Die Studies - What's the Point?

[John Conduitt]

I have a few questions about die studies. Obviously, a die study can tell you the chronology of the dies and perhaps even the date of the coin. But there are a lot of unknowns that make interpreting the results tricky.

- I’ve read obverses last twice as long as reverses. So, there should be twice as many reverse dies. But often they are much more even than that. Does that mean they stopped using obverses more quickly than necessary or there should be more reverses out there to be found?

- If a mule exists, does that say anything about how close in time the two series were struck? How likely is it that they just left the die in storage for months or years? Has that been shown to have happened? What if the die had a break – would they still keep it for a different issue?

- How different can two coins be and yet be die matches? I understand the die might be re-cut, but if it isn’t, some dies are surely the same (due to die breaks etc) and yet look different. How different can the strike or wear make the style look? Or is there a point when you say the die breaks are more likely to be coincidental?

- Is it really possible to determine an engraver by style? The Roman ‘template’ seems to have been very prescriptive. Some coins look incredibly similar even when they can’t share an engraver. Were some engravers just really good at copying? With late 4th Century coins, the simplistic style doesn't help, but they can look very different. Yet at other times they come very close to each other even when it's not likely to be the same engraver.

I assume the answers are mostly ‘possibly’ but that doesn’t really help, since if everything’s on the balance of possibilities it quickly becomes meaningless.

Here is a reverse die match. I think.

Helena Follis, 324-325

Londinium. Bronze, 20mm, 2.93g. Bust of Helena, wearing necklace and mantle, right; FL HELENA - AVGVSTA. Securitas, draped, standing left, raising pallium with right hand and lowering branch with left hand; SECVRITAS - REIPVBLICE; PLON in exergue (RIC VII, 299).

Helena Follis, 324-325

Londinium. Bronze, 19mm, 2.99g. Bust of Helena, wearing necklace and mantle, right; FL HELENA - AVGVSTA. Securitas, draped, standing left, raising pallium with right hand and lowering branch with left hand; SECVRITAS - REIPVBLICE; PLON in exergue (RIC VII, 299). Found in Yeovil.

[Heliodromus]

1 hour ago, John Conduitt said:

- I’ve read obverses last twice as long as reverses. So, there should be twice as many reverse dies. But often they are much more even than that. Does that mean they stopped using obverses more quickly than necessary or there should be more reverses out there to be found?

Well, something else that die studies are useful for is estimating number of original dies as a function of number of coins under study and number of distinct dies used to strike them. Warren Esty developed an estimation formula that is often used:

https://www.academia.edu/573364/The_Geometric_Model_for_Estimating_the_Number_of_Dies

So, I guess it is what it is - whatever the ratio of estimated obverse to reverse dies given by such a formula must be close to the truth. I wonder how much this ratio differs between different mints, time periods, etc ?

For anyone unaware, the reason for the different lifetime of obverse vs reverse dies is due to the obverse usually being the bottom die and the reverse the top one, taking the brunt of the hammer strike.

1 hour ago, John Conduitt said:

- If a mule exists, does that say anything about how close in time the two series were struck? How likely is it that they just left the die in storage for months or years? Has that been shown to have happened? What if the die had a break – would they still keep it for a different issue?

I can only recall seeing mules (during Constantine's time) among types belonging to the same issue, as might be expected if multiple dies are in use at the same time. Even in (rare?) cases where old dies were kept for potential reuse, I'd imagine they were typically not kept in the same area as the dies in daily use, so it'd seem unlikely to have a non-deliberate reuse of an old die (but would be interesting to see one!).

1 hour ago, John Conduitt said:

- How different can two coins be and yet be die matches? I understand the die might be re-cut, but if it isn’t, some dies are surely the same (due to die breaks etc) and yet look different. How different can the strike or wear make the style look? Or is there a point when you say the die breaks are more likely to be coincidental?

I think the general idea is to look for multiple points of almost-certain matches, or any slam-dunk non-match, and pretty much ignore any points where it's unclear if they are the same or not. Different strikes can certainly make things individual letters of the legend look quite different, even when it's apparent that they are from the same die.

Maybe that Helena is a double die match ? I'm not seeing any super-obvious points of non-agreement.

 

Edited December 20, 2023 by Heliodromus

[Rand]

A lovely pair @John Conduitt

 

I love die links and watching the progression of coin minting. This could be my way of playing a puzzle game or my personality trait. Different people enjoy collecting in different ways.

However, the die studies could benefit numismatics as science and broader historical research.

The number of dies reflects the number of coins produced, which may describe the economic state or historical events, such as preparation for military campaigns.

