Rarity Scales: A Comparison

Discussion in 'Coin Chat' started by John Conduitt, Feb 26, 2021.

  1. John Conduitt

    John Conduitt Well-Known Member

    Often a coin’s description ends with a comment such as ‘Rarity: 3’ or even just ‘R3’. Almost as often there’s no indication of what this means. This is the mysterious world of the rarity scale. In my struggle to identify and understand them, I created a reference table, which is at the end of this post. And in an attempt to get ‘under the hood’, I tried to create my own scale. How hard can it be?

    It must be said there’s absolutely no need for another. There are many scales out there. But while they look simple, they’re confusing. Which direction does it go in? How do I know which scale is being used? How are they different? Why can’t there be just one? Some claim to be universal, others to be relevant to their niche. To some it’s just meaningless marketing, but I want to know – is this coin rare?

    Denga from the time of Vasily I Dmitriyevich, 1391-1402
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    Tarusa. Silver, 1.23g. Imitating the Golden Horde dangs of Jochi, son of Genghis Khan. This coin was given a rarity of R1, without naming the scale. So, is it rare or not? Is R1 rarer than R9? That very much depends on the scale.

    Somewhat surprisingly, often it isn’t clear which scale is being used. This seems to be because the seller assumes you know it relates to the coin’s origin or type, although it’s perfectly possible for them to have conjured up their own. The above is a Russian denga, so the scale is probably Kleschinov & Grishin’s in my table below. But what does it mean?

    What is rarity?

    I had thought this was the key question. But for most rarity scales – modern and ancient, mass-produced and patterns – the answer is very similar. Rarity relates to the number of surviving coins (or a proxy thereof). This can also help make a scale meaningful. Scales that use numbers as the dividers (e.g. 11-20 is ‘rare’) give a much better perspective than those using only words like ‘very rare’ and ‘scarce’.

    What isn’t rarity?

    Something I hadn’t appreciated is that rarity has nothing to do with demand or even availability. If there’s no demand for a unique coin, it’s still rare. If the owner of all 10 of something puts them up for sale, they’re suddenly more available, but they haven’t got any less rare. Neither is the price relevant. A coin can be common, but popular, so it costs more than a rarer specimen. Just ask anyone trying to buy an Attica Owl.

    Maximian I Follis, 300
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    London. Bronze, 26mm, 9.4g. IMP C MAXIMIANVS P F AVG. GENIO POPVLI ROMANI (RIC VI 6b). Described as having an uncommon legend. The legend isn’t rare, or scarce, but with no definition of common, who’s to say it isn’t uncommon? The fact that a rarity scale wasn’t used makes it meaningless, as there’s nothing to compare it to.

    Absolute or relative

    I don’t know if Einstein ever designed one, but it seems the crucial issue for rarity scales is relativity. The assumption that rarity is relative is the reason for the proliferation of scales – a rare coin of the usurper Saturninus would have to be a single aureus, while the rarest Morgan dollar is one of ten thousand. So, it is presumed, they can’t use the same scale. The question is, are they all ‘coins’ or are the subsets incomparable? Can you even have a rare Morgan? Or a common Saturninus?

    The problem is that ‘relative’ rarity is infinitely diverse. For a universal scale, and to avoid endless scales to suit every collector’s unique wish list, rarity would have to be absolute. Take Indochinese Tigers and Red Wolves. There are less than 400 of either left. But there are 600m cats and 900m dogs. Tigers are 400 of 600m, wolves 400 of 900m. Is the wolf rarer because it’s proportionately less common than the average dog? As mammals, they’re equally rare.

    Some collectors have such similar goals there’s a critical mass that might make a separate scale useful – Morgan collectors for example. But generally, people’s interests aren’t so tight. So, for my scale I’m going universal. But it’ll mean no Morgans will count as rare. To be fair, that’s surely the case. There are 6,000-12,000 of the ‘rare’ 1893‑S Morgan in existence. A few dozen get sold at major auctions every year. It might be expensive, but that’s because rich Morgan collectors aren’t rare either. The rarest Morgan is like the rarest washing powder – rarity isn’t what matters. And for rarity, they still have all those die varieties.

