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To calculate the original
number of dies that have been used to produce this series, we will use the
statistical procedures published by several authors, which we find perfectly
detailed in the work of Leandre Villaronga (1).
The estimates are based on the proportion between the number of known coins of a
certain type and the number of dies used to produce this type; we collect this
information in the database. For example:
we have registered 200 coins with the obverse of a specific emperor and in this
set we have observed a total of 40 different dies; this would give us an average
proportion of 5 coins for each die.
These two parameters are sufficient to apply the Guilbaud and Carter methods,
while the Goods method requires additional information: the number of singleton
dies, which are the dies of which we know only a single coin.
All of these statistics are automatically calculated in the database every time
a new coin is added.
The precision of the estimate improves as the number of coins registered in the
database increases and the coin/die ratio increases.
According to Villaronga (Op.Cit, p.98-102), a proportion between 2 or 3
coins per die is considered quite reliable in order to know the original number
of dies for this type; if the ratio is greater than 4, we have around a 95%
chance of knowing all the original dies for that type.
The following tables show the current status of the estimates.
| Emperor |
Coins Registered |
Diferent Dies Known |
Rate Coins/ Known Dies |
Number of Original Dies Estimated by Goods' Method |
|||
| Dies | Stand.Dev. | Singletons | %Known | ||||
| Augusto | 318 | 69 | 4,61 | 72 | 2 | 12 | 96,2% |
| Vespasiano | 316 | 76 | 4,16 | 80 | 2 | 15 | 95,3% |
| Tito | 250 | 50 | 5,00 | 51 | 1 | 7 | 97,2% |
| Nervae | 135 | 19 | 7,11 | 19 | 1 | 3 | 97,8% |
| Traiano | 408 | 91 | 4,48 | 95 | 2 | 16 | 96,1% |
| Hadriano | 90 | 24 | 3,75 | 28 | 2 | 12 | 86,7% |
| Antonino | 541 | 94 | 5,76 | 96 | 2 | 14 | 97,4% |
| Marco | 98 | 18 | 5,44 | 18 | 1 | 1 | 99,0% |
| Commodo | 231 | 47 | 4,91 | 49 | 1 | 8 | 96,5% |
| Severo | 107 | 19 | 5,63 | 20 | 1 | 4 | 96,3% |
| Alexandro | 304 | 51 | 5,96 | 53 | 1 | 10 | 96,7% |
| Total | 2798 | 558 | 5,01 | 579 | 5 | 102 | 96,4% |
(*) In Total cells the global estimation is reflected, not the sum of
partial estimations.
| Original Reverse Dies Number Estimated | |||||||
| Type | Known coins | Known Reverses |
Coins/ Dies Rate |
Estimated Reverses |
Stand.Dev. +/- |
Singletons | % Known Reverses |
| Aquila | 1072 | 206 | 5,20 | 217 | 3 | 52 | 95,1% |
| Pira | 1726 | 361 | 4,78 | 383 | 4 | 100 | 94,2% |
| Total | 2798 | 567 | 600 | 5 | 152 | 95% | |
An example - Nerva
Let's take as an example
the restitution coins for Nerva which, although not the most abundant in the
database, have a high proportion of known coins by die (7.11).
Therefore, an estimate of the original number of Nerva dies is considered to be
more reliable than in the case of Antoninus Pius which, despite having a greater
volume of documented coins, has a smaller ratio of known coins per die (5.76),
due to the large number of different dies identified so far.
Statistical methods predict that these 19 known dies could be 20 originally with
a reliability of 96.4%.
Minting considerations
If we consider the entire
set of registered DiviSeries coins, we have a sample close to 3000 coins,
exceeding the global proportion of 5 coins per die; being higher than that value
in most subtypes.
A sample of this size, and with this proportion of coins/dies, allows us to
identify practically all of the original dies, with a reliability greater than
95%. In fact, rarely when incorporating new coins into the database do we find a
new die.
According to our current data, we estimate that around 600 obverse dies were
produced and a few more for the reverse, distributed among the different types.
At the end of the chapter on mint attribution and issuing authority we noted a
certain constant regarding the participation of DiviSeries coins within
the hoards closed after the reign of Trajan Decius, we estimated it between 2%
and 3%. Now that we also have an estimate of the total number of original dies
for Divi, we can think about making a rough estimate of the total volume
for antoninians that were produced during the reign of Decius. In this estimate
we will not differentiate between the coins that Decius minted in his name and
those that he minted in the name of the empress or her children, in the same way
that we will not differentiate by mint; since when studying the volumes of coins
within the hoards we have not differentiated by person represented on the
obverse or mint of origin.
This opens up the possibility of, by extrapolation, estimating the volumes of
emissions for other reigns. We understand that the error in the estimates can
increase if we work exclusively with the presence of coins in hoards. That is
why we would have to carry out studies of original dies for certain series in
order to limit the error, which the calculation only through hoards can imply
and which is much greater than the error that occurs when applying statistical
methods based on the proportions of coins/dies.
From what we have seen so far, if the proportion in hoards of coins between the
DiviSeries and the issues in the name of Decius and his family is 2.5% (1
to 40), we can make a first estimate of 24,000 (600 x 40) as a number of
original dies for the issues ordered by Trajan Decius.
Given the years that I have spent calculating the original dies of the
DiviSeries, the proposed new work for Decius' antoninians is a task that
exceeds the effort of one person. The proposal remains made as a line of work
for future generations.
(1) Villaronga i Garriga, L., Statistics applied to Numismatics, Spanish
Numismatic Association, Barcelona, 1985, pp 98-102.