Obverse/reverse ratios vary depending on manufacturing technology. Overall, for Anastasian coins, the number of obverses and reverses was comparable. The 2227 solidi I have had time to sort by dies were produced using 1268 obverse and 1276 reverse dies. However, some Western series have multiple reverse dies per obverse die.

Die links help to understand how mints worked. For example, there is a huge discrepancy in the number of Anastasian solidi produced by different officianae. It is possible that officianae were not just numbers assigned to mint workshops but had additional purposes, perhaps producing coins for particular needs.

There are distinct engraver styles for Anastasian solidi. Dies produced by different engravers are often die-linked, so more than one die engraver was employed simultaneously.

Concerning the Anastasian period Western mints, die studies help to say whether coins were produced by established city mints (die/style progression) or by temporary mobile mints following Barbaric armies. The latter coins were often produced from a single die pair - we need a die analysis to calculate the probability of the existence of a second die. For example, if there is a type six with known coins all from the same die pair, the chance of other dies being used is less than 5% (which means unlikely). 

During the Anastasius period, dies were usually replaced rather than repaired, except possibly some Burgundian and other Western coins. 

For some coins of the Anastasian periods, only die links prove that differently-looking dies were part of the same issue.

Unfortunately, I do not own enough coins to illustrate all those points.

PS. Some of my comments overlap with the previous reply. I did not type fast enough.
 

Edited December 20, 2023 by Rand

[Heliodromus]

On the subject of die matches, here's a (mildly 🙂) interesting one I recently bought.

This is a double die match to this specimen in the ANS collection:

What's interesting here is that double die matches are not at all common among LRBs (even single die matches can be very hard to find among common issues), while they are actually common among very rare issues where there were few dies (maybe just one or two in some cases) in the first place.

There's no a priori reason to think that this type would be especially scarce for Constantine, but it does seem to be (other than these two I've only noted one other on Lech's Not In RIC site), and this double die link tends to support that.

 

[Ocatarinetabellatchitchix]

1 hour ago, John Conduitt said:

- Is it really possible to determine an engraver by style?

This is an interesting study about the different engravers. Sorry but it’s in French…

« We will try, based on the coins in this collection, to identify, by workshop, the different engravers who officiated. It is also possible that a workshop had several engravers under the direction of a master engraver, which can explain the slight differences that can be encountered for the same type of coin. »

https://collection-cdoue-romaines.jimdofree.com/les-graveurs-sous-gallien/

[John Conduitt]

34 minutes ago, Heliodromus said:

Well, something else that die studies are useful for is estimating number of original dies as a function of number of coins under study and number of distinct dies used to strike them. Warren Esty developed an estimation formula that is often used:

https://www.academia.edu/573364/The_Geometric_Model_for_Estimating_the_Number_of_Dies

So, I guess it is what it is - whatever the ratio of estimated obverse to reverse dies given by such a formula must be close to the truth. I wonder how much this ratio differs between different mints, time periods, etc ?

Yes Warren has written and broadcast quite a bit about die studies, which is very helpful. As he says, the formula relies on a minimum volume of data and I wouldn't be reaching that, but he gives a few ways to calculate the same thing so you can work out a sensible estimate even if it's statistically shaky.
 

42 minutes ago, Heliodromus said:

Maybe that Helena is a double die match ? I'm not seeing any super-obvious points of non-agreement.

Helena's London dies are few in number but they're very similar and the coins are mostly corroded, so it's not easy. Her portraits all look the same and yet somehow different, but it's hard to pinpoint specific differences. Any weakness of strike (how many strands of hair?) or knocks from circulation make them look different when they're not. The legends are often easier. I think the obverses of these two are different because the legend of the second comes further down on the right - the N and A are under her chin, not just the A. But as you say, lettering can look different because of the strike, which makes this potentially unreliable. I've certainly seen letters that look bigger or closer together even when the die must be the same.
 

52 minutes ago, Heliodromus said:

I can only recall seeing mules (during Constantine's time) among types belonging to the same issue, as might be expected if multiple dies are in use at the same time. Even in (rare?) cases where old dies were kept for potential reuse, I'd imagine they were typically not kept in the same area as the dies in daily use, so it'd seem unlikely to have a non-deliberate reuse of an old die (but would be interesting to see one!).

Yes so any mule would be deliberate, and probably just run on from the previous issue if the reverse had broken but the obverse still had life left in it. In the early Empire it's a bit easier as they had to get the COS, DES or whatever else right but later on they could re-use an obverse without anyone noticing. Presumably, in gold they would often have relatively fresh dies left over.

