A few times now (here and here) I have quoted a comment made by Peter Opie in his Accession Diaries
It took me some time before I realised that 'rare books are common.' I probably acquire an item or two which is unique, or almost unique, every month of the year.
Opie's "rare" and "common" sound like they mean something, but this paradoxical-sounding comment suggests that they are, in reality, meaningless terms. Most collectors know from experience that rare and common are assessments made by dealers and collectors based on a combination of personal experience and knowledge of the experience of others (gleaned for reference works, catalogues, a lifetime of browsing in shops etc.).
John Carter says: "The definition of 'a rare book' is a favourite parlour game among bibliophiles" (ABC for book collectors, 8th ed. (2006), 183), but goes on to differentiate Absolute, Relative, Temporary and Localised rarity. Geographical rarity has lost most of its meaning thanks to the Internet and, partly for this reason, I suspect that temporal rarity has too. (It is now easy to collect books which do not exist at all in Australia, or which previously may have appeared among local dealers only once in a generation.)
For eighteenth-century books, absolute rarity—the number originally printed—is certainly a limit (editions larger than one thousand appear to have been quite uncommon), but the primary consideration for collectors and dealers is clearly relative rarity, which Carter defines as "A property only indirectly connected with the number of copies printed. It is based on the number which survive, its practical index is the frequency of occurrence in the market, and its interest is the relation of this frequency to public demand."
Carter suggests online catalogues like the English Short-Title Catalogue (union catalogue of books printed in English or in English-speaking countries up to 1800; here) promise to make it possible to list "all surviving copies of a book" (184). Anyone who uses ESTC regularly will know how few copies survive of most of the books printed before 1800: as my sample suggests, few works survive in numbers larger than one hundred. I have often wondered what the statistics are across the whole of the ESTC for the number of copies recorded for each item, but I know that some types of material are more likely to survive than others, large formats, "collectible" and highly-regarded authors etc.
My own experience, maintaining my Bibliography of Haywood over the last ten years, also suggests that—as ESTC grows to include more and more institutional collections, as it becomes more comprehensive in its coverage—it is more likely that more copies will be added of books which already survive in the large numbers. That is, common books become more common.
But returning to our "parlour game" and the statement "rare books are common"—the best antiquarian dealers tend to precision ("no copy sold at auction since 1984," "only two copies on ESTC" etc.), but I have long preferred the Rarity Scales used by coin collectors (see here). There is a gloriously-empirical Universal Rarity Scale, which I think should/could be used by dealers and collectors of ESTC books.
Rarity Number of known coins
URS 0 None known
URS 1 1, unique
URS 2 2
URS 3 3 or 4
URS 4 5 to 8
URS 5 9 to 16
URS 6 17 to 32
URS 7 33 to 64
URS 8 65 to 125
URS 9 126 to 250
URS 10 251 to 500
This is almost an exponential scale: 1, 2, 4, 8, 16, 32, 64, 128, 256, 1024. Applying this scale to my own very modest collection of 420 ESTC items
URS 1 1, unique (11: 2.62%)
URS 2 2 (12: 2.86%)
URS 3 3 or 4 (17: 4.05%)
URS 4 5 to 8 (68: 16%)
URS 5 9 to 16 (87: 21%)
URS 6 17 to 32 (121: 29%)
URS 7 33 to 64 (79: 19%)
URS 8 65 to 125 (23: 5.48%)
URS 9 126 to 250 (2: 0.48%)
URS 10 251 to 500 (0)
(Note, "URS 0 None known" is impossible since, if I have it, I know of a copy—i.e., none of these unique items are on ESTC and, from the perspective of ESTC, all of these are "none known").
This example suggests that the scale is not ideal: it has a peak at URS 6 (which, with URS 4,5,7 constitutes 85%), and is pretty flat at URS 0–3 and URS 8–10. A better scale might require a lower multiplication factor. Rather than multiplying by two each time, if we were to multiply 1.5 by 1.5 etc., and round to whole numbers, the sequence is: 1, 2, 3, 5, 8, 11, 17, 26, 38, 58, 87, 130. Using my proposed PS Scale:
PSS 1 1, unique (11: 2.62%)
PSS 2 2 (12: 2.86%)
PSS 3 3 or 4 (17: 4.05%)
PSS 4 5 to 7 (51: 12.04%)
PSS 5 8 to 10 (38: 9.05%)
PSS 6 11 to 16 (66: 15.71%)
PSS 7 17 to 25 (76: 18.10%)
PSS 8 26 to 37 (63: 15.00%)
PSS 9 38 to 57 (53: 12.62%)
PSS 10 58 to 87 (21: 5%)
PSS 11 88 to 130 (10: 2.38%)
PSS 12 131+ (2: 0.48%)
There is a peak at PSS 7 (which is more modest and, with PSS 6,8,9, constitutes only 61%), and a more even distribution above and below.
Two other rarity scales used by coin collectors are the Sheldon rarity scale and the Scholten Rarity Scale. The Sheldon scale ranges from "R1 Common, readily available" to "R8 Unique, or nearly so"; most eighteenth-century books would be at the upper end of the scale (R5 to R8) and only a few of the most common books would sit at R5 (Rare - unlikely more than five at shows or auctions each year)—leaving only three grades for the rest:
R6 Very rare - Almost never seen, only one may be offered for sale in a year’s time [=URS 5 to 7?]
R7 Prohibitively rare - one may be offered for sale once every few years [=URS 2 to 5?]
R8 Unique, or nearly so [=URS 0 to 2?]
The advantage of the Sheldon rarity scale is that it picks up Carter's "frequency of occurrence in the market"—which is important. Some books are not uncommon in institutions but are extremely rare outside of them. (There are scores of Haywood items, for instance, which are recorded in numerous copies, which I have never seen for sale: like a first of Betsy Thoughtless). But, like the numerical Universal Rarity Scale, only a short section of the scale applies to ESTC items and so this scale would also have to be adapted. Which, if I were a dealer, I'd be tempted to do. As a bibliographer, I am not sure I can justify spending any more time on this parlour game.