by Lin Yangchen
        Laboratory of Computational Philately
        Coconut Academy of Sciences

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Stamp catalogues are among the mainstays of philately. Many catalogues of varying scope are published in different countries. Yet stamp pricing is like a black box to many philatelists. Do catalogue editors base their prices on hard data, like stamp requisitions? Or on their observations in the course of stamp dealing? Or on gut feeling? Given the vast number of stamp issues in existence, catalogue publishing probably calls for every tool in the box.

Robinson (2000) posits that “objective measures of commonness and rarity should be scaled geometrically”, in addition to being based on empirical observations and historical narratives. That means if catalogue prices are to qualify as such a measure, there should be a few highly priced stamps and many cheap ones, with prices scaled multiplicatively rather than additively. This is because the frequency distribution of stamp varieties tends to follow this pattern, as revealed by Robinson’s study of cancel names on nearly 2000 BMA 8¢ stamps.

I analysed the catalogue prices and print quantities of the coconut definitives (Lin 2021d) to see whether they obey this fundamental law that has been found in natural phenomena ranging from the sizes of craters on the moon to tree species composition in the tropical rainforest to word frequencies in languages. The coconut definitives are a pleasing case study owing to their unified design spanning considerable historical time and geographical space.

Catalogue price data

Five catalogues of varying coverage of the coconut definitives were used: Stanley Gibbons British Commonwealth 1995, International Stamp & Coin Malaysia-Singapore-Brunei 1999, Murray Payne Commonwealth KGVI 2015 (does not list QEII), StampWorld online catalogue (accessed in April 2020) and CS Philatelic online price lists for Straits KGV and KGVI (accessed in April 2020). Although these catalogues are not all the most recent, they collectively span a quarter of a century of pricing and should reveal “timeless” patterns. Unfortunately, I do not have the Singapore data from the Murray Payne catalogue, and the Scott catalogue was unavailable.

The catalogue listings were digitized by optical character recognition using the Tesseract library in the R Language for Statistical Computing. Then text string matching was used to find and correct systematic errors, remove unneeded text and extract the denominations and catalogue values. The output was quite accurate, with only minor errors like the occasional missing decimal point or wrong character, for example “S” instead of “5” or “3” instead of “8”. The catalogues were in different formats and fonts, requiring slightly different code and spawning different errors. Everything had to be cross-checked by eye, but the computer still saved time as it automated much of the process over the many sets of coconut definitives.

In this study, “set” refers to a set of values from 1¢ to $5 that bear a particular head in the vignette and a particular territory inscription at the bottom. For the Straits KGVI set, I excluded Die II stamps that were not denomination-colours carried over from Die I (2¢ orange, 3¢, 15¢). For the Singapore 1949, Malacca KGVI, Penang KGVI and Malay states sets, I excluded stamps first issued in 1952 or later due to changes in postal rates (5¢, 8¢ green, 12¢, 20¢ blue, 30¢, 35¢). The idea was to get a “tidy” series of denominations for each set and prevent the analysis from getting too “noisy”. I excluded special items such as overprint and watermark errors, imperforates, plate flaws, forgeries and unissued stamps.

For denominations with two or more shades of the same colour, regardless of die number or paper type, I calculated a weighted arithmetic mean of their catalogue prices, the weight being inversely proportional to the catalogue price. This yields a mean value closer to the cheaper and presumably more common shade, but gives due recognition to rare shades. It gives a fair measure of the overall abundance of a given set-denomination occurring in multiple shades. Separate mean values were calculated for mint and used prices. For the BMA $5, I combined the old and new colour schemes in one mean value, because the reason for that particular colour change had been that the old colours ran out rather than a change in postal rates.

For catalogues published before 2020, the prices were converted to today’s money using the relevant country’s Consumer Price Index obtained from the UK Office for National Statistics and the Department of Statistics Malaysia. According to the CPIs, £1 in 1995 became £1.65 in 2020, £1 in 2015 became £1.09 in 2020 and one Malaysian ringgit in January 1999 became MYR1.55 in January 2020. All prices were then converted to pound sterling using exchange rates on on 3 April 2020. I visually checked using forex charts that the rates on that day were very close to the average over the last three years. The StampWorld and CS Philatelic prices were converted from Singapore dollars at a rate of SGD1.76387 to £1, while the ISC prices were converted from ringgit at MYR5.35264 to £1.

Pricing patterns

Figure 1. Relationship between denomination and catalogue price on logarithmic scales. Each line represents a set in a particular catalogue and particular condition (mint or used). Red lines represent Straits KGVI mint sets.

