Statistics and Stamp Collecting: An Example

I describe in this section an example of the importance of statistics in stamp valuation. It happens often that stamps are valued incorrectly in various catalogs, and I illustrate here an example of how this could happen. I have selected 48 specimens of the 1880s Russia 7 kopecks definitive and will ignore perforation in this example. This is a very common stamp, but since this is an example, I will take the liberty of making up a simulated story to prove my point.The 48 stamps used in this topic page are described in detail in Article 84: Russia 1880s 7 Kopecks, and a statistics example. I include the quick links for that article here. Quick links: main page / Stamp list for all 48 / Group One: Stamps 1 to 8 / Group Two: Stamps 9 to 16 / Group Three: Stamps 17 to 24 / Group Four: Stamps 25 to 32 / Group Five: Stamps 33 to 40 / Group Six: Stamps 41 to 48 / Selections from sections of the stamp: crown for selected stamps between 4 and 16 / 19 to 32 / 33 to 47 / eagle for selected stamps between 6 and 20 / 21 and 34 / 35 and 47 / Numeral seven showing various types of background shifts and wear of plate for selected stamps between 1 and 16 / 18 and 29 / 32 and 40 / Selections from stamps with various line breaks / background shifts / Lower legend selections.

Assume that only the 48 specimens described here are all the specimens extant of this stamp. This could have happened if this stamp was an error of color, the printer made a mistake in which plates to use, etc. Again, this is a fictionalized scenario. Since these stamps were in use in the 1880s, let us assume that the first time this stamp was valued was in 1910, and that at the time, only 8 specimens were available to make the valuation, but it was common knowledge that as many as 30 specimens were accounted for. Using only the first eight specimens, this is what we can say about this stamp:

  • Only one specimen is ultramarine blue (shown left). If the total number assumed to exist is 30, then there could be as many as four specimens of this color available.
  • The average quality is 3.44 (I use a scale of 1 to 6 for quality and have assigned a number to each stamp as shown in the complete listing, and add to these values 0.25 if the specimen has the year legible, and 0.5 if it has a purple postmark). The average for all 48 specimens is 3.84, but you are not supposed to know that in the 1910 scenario.
Based on the limited information available in the 1910 scenario, ultramarine blue is represented by 12.5 percent of the number verified (8), and the expected total number (30). The total numbers are 18 for light blue (37.5 percent of 48), 19 for medium blue (39.6 percent of 48), and 11 for ultramarine blue (22.9 percent of 48). The rarity of the ultramarine blue color is over estimated by 83 percent! In addition, because the total estimate is 30 versus the actual number of 48, someone in 1910 could have rated this stamp at 3 times its actual rarity. At this time, none of the specimens dated 1887 and 1889 are available for the valuation. In 1910, it is assumed that this very rare stamp was only used in 1885 and 1886.
Fast forward to the 1925 scenario. It is the roaring 20s and the Czar is out. A Parisian catalog would have access at this time to 8 additional specimens for an updated valuation. If we look in the complete listing, none of the additional 8 specimens are ultramarine blue. Assume the expected total number has risen to 35. Even though we have 16 out of expected 35 well-known and accounted for, the ultramarine blue stamp shown above has now risen in rarity considerably because now it is one of 16, or two of 32.

Using the first 16 specimens, this is what we can say about this stamp:

  • The average quality is 3.80, which is much closer to the average for all 48 specimens of 3.84. It only took 16 specimens for the accounted specimens to have a quality distribution very similar to that of all specimens. There are now six specimens of quality 4 and four specimens of quality 5.
  • If only the lower quality specimens had been available for a valuation, any specimens rated a 5 would have been over-valued.
  • The medium blue stamp is no longer as rare when compared to the light blue stamp. In the 1910 valuation, there were only 2 medium blue stamps to 5 light blue stamps, and now the ratio is 6 to 9. The ratio of known specimens for these two colors has decreased from 5/2, or 2.5, to 9/6, or 1.5.
  • 1885 and 1886 are still the known years of use.
Fast forward to 1935, and a major collector has donated the two specimens shown here to a museum. This is bad news for the marked because these are specimens 4, and 10. Instantly, the average quality for the market specimens diminishes from 3.80 to 3.63, and the number of available ultramarine blue specimens in the market shrinks to zero. The donations to museums divide the population into two groups: those known, and those available for purchase. It is the latter population that is used for a valuation, and for scarcer items, the difference between these two populations can be large.
In the 1950 scenario, a third batch of specimens is available for valuation. In this batch, there are three ultramarine blue specimens (one is shown below). In addition, another collector has bequeathed a specimen to a museum: specimen number 3. With the additional specimens, and the specimen lost to a museum, the market quality average is now at 3.80, and the known population quality average is now at 3.91. With the addition of a third batch, the valuations are representative of the expected population, at 40 by this time, and of all specimens known (48).

Using the first 24 specimens, this is what we can say about this stamp:

  • Although one ultramarine blue specimen is in a museum, three additional specimens are in the market, for a total of 4 out of the expected 40 total. This shade is now 10 percent of the expected population. This is a low number when compared to the actual value of 22.9 percent, but considerably better than 1 in 35 before 1950.
  • The medium blue stamp is again scarcer than expected when compared to the light blue stamp. In the 1925 valuation, there were 6 medium blue stamps to 9 light blue stamps, and now the ratio is 7 to 13. The ratio of known specimens for these two colors has increase from 9/6, or 1.5, to 13/7, or 1.86. These two shades have a ratio of 18/19, which is close to 1, when looking at all 48 specimens.
  • A specimen dated 1887 is known.
We can stop here. With the data available in Article 84: Russia 1880s 7 Kopecks, and a statistics example, we could see what happens when we add even more ultramarine blue specimens in batches four and five, and how the relative rarity of the ultramarine values rises once again with batch six when 8 more specimens are added to the final number of 48, and not a single one is of this shade. I hope you find this simulated scenario useful! For some of the stamps that are described in somestamps, the catalog valuations have been well off the mark in some cases because the valuation was performed on a limited sample of specimens that was not representative of the known population!
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