    Massalia Hemiobolion, 150-120BC
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    Massalia (Marseilles), France. Bronze, 15mm, 3.92g. Apollo. Bull (ABC 115). One of about 20 found in England and as such was rated RR on Chris Rudd’s scale. The same rarity could be described as URS-6 (Bowers’ Universal Rarity Scale), CFR 9.1 (PCGS CoinFacts) or R4 (Sheldon or Seaby & Rayner). Could it be any clearer? Well, yes.

    What is a coin variety?

    The other side of the relativity coin is the definition. What makes a variety distinct enough to be rated separately? The Maximian above was called ‘uncommon’ because of its legend. But Roman coins were handmade and most differ from each other in ways that by modern standards would make them variants. Some coins are rated on the rarity of their condition. Here, you can get into the minutiae of grading, to decide one coin is rarer than another based on the intrusiveness of any scratches. The Gallic hemiobolion above is rare if you include the find site, England, in its definition. Otherwise, plenty more are found on the continent. The find site is usually irrelevant, but here it’s central to the coin’s place in the evolution of British coins.

    So, the same coin could be both rare and common depending on how you describe it. This, though, is not a problem with the rarity scale itself. Rather, this is down to the plausibility of the seller’s description and whether the buyer’s convinced. The rarity scale helps by providing an objective assessment against the subjective definition.

    What’s the point of a rarity scale?

    Although perhaps not the original intention, for me there are three purposes to a rarity scale, all related to the sales process:

    1) For the buyer to quickly determine how long they might wait to see one. Do I need to research that coin before it’s gone? How do I prioritise it with my limited budget?

    2) For the seller to instil (objectively justified) urgency into the buyer in an eye-catching way.

    3) To give the buyer post-sale satisfaction in having acquired a rare coin (‘bragging rights’). It’s said dramatic car ads are not intended to sell but reassure existing customers they made the right decision.

    In each case the scale provides an objective assessment of a coin’s rarity against the description provided. The description may be susceptible to manipulation, but once on a scale it’s easier to assess than such lines as ‘not in any reference’ or ‘the first I’ve seen’, which don’t relate to a surviving population. Narrandera, Australia promotes itself as home to ‘the largest playable guitar in the Southern Hemisphere.’ The scale (the Guinness Book of Records) provides the objectivity. The caveats do the rest of the work for you.

    What isn’t it for?

    I don't think a rarity scale needs to rank every coin. Some coins are common, others very common, and most buyers are fine with that without making a distinction. Some scales don’t even reach ‘common’. It doesn’t need to fit every situation, or to map the probability distribution of every variation.

    George V Sixpence, 1914
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    London. Silver, 19mm, 3g (S 4014). The 1914 George V sixpence had a mintage of 22,714,602, the second highest in the 10 years it was issued. In British culture, sixpences are seen as lucky, and a great many people would’ve wanted a bit of luck in 1914. Chances are, there are a lot of these around. Unsurprisingly, it wasn’t sold with a rarity score, and I didn’t need it to be.

    How is rarity calculated?

    We come to the elephant in the room. How is the number of surviving coins estimated?

    1) The mintage figures. A good starting point, but coins are lost and melted down, often at very different rates. For ancients, these figures aren’t even available (although there are databases of finds).

    2) The number held in major collections. This is used in RIC (Roman coins) as a proxy for surviving coins. But it’s subject to the preferences of museum curators and won’t work at the common end of the scale, since museums aren’t going to keep several of something just because there are more of them. They might also have more of a rarity because it’s more interesting or they were in the same hoard.

    3) The number appearing at auction or for sale. This seems to be the preferred method, since volumes are high. It also reflects the numbers on the market, which is why collectors want a rarity scale in the first place. But it has problems. Some coins are so common they aren’t auctioned individually very often and sales through dealers might not be included.

    4) Third-party grading company populations. Despite appearing accurate, by the TPGs’ admission they’re not. Certain coins are graded in far higher numbers than others, particularly if they tend to be more valuable or in better condition, or are American. And many of the coins counted are resubmissions from dealers or collectors trying to improve the grade.