As expected, catalogue prices generally increase with denomination. There is much overlap in the prices of mint and used stamps. However, low denominations of Straits KGVI in mint condition are priced very high for their denomination by all the catalogues examined (red lines in Fig. 1). In fact, the mint price of the Straits KGVI 8¢ grey in the Gibbons catalogue is 420 times the used price; the difference is not much less in the other catalogues. This, as we know, can most likely be traced back to the bombing of De La Rue in World War II and the ensuing stamp shortages.

A remarkable phenomenon is the price oscillation along the denomination dimension (Fig. 1). This oscillation is highly synchronized across catalogues and sets. It appears to be a result of the interplay of postal rates and stamp denominations.

One of the “peak-priced” denominations is 3¢. From 1945 to 1955, only four postal rates were 3¢, out of more than 150 rates quoted for different package types, weights, transport modes and destinations (Stanway 2009). The 3¢ rates were for certificates of posting to three different parts of the world and for an extra 2 ounces of newspapers by air. The vast majority of the other rates either could not be constituted using 3¢ stamps, or there were stamp denominations matching those rates already. As a result, demand for the 3¢ was relatively low and the total number of 3¢ stamps printed after the war (excluding BMA) was the second lowest among the single-digit denominations (Lin 2018e). Although there was no 1¢ rate at all, the 1¢ stamp was more flexible in making up stray cents to get some required rate and presumably in greater demand. More 1¢ stamps were printed than 3¢ (Lin 2018e, Stanway 2009).

Other “peak-priced” stamps include the 8¢. This one went through two colour changes, from grey to scarlet to green. Stamps in each colour are correspondingly less abundant and fetch a higher catalogue price. There is also the 20¢, whose initial black-and-green colour scheme lasted only a couple of years before giving way to blue. Postal rates never sat still for long; new or revised rates were introduced every year from 1945 to 1953 (Stanway 2009).

The 25¢ and 40¢ experienced an “abundance inversion” between the pre-war and post-war periods. In the early days of World War II, the 25¢ was depleted by heavy usage in British military air mail (Carpenter 1990). So mint pre-war 25¢ stamps are hard to find and fetch a high price compared with the very common post-war 25¢. The 40¢ went the other way; it was in stock throughout the earlier years but lasted only a short while after the war before being superseded by the 35¢ in 1952 and the 30¢ in 1955 for air mail. The contrast between the 25¢ and 40¢ is manifested in the opposing slopes of the red and black lines in Fig. 1.

As expected, the most expensive small heads issues are mint $5’s. The Singapore 1949 $5 mint is the most expensive by far in all three catalogues from which I have data. The highest quote after converting to today’s money is more than £300.

Some anomalies

Figure 2. Relationships between denomination and catalogue price for Negri Sembilan small heads issues, by catalogue and condition.

For a number of Malay states, such as Kedah, Kelantan, Negri Sembilan, Pahang and Trengganu, the Murray Payne catalogue deviates from Gibbons, ISC and StampWorld. It is the only catalogue among them in which the top values $2 and $5, and sometimes $1, are more expensive used than mint (Fig. 2). But this does not happen for states like Johore, Perak and Selangor. As can be seen later, these states had the largest populations, which presumably generated more economic activity and more stamped correspondence.

Figure 3. Relationships between denomination and catalogue price for Malacca and Penang QEII small heads issues, by catalogue and condition.

Another anomaly appears in Malacca QEII mint prices, which plateau out below used prices across the top values in all catalogues, while Penang QEII mint prices show normal trajectories (Fig. 3). Malacca had only half the population of Penang at the time (see Lin 2018e), so one could imagine lower stamp usage rates and more mint stamps surviving out of Malacca.

Figure 4. Relationships between denomination and catalogue price for BMA stamps, by catalogue and condition.

The BMA 12¢ is a striking example among stamps that cost more in used condition. In the Gibbons, ISC and StampWorld catalogues, used examples of the 12¢ are priced about twice as high as mint. In the Murray Payne catalogue, the price difference is more than 10-fold (Fig. 4). The overseas surface letter rate increased to 15¢ in 1941 (Robertson 1999), rendering the 12¢ quite obsolete. Yet three years later, the postal authorities seemed to have overlooked this fact and had the 12c overprinted BMA. The 12¢ even got a special mention in The Straits Times on 14 January 1946, in an article about philatelists scrambling to buy BMA stamps before the civilian government took over. As the Murray Payne catalogue is arguably the most specialized in BMA among the catalogues studied, it probably considered additional historical knowledge when pricing the stamp.

