I may be misunderstanding what you are saying, but it seems you are saying the known records were tabulated and then scaled up (extrapolated) to allow for a proportional increase in all the categories in the tabulation. That means the tabulation in TPS was over reported (above what the records revealed), not under reported. For instance, if 20% of the records were missing and they tabulated 4 guns of a certain specification, then the count in the book would have been listed as 5. So a 1 of 5 gun may have been really a 1 of 4 gun. Or a 1 of 6 gun. No one can really say. What you can say is that it is very rare. The other fact is that if, for instance, only 1 or 2 guns of a specification were found in 80% of the records, there is a better than average chance that no more were made in the smaller number of lost records. Additionally, the scaling could be right or wrong depending on what is being considered. For instance, there may have been more or less records lost during the time Bernard barrels were used vs Parker Special. A different scaling factor would have been required for each specification and time period.
I have never heard any mention of extrapolation, but I am surprised it was done. I always assumed that everyone realized it was a count from the known records and that some of them are missing. Generating biased data doesn't seem something that would have been really helpful.
In the case of rare specifications, it really doesn't change much. Unless the majority of the records are missing, the number doesn't even change. Extrapolating the number of 1 or 2 guns will still round off to 1 or 2. For 3 or 4 guns it may round off to 4 or 5. I think it is very, very unlikely that the records show only 1 or 2 guns of a certain specification and then a search of the lost records turn up a batch of 50 of them. They are rare for a reason in the existing records. I think everyone knows that the records are not perfect. There are many known instances where the records are simply wrong based on the gun as found. The only baseline we have to use as a measure of rarity is the tabulation published in TPS and will not change barring a finding of the missing records.
A good question is: how many guns are missing from the records vs the serial numbers used? We all know the serialization book is incomplete compared to the known records due to leaving out the many of the lower grade guns during certain periods. However, we know what serial numbers are recorded in the order books and we know there is an accepted total number of serial numbers, so how much was this "extrapolation"?
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