[John Conduitt]

39 minutes ago, Rand said:

The number of dies reflects the number of coins produced, which may describe the economic state or historical events, such as preparation for military campaigns.

Obverse/reverse ratios vary depending on manufacturing technology. Overall, for Anastasian coins, the number of obverses and reverses was comparable. The 2227 solidi I have had time to sort by dies were produced using 1268 obverse and 1276 reverse dies. However, some Western series have multiple reverse dies per obverse die.

I've read that a die could produce between 1 and 15,000 coins. But how much does that vary by type of coin? I presume a solidus die would be less likely to be used to destruction but they certainly got through more than one per issue so maybe not. But then gold might be easier on the die.

It's interesting that the ratios can be so different. I'm not sure what they were doing to make the reverse last as long as the obverse, unless they were able to turn the dies over so the obverse took just as much abuse.

46 minutes ago, Rand said:

There are distinct engraver styles for Anastasian solidi. Dies produced by different engravers are often die-linked, so more than one die engraver was employed simultaneously.

I suppose what I need to know is whether it is possible to tell if the same engraver was responsible for two different dies, and definitely not responsible for dies that aren't similar. Anastasian dies all look very similar anyway and I don't know how much of the similarity or difference (which is presumably obvious when you've seen a lot) is down to a style the individual engraver can repeat (and so would be like a signature), or just how each turns out when made by any of the team of engravers, who were presumably all trained by the same people to engrave in a certain way.
 

54 minutes ago, Rand said:

Concerning the Anastasian period Western mints, die studies help to say whether coins were produced by established city mints (die/style progression) or by temporary mobile mints following Barbaric armies. The latter coins were often produced from a single die pair - we need a die analysis to calculate the probability of the existence of a second die. For example, if there is a type six with known coins all from the same die pair, the chance of other dies being used is less than 5% (which means unlikely). 

For some coins of the Anastasian periods, only die links prove that differently-looking dies were part of the same issue.

I wonder if that's true of other army mints. I imagine it would be a bit of a risk only taking one die pair, but they probably didn't take a team of engravers with them.

Does a die link prove it was the same issue? From what Heliodromus says, probably yes.

[Heliodromus]

14 minutes ago, John Conduitt said:

Yes so any mule would be deliberate, and probably just run on from the previous issue if the reverse had broken but the obverse still had life left in it. In the early Empire it's a bit easier as they had to get the COS, DES or whatever else right but later on they could re-use an obverse without anyone noticing.

During Constantine's time there were often different reverse types for the caesars vs augusti as part of same issue, or sometimes different reverses for different emperors, so we do sometimes see non-intentional pairings such as these (not my coins).

[John Conduitt]

48 minutes ago, Heliodromus said:

What's interesting here is that double die matches are not at all common among LRBs (even single die matches can be very hard to find among common issues), while they are actually common among very rare issues where there were few dies (maybe just one or two in some cases) in the first place.

There's no a priori reason to think that this type would be especially scarce for Constantine, but it does seem to be (other than these two I've only noted one other on Lech's Not In RIC site), and this double die link tends to support that.

It is a bit of a paradox. At first sight it seems logical that if there were very few coins made, they would be more double die matches, as there are fewer dies to be paired up. But if a die can make 15,000 coins, every die pair could make up to 15,000 double die matches whether it was rare or not. It's not like they switched the dies around regularly. So either the rarer coins have survived in proportionately higher numbers than the common coins, or I suppose it's just easier to spot double die matches when you only have half a dozen coins to check.

[Heliodromus]

58 minutes ago, John Conduitt said:

Helena's London dies are few in number but they're very similar and the coins are mostly corroded, so it's not easy. Her portraits all look the same and yet somehow different, but it's hard to pinpoint specific differences. Any weakness of strike (how many strands of hair?) or knocks from circulation make them look different when they're not. The legends are often easier. I think the obverses of these two are different because the legend of the second comes further down on the right - the N and A are under her chin, not just the A. But as you say, lettering can look different because of the strike, which makes this potentially unreliable. I've certainly seen letters that look bigger or closer together even when the die must be the same.
 

Yes, of course you're right. I misread and thought the obverses were the same and so was looking at the reverse.

Edit: In fact I was looking into these myself a while back, and hadn't noticed a single obv die link among 12 specimens I had photos of.

