April 4th–August 1st, 527 CE])21. It turns out that such a daily average of c. 3,000 coins fits with medieval and modern evidence.

Moreover and put in perspective, survival ratios argue for a high average productivity in ancient times, unlikely to be lower than 10,000 coins per die. Indeed, the fact that Greek coinages are, as a rule, better documented today than medieval coinages and even modern coinages (often 10 coins per obverse die for Greek coinages to compare with much lower values for recent times) ask to adjust our ideas as it turns out from written sources that the survival ratio for medieval coinages is c. 1 out of 5,000/10,000 produced coins while it is close to 1 out of c. 2,000/3,000 for eighteenth century coinage 22. Postulating then an average output per die inferior to 10,000 for ancient coinages forces to assume a survival ratio superior to 1 out 1,000 (which is in turn very high if put in perspective).

For the sake of simplicity, the average productivity for an obverse die has therefore been uniformly fixed here to 20,000 coins. It is a stopgap measure that applies primarily to large silver denominations such as tetradrachms. This is not a 'rigth number' but an average value which may be divided or multiplied by two (from 10,000 to 40,000 coins), but not 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 may be adjusted depending of the kind of coinage

Estimating ancient monetary productions in modern weights of silver

All the coin productions in precious metals (gold, electrum, and silver) have been converted in weights of silver (tons and kilograms). This appears as much more convenient than to express the final results in 'equivalents of obverse dies for Attic drachms' (or any similar monetary comparison). For the sake of simplicity too, it has been decided to proceed mechanically attributing to gold and electrum 10 times the value of silver (whatever the real ratio of the time and the area). Bronze issues have been logically excluded from that kind of calculations due to our great ignorance of their real legal values.


  1. ^  Buttrey, Theodore V. (1993), "Calculating ancient coin production : facts and fantasies," Numismatic Chronicle, 153, p. 335-351
  2. ^  Buttrey, Theodore V. - Cooper, Denis (1994), "Calculating ancient coin production II : Why it cannot be done," Numismatic Chronicle, 154, p. 341-352.
  3. ^  Callataÿ, François de (1995), "Calculating ancient coin production : Seeking a balance," Numismatic Chronicle, 155, p. 40-54.
  4. ^  Buttrey, S. E. - Buttrey, Theodore V. (1997), "Calculating ancient coin production, again," American Journal of Numismatics, 2nd ser., 9, p. 113-135.
  5. ^  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.
  6. ^  Esty, Warren W. (1984), "Estimating the size of a coinage," Numismatic Chronicle, 144, p. 180-183.
  7. ^  Esty, Warren W. (2006), "How to estimate the original number of dies and the coverage of a sample," Numismatic Chronicle, 166, p. 359-364.
  8. ^  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.
  9. ^  Faucher, Thomas (2011), "Productivité des coins et taux de survie du monnayage grec," in François de Callataÿ (ed.), Quantifying monetary supplies in Greco-Roman times, Bari, Edipuglia, p.113-126.
  10. ^  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.
  11. ^  Esty, Warren W. (2011), "The geometric model for estimating the number of dies," in François de Callataÿ (ed.), Quantifying monetary supplies in Greco-Roman times, Bari, Edipuglia, p. 43-58.
  12. ^  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.
  13. ^  Albarède, Francis - Callataÿ, François de - Debernardi, Pierluigi - Blichert-Toft, Janne (2021), “Model for ancient Greek and Roman coinage production”, Journal of Archaeological Science, 131, DOI 105406 (
  14. ^  Callataÿ, François de (2023), "The Yehud Coinage: An Essay on Quantification", in Haim Gitler - Catharine C. Lorber - Jean-Philippe Fontanille, The Yehud Coinage. A Study and Die Classification of the Provincial Silver Coinage of Judah, Numismatic Studies and Researches XII, Jerusalem, p. 307-334.
  15. ^  Kinns, Philip (1983), "The Amphictionic Coinage Reconsidered", The Numismatic Chronicle 143, p. 1-22, pl. 1-4.
  16. ^  Marchetti, Patrick (1999), "Autour de la frappe du nouvel amphictionique," Revue belge de Numismatique, 145, p. 199-113.
  17. ^  Sellwood, David G. (1963), "Some experiments in Greek minting technique," Numismatic Chronicle, 7th ser., vol. 3, p. 217-231, pl. 23-25.
  18. ^  Faucher, Thomas - Téreygeol, Florian - Brousseau, Louis - Arles, Adrien (2009), "A la recherche des ateliers monetaires grecs : l'apport de l'experimentation," Revue Numismatique, 165, p. 43-80.
  19. ^  Price, Martin J. (1989), "The Larissa, 1968 hoard (IGCH 237)," in Georges Le Rider, Kenneth Jenkins, Nancy Waggoner and Ulla Westermark (eds.), Kraay-Mørkholm essays : numismatic studies in memory of C. M. Kraay and O. Mørkholm, Louvain-la-Neuve, p. 233-244.
  20. ^  Callataÿ, François de (1997), L'histoire des guerres mithridatiques vue par les monnaies, Numismatica Lovaniensia 18, Louvain-la-Neuve, XIII + 481 p. et 54 pl.
  21. ^  Metcalf, William E. (1988), "The joint reign gold of Justin I and Justinian I," in William E. Metcalf - Wolfgang R. O. Hahn (eds.), Studies in early Byzantine gold coinage, New York, p. 19-27.
  22. ^  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.