Note that the inventory problems that Ryan Dancey documents were in 1997, a dozen years after Gygax's ouster, and we have no indications that such problems existed during his tenure there. Gary received per-unit royalties on sales of D&D and AD&D books, and continued to do so even after leaving TSR, so he had hard, verifiable data on a quarterly basis of how well product was selling (assuming TSR paid out royalties on something like units distributed minus returns). He presumably applied his own logic to those numbers to arrive at the number of players. That logic may have been flawed or incomplete to some degree, but not likely badly so -- if he estimated 5 million players the actual number could well have been 4 million or 6 million, but not likely 2 million or 9 million.