I'm researching a group of very rare coins and I would like to estimate the size of the original issue or the number of dies involved in the isssue. I know of: 21 coins in existance. I identified: 3 die-links (obverse and reverse) 2 obverse die-links 1 reverse die-link So with 6 out of 21 coins showing at least one die-link, I imagine that the overall issue was rather small, i.e. that only relatively few dies were involved. Is there a way to get a more formal estimate out of these numbers?
Hill G. F., "The frequency-Table", NC 1924, p. 76-85. de Callataÿ F.,"Calculating ancient coin production: seeking a balance", NC, 155 (1995), p.289-311.
Do you like videos? Warren Esty gave a talk at the ANS on this. The talk is online. You can also read his 2006 paper in the Numismatic Chronicle at https://www.academia.edu/1293727/Ho...l_number_of_dies_and_the_coverage_of_a_sample (it is also on JStor).
I would think there are a tremendous amount of variables. A guess could statistically calculated, but real world variable also would be crucial. Examples would be soil in which they were deposited, (some soils less conducive to preservation), metal they were struck in, (nickel famous for destroying dies, bronze next bad, then silver and then gold), economic situation afterwards, (if stable currency leads to lower survivals, economic trauma leads to hoarding and more survival), political situation, (did new rulers intentionally melt down previous issues?), etc. Any calculation would need to have extremely wide bands of possibility due to these and other factors.
See here for lots of lovely formulae: https://glebecoins.net/paleos/Notes/Estimating_Die_Numbers/estimating_die_numbers.html Ross G.
Thanks a lot for all the information. I'm afraid, that my tiny sample does not permit any quantification of the number of dies involved.
According to my calculations the total number of dies is 98. Cover ratio = 1- 12/21 Total dies = 36/cover ratio * (1+12/(2*36) = 98 According to one article, this estimate is probably too low and I should incorporate a "spread factor" to account for low output dies, not represented in the sample. Does 98 dies sound reasonable?
According to my calculations, there is a 95% chance that the original number of dies lies between 54 and 316. This is a large confidence interval, reflecting the fact that the sample is very small.
Hi Tejas I don't quite follow your calculation here - what are values for d1 (the number of dies occurring only once, and d (the total number of different dies)? You need separate figures for the obverse and reverse dies. Ross G.
Hi Ross, Ok, I didn’t use separate figures for obverse and reverse dies. Thanks for the clarification. I have redone the calculations: Obverse dies = 54, with 95% confidence interval 27 - 133 Reverse dies = 89, with 95% confidence interval 26 - 275 Does that sound plausible? I guess the fact that the number of reverse dies is much higher than obverse dies is plausible. Best Dirk
If the estimated numbers of obverse and reverse dies is correct, what could be derived from them? Was it a brief and small issue? On stylistic grounds I identified the work of 8 different celators in the total group of 21 coins. The stylistic differences among the 8 celator-groups are very large and the stylistical differences within the 8 celator groups are very small, i.e. the coins within a celator group are remarkably similar to the extend that it is sometimes difficult to decide if coins are from identical dies or not.
Your figures sound quite reasonable. I'd call this a medium sized issue although we don't normally see such a large number of different celators for an issue like this. Perhaps this suggests that this was an issue done in a hurry for some reason. Ross G.
At a Roman mint when die-engravers are working day in and day out cutting dies and having developed their skills, possibly over years, we may be able to distinguish different styles. There is one Republican issue commonly divided into two styles attributed to two engravers. But when the issue is small it is likely there was one engraver getting better and better, or changing his ideas about how it should look, or just not being consistent. It is known that it doesn't take long to engrave a die (hours, not days) and one engraver can easily keep a small mint supplied. At, say, 20,000 coins per die (a common estimate) and 5,000 coins struck by one team per day, you can see there is no need for more than one engraver.
I agree with Valentinian - 8 celators sounds more than a little odd. But then I haven't seen the actual coins. Ross G.
I should have been a bit more transparent regarding the coins that I am researching. I'm looking at so called Half-Siliquae of Sirmium, which were minted sometime around AD 500. I currently know of 21 coins, 16 of which are in my collection, which puts me in a good position to do some die analysis. From pictures alone, it can be very hard to decide whether dies are identical or just very similar. I feel that I'm trying to squeeze out a lot of information from very small basis of evidence, but it is all we have. What is sorely missing is find spot evidence. There is no doubt that the original series started out in Sirmium, as indicated by the central letters SRM on the reverse. However, I imagine that imitations of these coins may have been made in two other nearby towns (Singidunum and Bassiniae). Interestingly, I have one specimen with findspot in southern Germany, near a place were some 20 Sirmium Quarter-Siliquae have been scientifically excavated in a grave. So sometimes these coins got displaced, but there is no doubt that they were made for local use in and around Sirmium. The differences in styles are so large that it is difficult to believe that only one or two craftsmen were at work, who improved over time or for some reason experimented with different styles. Pictures can be seen in my article here (which does not include all known coins): (99+) (PDF) The "Sirmium Group" - an overview | Dirk Faltin - Academia.edu One important question is when these coins were made. The region and in particular Sirmium was strategically important and prestigious as former birthplace and base of Roman emperors. However, in around 500 the region was highly volatile and subject to raids by Germanic Heruls, Langobards and the hords of Mundo, a nephew of Traustila, who had held Sirmium in the 470s as king of the Gepids. In AD 500 the city was held by Traustila's son Thrasaric and further to the east roamed another Gepidic warlord called Gunderith who's relationship with Thrasaric is uncertain. In 504, Theoderic's Goths, who had held Sirmium before Traustila, retook the city, possibly to preempt an alliance between Thrasaric and Gunderith. During the campaign Theoderic's "generals" Pitzia and Herduic aided Mundo against a Roman force of Bulgar federates under a general Sabinianus, which in turn soured relationships between Theoderic and Anastasius. It was in this environment that the need for silver coins arose in Sirmium, perhaps because things stabilized for a while and trade began to flourish. Indeed, maybe the time around 500 was volatile, but incomparison to previous decades when the city was overun by the Huns, it was relatively stable. We know of Quarter-Siliquae, which started out as pure imitations of Gothic coins from Milan and we know of the extremely rare Half-Siliquae, which are an independent coinage, that makes to reference to the Gothic kingdom, but instead seems more in line with East Roman silver. I like Ross' idea that the Half-Siliquae were produced in a hurry and only for a short period of time. It is not impossible that they were minted under Thrasaric, if only to create the appearance of a return of Roman civilization to a once glorious city that had been ravaged by war. We should not forget, that these barbarian kings were eager to emulate Rome. Thrasaric had fled to Constantinople after the defeat of 504. His recently discovered grave stone, put his Roman title "comes domesticorum" before his title as king of the Gepids. Best Dirk
