We have some production numbers for some brands, from the journals of the period and the breakup legal cases. Packs produced in a year does not equal cards though; the ledgers and records indicate relatively short pack-issue periods for a particular set of cards and many packs appear to have had no cards even for brands that were among the frequent issuers of the cards.
Most estimates seem off base to me because they are almost all ignoring the non-baseball cards and/or the lack of cards at all for certain periods.
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