The real question you would need to address is "What is the probability of someone who owns card X submitting it to be graded in the first place?"
Scrolling through PSA pop reports I notice that there are a lot of 1988 Donruss commons with pops of zero (or 1 or 2). This obviously means that the odds of someone submitting a 1988 Donruss common are zero (effectively). We can't draw any conclusions as to how many 1988 Donruss cards there are from the pop reports obviously (actual number: way too many).
At the other end of the scale you have the T206 Honus Wagner. Are there any copies of that which haven't been graded (anyone know)? The odds of that are pretty close to 100% given its scarcity and value, which create a high incentive to owners to have them graded.
Most pre war cards and ones from the 50s fall somewhere in between these two and I think for a lot of them you could actually do some statistical modelling to predict the likelihood of a card being submitted. Some stuff we do know from pop reports:
The relative probability of an individual player's card in a given set being submitted compared with a common card. Like Mickey Mantle cards might be 20 times more likely to be graded, Willie Mays 15 times, Warren Spahn cards 10 times, Richie Ashburn 4 times, etc etc.
The relative probability of a valuable card in a given set being submitted compared to a less valuable card. Like a 100$ card might be 10 times more likely to be submitted than a 20$ card, etc etc.
You could easily identify a number of other variables to measure like that from existing data (rookie cards or not, desirability of specific sets, team populartity, grade of the cards etc etc). From all of these categories you could probably identify the relative likelihood of a card being graded to that of a common from the same set.
This in itself doesn't tell you anything about total numbers in existence, you would still need a key to work back from. That might be found in more recent sets where we do know the number of total cards out there. If you have a set with a print run of 10,000 and 10% of the cards of the key player which is valued at 200$ have been graded, you know that the odds of someone with a 200$ key player card having it graded are 1 in 10.
You could then try to figure out if that ratio is likely to fit a set from say the 1950s. You would have to figure out some way for controlling for differences (ie the fact that the modern set probably has most of its cards still in top condition, the fact that the older set might be more iconic and thus more likely to be graded, etc). This would be indelicate work but you could probably at least get a way of getting a ballpark estimate from it.
Has anybody ever done this before? Way too much work for me to try it.
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