    Often the estimate needs to be done by the seller, particularly for unlisted variants or where the references are out of date. The skills and knowledge of each seller will vary hugely, as will their propensity to exaggerate. But the buyer should be doing their homework too. The rarity scale is a marketing tool and you can trust it no more than you can the asking price.

    Clearly, it’s imperfect. But what estimate isn’t? We happily follow weather forecasts, or track share prices or opinion polls. What’s important with any estimate is to realise it’s imperfect and not to get into too much detail that relies on dubious accuracy.

    Halsall Condor Token from the time of George III, 1784-1787
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    Soho Mint, Birmingham. Bronze, 33mm, 16.40g. Arms of the Earls of Peterborough. HALSALL D (Lancashire D&H 1). PCGS haven’t given it a rarity rating. They only have two on their database (including this one), so as far as they know it’s CFR 9.9 (ultra rare). It isn’t – and because it’s not a US coin, their ‘top rare coin experts of all-time' (as they describe them) won’t rate it.

    What characteristics should a rarity scale have?

    So, given all the above, what should my scale look like? (This is just my opinion):

    1) Relevant, with a purpose for each range. Do we really need to distinguish populations of 1-2 from 3-4? Some scales even have a rating for zero coins known. If the purpose is to highlight rare coins, populations of 2 or 3 are both ‘extremely rare’ to a buyer. And if a coin is unique, the seller will point that out anyway. Along with a caveat that it might not be. These are estimates after all.

    Conversely, the Van Allen & Mallis (VAM) scale distinguishes R2 (several million) and R1 (tens of millions). 10 million is enough to give one to every collector in the US. Hartill (oriental coins) has 7 shades of common – more than adjectives to describe how common. You can’t even conceptualise it. If you look into a clear night sky, you’ll see a lot of stars. Yet you can see no more than 5,000 with the naked eye. There are 100,000,000,000 in the Milky Way. Do we need another adjective for the other 99,999,995,000? Something more than a lot? Do we need to break it down into ranges of 10,000?

    2) Workable. If it’s too precise, no-one can categorise anything. It’s only a guide. Not all coins have been in an auction or even reported. PCGS’s 101-point rarity scale is, well, rather over-categorised. It literally needs a panel of experts to maintain it.

    Similarly, a rarity scale needs to be flexible. Rarity changes. If someone digs up a cache of 100,000 EID MARs, people will start using them as earrings. The scale can’t be too precise. Yes, the scores given using the 5-point scale in RIC II are sometimes off but that was published in 1926.

    Galerius as Augustus Follis, 305-307
    upload_2021-2-26_12-24-50.png
    London. Bronze, 26mm, 9.59g. IMP MAXIMIANVS PF AVG. GENIO POPV-LI ROMANI (RIC VI 52b). This was described as R1, which if on the RIC scale (it wasn’t labelled as such) means it’s rare, but not extremely so, and there are 26-50 in the collections examined. I’ve no idea how many that means there should be in the wider world, but it took me a year to find one, so it seems to fit.

    3) Usable. A seller is not going to label any coin ‘common’, in the same way the smallest cappuccino on the Starbucks menu is ‘tall’. Incidentally, if you go into a Starbucks and order a ‘large cappuccino’ they’ll give you a 20-ounce Venti, even though the exact translation of their Grande option (a mere 16 ounces) is ‘large’. Buyers are also less interested in the higher-volume end of the scale – they won’t want to brag about how common their coin is.

    One complaint of Sheldon’s rarity scale is that for very common issues, few varieties have low enough survival rates to fall into any of the brackets. Surely, though, for those issues, where all varieties come to market regularly, rarity scales are redundant. It’s useful to know rarity is irrelevant, but how irrelevant doesn’t matter.

    4) Immediately understandable. Numbers can go in either direction – is 1 or 9 rare? What’s the minimum and maximum? On descriptive scales, you need a key to work out the hierarchy. ‘Rare’ and ‘scarce’ are invariably used but shouldn’t be increments on the same scale. The true definition of scarce is that demand is greater than supply, so if 1,000,001 people are chasing 1,000,000 coins, it’s scarce but not rare. Rare refers to the absolute number. If no-one wants a unique coin, it’s rare but not scarce. Some things are rare for a reason. A confused use of terms makes the scale confusing.