 

Edited December 20, 2023 by Heliodromus

[John Conduitt]

54 minutes ago, Ocatarinetabellatchitchix said:

This is an interesting study about the different engravers. Sorry but it’s in French…

« We will try, based on the coins in this collection, to identify, by workshop, the different engravers who officiated. It is also possible that a workshop had several engravers under the direction of a master engraver, which can explain the slight differences that can be encountered for the same type of coin. »

https://collection-cdoue-romaines.jimdofree.com/les-graveurs-sous-gallien/

Thank you. It's the sort of analysis I'm a bit afraid to make, because it determines the engraver by the style even when there is not such a huge difference. Some of those later Rome coins are very close and I can imagine the engraver just deciding to make some changes. Are they by different people? I can look at three paintings by Van Gogh and see three different artists or three identical artists depending on the period of his life they come from. But if you line up some of his portraits or still life studies next to Cezanne's I might struggle to separate them.

[Heliodromus]

9 minutes ago, John Conduitt said:

It is a bit of a paradox. At first sight it seems logical that if there were very few coins made, they would be more double die matches, as there are fewer dies to be paired up. But if a die can make 15,000 coins, every die pair could make up to 15,000 double die matches whether it was rare or not. It's not like they switched the dies around regularly. So either the rarer coins have survived in proportionately higher numbers than the common coins, or I suppose it's just easier to spot double die matches when you only have half a dozen coins to check.

Yes - I suppose the double die links are out there too for the common types, but the chance of finding them is small without inspecting huge numbers of coins, whereas for the rare types you may have trouble finding one in the first place, but if you do it's got a good chance of being linked to the other known specimens, which will be easy to find by way of having attracted attention.

My Constantine festival of Isis type that I recently posted is a case in point. Took a long time to find one, but it turns out to be a double die link to the only two other specimens I'm aware of - thanks to someone else having scoured museums looking for them to write a paper!

 

[Rand]

My speculations, but factors influencing the longevity of dies may include:

• The quality of dies, for example, using hardened alloys
• The temperature of the flan. Gold is soft to start from and can be softened further with optimal heating/transfer of the flan from heat to evil. Imperial coins usually have an area of flatness over the rim, which typically does not affect the legend - likely from tongues. 
• Workflow controls. Dies may have been used for a predefined number of days or coins.

 

I am unsure if solidus dies were used till destruction. There are plenty of very damaged Western dies. I do not see very worn imperial dies. Even when imperial dies are broken, I usually cannot find a coin without the damage. It looks like the die was defective during manufacturing or early during use. Coins below were bought from different dealers on different years.

Anastasian dies may look similar, but this is like handwriting in the same language - same patterns, but we can easily see different hands. Over hundreds of dies, it becomes easier to see different hands. The image can be split into many small parts (details of the helmet, shield, horse and rider on the shield, the distance between chest bands and so on). It should be possible to develop AI algorithms, but even without the difference between engravers, it can be quite obvious. This is with exceptions, of course.

Army mints likely varied in nature. Mints travelling with Augustus were probably very sophisticated. It could have been different with a Barbarian army when they only minted coins from gold booty from a captured town to share between the combatants. Possibly, they did not have gold for more than a die pair. Some dies can be very broken. For example, I really like this coin even if it is not very attractive. It has a fascinating story.

Does a die link prove it was the same issue? Sometimes, it certainly does. I know of an example of a small issue (two coins and both not mine) with a different reverse style, which I would not otherwise link. This is a distinct issue from a Western mint with a T on the emperor's chest, and there is no reason to believe it was a mule from two separate issues.
 

Edited December 20, 2023 by Rand

[Molag Bal]

For your question "Is it really possible to determine an engraver by style?'" I think the answer varies depending on the mint and time period. For coins of Gallienus at Cologne the portraits varied significantly. For example the first of these pictures, the lower engraver is very distinct, and as far as I have seen, never engraved portraits with the spear and shield with GALLIENVS AVG GERM V legend. This suggest some level of organization or structure in my opinion.

 

Today I got in a new coin pictured below: 

 

Gallienus, 253-268. Antoninianus (Silvered bronze, 21 mm, 3.50 g, 5 h), Mediolanum, 263. IMP GALLIENVS AVG Radiate, draped and cuirassed bust of Gallienus to right, wearing aegis on his left shoulder. Rev. VIRTVS AVG Virtus standing front, head to left, holding spear in her left hand and placing her right hand on shield set on ground. Cohen -. MIR 1158s (2 examples). RIC -. 
From the E. Mensch & A. Bauer Collection of coins of Gallienus.

This looks like an obverse die match to the example in MIR:

It's also a die match to a coin in the N.M.McQ. Holmes collection:

The one in the Holmes collection is from the 3rd emission at Milan according to Gobl. But mine is from the 4th emission. Does that mean one needs to be assigned to the other emission? Or were cross emission die matches possible? 

