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Tuesday 9 April 2019

The Mathematics of Rarity Pricing.

This is a post for those who are better at mathematics than I am. I am just going to set out the basic idea which explains rarity pricing.

Suppose that country A (now dead) issued 100 stamps. Ninety nine of these are very common (millions of them) and can be bought for one peso each in any currency. But one is very, very rare - only a few dozen are believed to exist.

Suppose there are 1000 collectors of this dead country. Most are prepared to budget 1000 pesos to form a collection and they are very happy to find that they can achieve 99% completion for just 99 pesos. A few are prepared to budget more than 1000 pesos. All would like to have the 100th stamp which will complete the collection and most will bid in auction when one of these rare stamps appears. The sale price will be determined by those with bigger budgets and of one thing you can be sure: it will exceed 901 pesos which is how much most collectors are prepared to budget to complete a collection of country A.

Now turn to country B (also dead) which also issued 100 stamps. Of these 50 are very common (millions of them) and can be bought for one peso each in any currency. But fifty are very, very rare - only a few dozen of each are believed to exist.

There are also 1000 collectors for this dead country and most are prepared to budget 1000 pesos and a few prepared to budget more.

Now everyone can achieve 50% completion for 50 pesos, leaving a minimum of 950 pesos in their budgets. But what should they do when one of the rare stamps appears at auction? How much of their remaining budget should they allocate to one stamp when they know that there are 49 more just as scarce and still to be bought? It is more than likely that they will bid low because a different rare stamp might appear next week. Probably they will bid more than the baseline average of 19 pesos which they would be able to pay for the missing 50 stamps and still stay within budget (19 x 50 = 950). However, there are also the guys with the bigger budgets. But they will have to make a similar calculation:  what is my budget for the remaining 50 stamps and how much of it would I risk on just one rare stamp now knowing a different one will come up next week. 

What is probable is that they will risk less than the 901 pesos which provided a clear rarity baseline figure for country A collectors.

In other words, if someone aims to collect a series in which there are rare stamps to be found, the greater the number of rarities in the series the lower the price which each, on average, will command - just because collectors are trying to stay within a budget, however notional and flexible it may be. The absolute rarity (in terms of numbers) of the stamp is not the critical issue; nor is it entirely a question of how popular a collecting area is.

So it is that rarities of Russian Civil War philately - from Armenia and Ukraine, for example, sell for small sums. There are just so many rarities and you can’t have them all if you spend all your money on one!


  1. It's a really interesting thought experiment. I like the idea that the valuation of intrinsically worthless items like stamps can be derived by looking at the supply and demand, not just for individual stamps but for stamps as members of a group. The budget constraint should be on a "per year" basis or something like that. I'd also argue that scale matters here: for "small" collecting fields like Armenia there are simply fewer collectors around, while for a field like Old German States there are tens of thousands, even though the supply situation might not be all that different. I may need to scribble some math on paper about this idea...

  2. Its a classic case of supply and demand, with an emphasis on demand -- as opposed to rarity. Stamps are probably the best realm of popular collectibles where there are plenty of unique pieces with low prices, owing to low or no demand. After all, if nobody wants a Podolia trident accidentally cancelled in Kharkov, then who cares if its unique?