Methodological Issues — SILVER (Die Studies Database, KBR Royal Library of Belgium)

Claims Supported by This Source

1. The estimation is a two-step process: first, the original number of dies is determined from the number of dies counted in the sample, and then this is multiplied by the average number of coins produced per die. Esty's alternative strategy is to estimate the coverage (the proportion of the total production represented by the dies appearing in the sample).
2. The subject is the obverse die (anvil side), because it wears out more slowly than the reverse die. Three values are needed: o, the number of dies observed in the sample; n, the number of coins in the sample; and f1, the number of singleton dies (dies known from only one coin).
3. In the 1970s and 80s, more than 20 methods based on probability calculations were proposed. When n/o is "sufficiently high" (at least 3), the results are similar. Below 3 requires caution, below 2 is dangerous, and below 1.5 should be avoided. For 600 coinages, n/o exceeds 6, and for 45, it exceeds 30.
4. Distribution models evolved from binomial (Good, Carter) → Poisson → to geometric distribution in the late 2000s (Esty 2011). Recently, a combination of a negative distribution (early breakage) and a binomial has been argued to be the most realistic. This explains why new dies continue to be found even in well-recorded samples, and why the proportion of singletons is large.
5. The average number of coins per obverse die is the most debatable point. Amphictyonic accounts give an average of over 10,000 coins per obverse die. Modern experiments only provide a lower bound. A comparison of survival rates suggests that the ancient average is unlikely to be below 10,000.
6. For simplicity, this site fixes the number at 20,000 coins per obverse die. This mainly applies to large silver coins such as tetradrachms. A factor of 2 (10,000–40,000) is possible, but not a factor of 3 (6,666–60,000).
7. References: Esty 1984 NC 144, pp. 180–183; Esty 2006 NC 166, pp. 359–364; Esty 2011 in Quantifying monetary supplies, pp. 43–58; de Callataÿ, Acta Numismàtica 21–23, pp. 31–48; Albarède et al. 2021 JAS 131

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