    Attica Tetradrachm, 454-404BC
    upload_2021-2-26_12-38-52.png
    Attica, Athens. Silver, 24mm, 17.19g. Athena. Owl (HGCS 4, 1593). There are lots of these, but they’re expensive, because a lot of people want them. It’s scarce, but not Scarce.

    5) Universal. This is the Holy Grail. Attempts have been made to create a general scale, not least with Bowers’ Universal Rarity Scale. So why isn’t that used universally? Well, for one it’s too precise. 5 of 21 categories are for coins where under 8 are known. Who are they for? It also starts with 1 for the rarest, while other American scales have 1 as the most common. Confusing.

    There also seems to be a belief you can’t have a scale to fit all coins. To fit their specialisms, Pollock and Overton's scales modify Sheldon’s by removing the ‘unique’ category and bringing down the threshold for the most abundant category. Was that really a problem? Were the Bust Half Dollars moved up to the most common category really less rare than the corresponding Large Cents in Sheldon, even if they existed in the exact same numbers? As the table below shows, the ranges for most scales are all but the same anyway.

    Antoninus Pius As, 154-155AD
    upload_2021-2-26_12-40-29.png
    Bronze. 8.63g. ANTONINVS AVG PIVS P P TR P XVIII. BRITANNIA - COS IIII (RIC III 934). Described as Scarce, a term used in RIC to mean both that it is ‘in most major collections’ and that there are 16-21 of them in such collections. Presumably, there are a little over 16-21 major collections. I don’t think it made any impact on my decision to buy the coin, because I didn’t understand it.

    The Conduitt Rarity Scale

    Now I’ve criticised others, it’s time to put my money where my mouth is. I’ve taken what I think are the best bits of the ‘real’ scales to make my own. It’s even named egotistically, in the spirit of numismatic scales. And to be honest, it’s not easy. Someone can object to the very definition of rarity, let alone whether a population of 30 should be considered as rare as one of 20 or 40.

    I’ve included numbers (else it’s too vague) and each threshold is ‘less than’ (else it’s too precise). It’s in multiples of 10, so there’s some chance of remembering it (RRR is under 10, RR is under 100 etc), with the ‘+’ at the midpoints. Repeated letters like RR seem more instantly understandable than R2, and since sellers wouldn’t use C for ‘common’ anyway, the threshold for that starts after most scales have stopped. (This means R starts at under 1000). I’ve included descriptive notes as I think they give an idea of what that rating might mean to a buyer - but of course these are very general.

    RRR+ (<5 known) - unique or nearly so.
    RRR (<10 known) - you may never see another.
    RR+ (<50 known) - you’ll have to wait to find another.
    RR (<100 known) - not always available without delay.
    R+ (<500 known) - usually available in a limited range of conditions.
    R (<1000 known) - you won’t wait long to see another, but you might for one this good.
    C (<5000 known) - readily available in various conditions. You can be discerning.
    C+ (<10,000 known) - very widely available. You can be price sensitive.
    CC (<50,000 known) - abundant. Price is all important.
    CC+ (50,000+ known) - most abundant. No-one is ever going to use this, but it has to exist conceptually. It’s a ‘small’ at Starbucks.

    Table of Rarity Scales

    Here’s the comparison table (Fuld, ERIC, Scholten, Michael Marsh and Stephen Album in addition to those already mentioned). Some are not directly comparable – most are based on estimates of surviving coin populations (which are the numbers given), but others (like RIC) are based on proxies. Some are just descriptive with no values assigned at all. But I’ve tried to align them roughly where it appears they were intended to fall.

    Yes, rarity scales are open to abuse. Sellers can link rarity and price when they shouldn’t be. They can even manufacture rarity in the way they define a coin – every coin is ‘unique’ after all. But you wouldn’t buy a coin based on a rarity scale. ‘Buy the coin, not the grade’. Rarity scales draw attention to interesting coins that might otherwise go unnoticed, and who doesn’t want that?

    Rarity Scales.jpg
     
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  3. Robidoux Pass

    Robidoux Pass Well-Known Member

    Well researched. Very useful and interesting topic. Thanks for sharing. I too am often confounded by rarity scales.
     
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