Print quantities

I also examined the relationship between catalogue prices and quantities of stamps printed. This part of the analysis is limited to post-war non-BMA small heads issues, using stamp production data and calculations from Stanway (2009) and Lin (2018e). The Singapore sets are excluded as the relative print quantities of the two perforations are unknown.

The number of stamps surviving today is of course smaller than the number printed, but we will never know how much smaller. The assumption this analysis has to make is that the rate of loss has been similar across different denominations and sets.

For each denomination in each set, I calculated a mint-used aggregate price by taking the weighted average of the mint and used prices, the weights being inversely proportional to price as done earlier for shade varieties.

Figure 5. Relationships among denomination, print quantity and mint-used aggregate price. Each point represents one denomination in a particular set in a particular catalogue. The wireframe surface was generated by fitting a generalized additive model and gives a rough idea of the overall trends.

Low quantities naturally beget high prices, but it is low quantity paired with high denomination that really drives up the price beyond expectations from print quantity alone (Fig. 5, red data points). The relationship is more nonlinear than a power law; even the double logarithmic scales are unable to straighten the bend (Fig. 5). Perhaps it is not only the information on the quantity of a high-denomination stamp that spurs philatelists to covet it, but also the psychological impact of the dollar sign inscribed in the tablet, and even the visual allure of the bicolour or tricolour print.

Figure 6. Mint-used aggregate price (a) and value for money (b) in relation to the number of stamps printed.

I also divided the mint-used aggregate price of each stamp by its print quantity. This can be interpreted as a measure of value for money or return on investment. In this formula, if stamps A and B cost the same but A was printed in smaller quantity than B, then A has more value for money. As it turns out, high denominations printed in low quantities may be more expensive (Fig. 6a), but they are still better value for money than the cheap stamps (Fig. 6b). In reality, of course, the 10¢ is so cheap that it does not matter that it is poor value for money according to this measure. Nevertheless, the value for money suggests that the high denominations are not overpriced, relatively speaking.

Figure 7. Comparison of population (in millions), print quantity and value for money of small heads issues across the Malay states. In the boxplots, the thick central horizontal bar indicates the median, notches on the sides demarcate approximate 95% confidence intervals, the bottom and top of the box are the first and third quartiles, and whiskers mark the extreme data points.

If one compares the Malay states, one sees an overall correlation of print quantity to state population (Fig. 7). The correlation has been weakened by, but persists despite, the pooling of data across catalogues and denominations. As expected, print quantity is in turn negatively correlated to value for money (FIg. 7). The two sets of boxplots are striking if not perfect mirror images of each other, indicating quite a strong correlation. Small heads issues from remote Perlis are the best value for money overall, while those from crowded Selangor are the worst among the sets shown here.

There are local deviations from the overall trend too. Kelantan and Kedah saw relatively quiet stamp scenes for their population size (Fig. 7), being relatively laid-back rural states. For Malacca and Penang, there are striking differences between the KGVI and QEII sets (Fig. 7), the latter having had a shorter run.


The results indicate that catalogue prices of the small heads issues are geometrically related to rarity, as recommended by Robinson (2000) as a criterion for measures of rarity. And within this overall curve, the catalogues captured many known characteristics and idiosyncrasies in the small heads issues that arose from postal rates and historical circumstances.

On the macroscopic level, the catalogues agree with one another despite spanning a quarter of a century of publication dates and great geographical distance, but this is not surprising since the stamps in question were issued many years before. Catalogue publishers would have sanity-checked amongst themselves over time, as a catalogue cannot deviate too much from others without good reason. The philatelic community has been rather cautious about using StampWorld, but my results suggest that differences between it and the mainstream catalogues are no bigger than differences among the mainstream catalogues themselves.

The small heads issues constitute only a small subset of the listings in any catalogue, but it already seems quite a task for the editor to assign the correct price relations in multiple dimensions across so many denominations and sets. One has to correctly scale the prices not only across adjacent denominations in a set, but also across Malay states at opposite ends of the peninsula, and across mint and used stamps.

In a dictionary, the meanings of words do not change; in the latest catalogue of a scientific equipment supplier, it is easy to quote prices in relation to design and manufacturing expenses. But in compiling a stamp catalogue, one is faced with an enormous number of designs and varieties where clues to the price are buried in fragmentary personal experiences and incomplete historical information filed away on dusty shelves. Stamp catalogues are probably unique among the catalogues of the world.


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