Estimation of the number of original dies 

To calculate the original number of dies that were used to produce this series, we will use the statistical procedures published by various authors.  The estimates are based on the number of coins and different dies that appear in the database.

These two parameters are enough to apply the methods of Guilbaud and Carter, while the method of Goods needs one more piece of information, the singletons, which is the number of dies which we know from only a single coin.  All these statistics are calculated automatically in the data base each time a new coin image is added.

The precision of the estimation improves as the number of coins found per die increases.  A ratio between 2 and 3 known coins per die is considered fairly reliable, if the ratio is greater than 4 then very possibly all the original dies have been accounted for.

Emperor Coins
Known Dies
Number of Original Dies
Estimated by Goods' Method
Dies Stand.Dev. Singletons %Known
Augusto 255 65 3,92 68 2 10 96,1%
Vespasiano 251 72 3,49 77 3 17 93,2%
Tito 204 47 4,34 49 2 10 95,1%
Nervae 104 19 5,47 20 1 5 95,2%
Traiano 310 87 3,56 93 3 21 93,2%
Hadriano 68 22 3,09 26 2 11 83,8%
Antonino 413 92 4,49 97 2 22 94,7%
Marco 72 18 4,00 19 1 3 95,8%
Commodo 181 44 4,11 46 2 6 96,7%
Severo 83 19 4,37 20 1 4 95,2%
Alexandro 235 49 4,80 58 2 37 84,3%
Total 2176 534 4,07 572 6 146 93,3%


(*) In this cells the global estimation is reflected, not the sum of partial estimations.
Original Reverse Dies Number Estimated
Type Known coins Known Reverses  Coins/ Dies
Estimated Reverses Stand.Dev.
Singletons % Known Reverses
Aquila 847 195 4,34 206 4 47 94,5%
Pira 1329 336 3,96 361 5 92 93,1%
Total 2176 531   567 6 139 94%


An example - Severus Alexander

Let us take as an example the restitution coins of Severus Alexander whose coins are not the most common within in the database, but have a high ratio of coins to dies.

It therefore stands that an estimation of the original number of dies for this emperor is of greater reliability than in the case of Antoninus Pius, with a greater volume of documented coins, but with a smaller coin-to-die ratio because of the large number of different dies identified.

The statistical methods predict that, in addition to the 36 dies that we know for Alexander Severus, we can expect there are an additional 5 or 6 not yet registered.

Since we associate a coin-to-die ratio greater than 4 with the identification of all dies, we would expect that by documenting from 165 to 200 coins for Alexander Severus, the remaining unknown dies would appear.

Minting considerations

If considering the entire series of Divi coins, a general sample greater than 2000 coins would surpass the ratio of 4 coins per die.  A sample of that size would allow us to identify practically all of the original dies, of which today, with a sample of 1000 coins, we know about 80%.

Based on our current data, it appears that there were 500-550 obverse dies, and 450-500 reverse dies, distributed between the eleven emperors.

Having estimated the number of dies that composed the series in its origin, we can then attempt to calculate the overall volume of Divi coinage.

According to the estimations of Duncan-Jones  on the number of dies produced during various reigns, the annual production of between 2000 and 3000 dies for the silver coinage would be acceptable for this period.

Whatever the precision of this estimate, it is understood that in our series we have a reduced number of original dies compared to the annual volume of production for mints of the time.

We can conclude that a mint working full time spent only a few months to produce our Divi series coinage.

Mattingly proposed for this period, the existence of 6 officinae in the Roman mint with each of the consecrated emperors assigned to just one officina .  This extensive operation of all officinae producing a total of 500 dies would be expected to take 2 or 3 months.

In a case where each emperor’s coins were only produced by a single officina, then die-links between different the types of coins would be extremely rare, and the die-links should be limited to only those coins of the same restored emperor or another emperor produced within the same officina.

In our study’s sample of 1400 coins, 81% have their dies chained in a single tree that contains all eleven emperors.

Therefore, our hypothesis is that this series was produced by only a single officina of the mint.  This requires that we multiply the time period of operation by 6, with a resulting estimate of 12-18 months for the striking of the Divi series coins.   This time frame matches with the chronologies previously espoused, and would place the production of the Divi series between the autumn of 250 A.D.  and the winter of 251 to 252 A.D.