On the surface, this seems like a silly question. Everyone knows what rare is. Getting struck by lightning or winning the lotto would be tip-of-the-tongue examples anyone would cite as exemplifying rarity. But, as it turns out, asking to have rarity defined precisely in terms of a percentage is bound to be controversial. The chances of getting struck by lightning, for example, is estimated to be somewhere on the order of 1 in 700,000. A 0.0000007% chance of being hit by a bolt out of the sky hardly makes me or anyone I know worried enough to take precautionary actions. These, coincidentally, are about the same odds of dying in a plane crash or getting a royal flush while playing poker. So we could all agree that those things are definitely rare, right? Well, not so fast. Let's look at gold. If you were to ask anyone why gold is so expensive they'd say it's because it's rare. And the numbers would seem to back it up. If all gold were evenly distributed throughout the earth (rather than concentrated in a few mines) you would have to sift through over 300 million pounds of dirt to recover your first pound of the yellow metal. In a back of the envelope calculation that's roughly fifty pyramids worth! And yet... don't you have some gold laying around in your own home? In fact, if all the gold that's ever been mined were to be taken out of the vaults and off the fingers of the married, remelted and redistributed, each and every woman, man and child would get about 23 grams; almost an ounce for everyone!
So if every day you hear someone winning the lottery somewhere, a plane crashes somewhere every so often and there's enough gold out there that everyone could have their own four solidi worth of it are any of those things rare? The answer is it depends. It depends because rarity is an undefined concept that gains meaning only when compared to something else. It is, in fact, rare to hit the jackpot when you consider that millions of people play the lotto every day unsuccessfully or that much of the otherwise common gold out there is inaccessible which makes it seem so much rarer than it in fact is.
Where it comes to ancient coins the definition of what constitutes rarity is muddied by the competing interests of dealers, scholars and collectors. A quick look on eBay reveals that out of some 50,000 ancient coins for sale fully 10% are listed with the word "rare" somewhere in their description. Rarity sells, of course, because whether we openly admit it or not a large part of the appeal of collecting is the bragging rights that come from showing off an item that is difficult to obtain. Rarity in and of itself is the easiest route to special whether we're talking about an Olybrius, a Van Gogh or a Mickey Mantle baseball card.
But still, when do we really know if we have a coin that is rare as opposed to merely common? A unique coin is most definitely rare. On the other hand a hundred coins of the same type could be either dirt common if there are only a dozen collectors interested or exceptionally rare if the whole world's after them. So, again, this question is meaningless until we have a point of reference. While no such reference is without controversy (as shown above) we can arrive at something of a consensus at least by analyzing the supply and demand in the marketplace. If we allow ourselves a chuckle over the 5,000 coins on eBay optimistically listed as rare it's only because intuitively we know that most of them aren't since they keep turning up over and over again. Wave a magic wand and overnight a million new ancient coin collectors are created worldwide and suddenly all 50,000 of those listings could be considered bona fide rarities as bidders drive up the price of even the most scrappy Constantines to dozens of times their former values. Yet, and this is the key, the coins did not actually become any rarer than they were a day before, right? Therefore it's not the absolute rarity of a given piece, or its condition, that is necessarily indicative of what we perceive as the "true rarity" because what we're really interested in is simply market availability.
So as a first step what we need is a realistic yard stick to come up with a definition we can all more or less agree on. The way to do this is by going back to the marketplace and gauging the frequency by which any given collectible turns up. If we arbitrarily say "let's call anything that turns up so often that we can buy it any time we want the most commonly available" then we have half of the equation - and so far I think few would disagree with that definition. On the other hand, what is the line in the sand by which we deem a collectible truly rare? One that turns up once in a lifetime? Ten years? Keeping in mind that it's an arbitrary answer no matter what, I've found that in the case of Roman coins a coin that is offered at auction only once in about 25 years - a generation - is a good working number. On the other end of the scale I've also found that once you can count 200 instances of a coin having been sold during that same span that we reach the point that it can be said to be so common that it's available pretty much "on demand".
Between the realms of the ultra rare and the utterly common lies the rich middle ground of the actively hunted pieces that drive the interest of the collector. The English language doesn't fail in giving us adjectives by which to label shades of gray. Between rare and common we find scarce and infrequent and seldom all of which can be further subdivided by as many adverbs as we care to employ. In a practical sense, a factor of 2 to 2.5 gives a rather neat stepping level as shown here in the diagram that will someday go into the next edition of my Encyclopedia of Roman Imperial Coins book.
I do wonder though if the algorithm is portable across the various domains of collectibles. I have no idea if 200 Babe Ruth cards would constitute a market glut or an unbelievably rare commodity but suspect that the underlying principle is sound. To define rarity in meaningful terms for a collector all you need do is determine the frequency in which any one group of collectibles are most commonly traded to arrive at the commonest classification and work backwards from there. Once properly defined, rarity stops being vague and confusing and becomes a useful tool.