[Heliodromus]

25 minutes ago, Molag Bal said:

The one in the Holmes collection is from the 3rd emission at Milan according to Gobl. But mine is from the 4th emission. Does that mean one needs to be assigned to the other emission? Or were cross emission die matches possible? 

In general it's only going to be the reverse that differs by emission/issue, so there'd be no logical need to discard obverse dies. Practices could of course have differed across mints/etc.

Here's a coin of mine that's an obverse link to one from the prior issue (BM specimen - 2nd coin).

\

Edited December 20, 2023 by Heliodromus

[DonnaML]

7 hours ago, John Conduitt said:

I suppose what I need to know is whether it is possible to tell if the same engraver was responsible for two different dies,

I can think of one occasion when it has occurred to me that two different reverses depicting two different personifications on two different types issued by the same mint for two different emperors, roughly contemporaneously, may have been engraved by the same person. Here are two coins of the brothers Carinus and Numerian, both minted in Ticinum (now Pavia, Italy):

Even though the first reverse depicts Felicitas and the second Providentia (albeit with the attributes of Annona), there's something about the style of the two profiles that makes me think that they may well have been the work of the same engraver.

[Coinmaster]

Interesting topic! There seems discussion about how many coins were struck with an obverse die. The oldest source I know dates from 1301 England, where was stated that the average output that year of a die was (an incredible) 42.000 coins. Average, so some dies might even hit 50.000 coins.

Of course this amount can't just be used for Roman coins (thicker coins, quality of the dies, type of metal, etc.), but when people suggest it was no more than 5.000 or 10.000, I find this less likely. I think an average between 20.000-30.000 per obverse die could be achieved.

Also, I understood the Esty-formula about how many dies could be made is not without discussion, but unfortunately I don't understand statistics very well..

[maridvnvm]

14 hours ago, John Conduitt said:

 It's not like they switched the dies around regularly.

Hmmm. I am not sure about that assertion. How do account for some coins where there are many known reverse dies to a single obverse die with only slightly more examples known to exist.

Die studies are invaluable in some sub-issues where there is not evidence other than die linkages to link coins to the same mint other than "style". Dies studies also help try to determine relative chronology of usage if you can see progression of die damage etc....

I am not a numismatist but in my own little corner of collecting I do study die linkages quite avidly. I have bought double die matches simply to support this. I don't think you want be dragging out the die linkages here though.

[shanxi]

video on youtube about Die Studies

 

 

Edited December 21, 2023 by shanxi

[Roman Collector]

Here's an example of how die studies establish chronology. 

THIS CERES reverse type ...

Was produced around the same time as the DIANA LVCIFERA reverse type because they are linked by their obverse die.

 

The latter was issued c. 170-171, so the CERES type must have been issued then, too. This is NEW information. 

[Ocatarinetabellatchitchix]

56 minutes ago, maridvnvm said:

I am not a numismatist

Sorry Martin but I disagree with this. Yes you are. And a good one.

[Heliodromus]

3 hours ago, maridvnvm said:

Hmmm. I am not sure about that assertion. How do account for some coins where there are many known reverse dies to a single obverse die with only slightly more examples known to exist.

In the case(s) you have in mind, does the obverse die paired with these various reverse dies for type 1 also then get reused with various reverse dies for different type 2 ?

One could certainly imagine different die rotation/retirement practices in effect at different mints. I wouldn't expect they would always just use an obverse die continuously until failure - maybe switch it out  to cool for a while after it gets too hot ? If multiple busts are in use for a given issue (e.g London 311-312), then how were these managed wrt die use?

 

Edited December 21, 2023 by Heliodromus

[maridvnvm]

I think that the most reverse dies I have combined with the same obverse die is 12 in my collection, of which these are about 10 different reverse types...

[Heliodromus]

Sorry, but I'm still not quite clear on the pattern. If there's an obverse die A (and maybe others B, C..), and 10 different reverse types T1, T2 .. T10, with T1 dies T1-1, T1-2, etc, T2 dies T2-1, T2-2, etc, then what are the pairings you have seen with obv A (and obv B, etc if applicable) ?

Are you saying that obv A is paired with 12 different reverse dies across these 10 types (e.g. paired with T1-1, T1-2 plus T2-1, T2-2, etc ,etc) ?

Are there also other obv dies/busts (B, C, etc) that are also seen in combination with these various T1-T10 reverse type dies ?

What are you referring to above by "with only slightly more examples known to exist" ?

 

Edited December 21, 2023 by Heliodromus

[maridvnvm]

Some of my die matches (a small sample) were illustrated in this thread....

https://www.numisforums.com/topic/3784-septimius-severus-another-obverse-die-match-aka-tales-of-a-severan-obsessive/#comment-45695