When it comes to Apple's (NASDAQ:AAPL) new Apple Watch, we don't know what we don't know. The Mac maker justifies this opacity by saying it doesn't want to tip its hand to its rivals, but at the same time it's not quite clear what competitors could even do with that information. It should come as no surprise that Apple is already the most successful smartwatch vendor on the market right now, a conclusion that's not hard to come by even without concrete data.

Here's what we know

The list of data points that investors know about Apple Watch's performance is quite small. We know that Apple Watch accounted for "well over 100% of the growth" in the Other Products category, so Apple Watch revenue was at least greater than $952 million, but could have theoretically been as high as $1.5 billion. The only other indication that Tim Cook gave on the conference call was this: "And to give you a little additional insight, through the end of the quarter, in fact the Apple Watch sell-through was higher than the comparable launch periods of the original iPhone or the original iPad."

Apple Watch launched at the end of April, so it was available for approximately two months out of the quarter, albeit severely supply constrained. To compare Apple Watch sales with the iPad, Apple sold 2 million iPads in just under 60 days after launch. So investors know for a fact that Apple has sold over 2 million Apple Watch units for "well over" $952 million. To be clear, even 2 million units sold is an unqualified success, immediately making Apple the top smartwatch vendor.

But what about 4 million?

Here's where the ongoing guesswork comes in. Two different market researchers have put out their estimates on how many units Apple was able to sell. Strategy Analytics believes that Apple sold 4 million Apple Watch units, while Canalys pegs the figure at 4.2 million. It's unclear what methodologies are used to arrive at these estimates, but 4 million seems a little bit too high. Here's why.

Let's say that Apple Watch generated $1.5 billion in revenue, which is probably an optimistic scenario. If Apple sold 4 million units, that would translate into an average selling price of just $375. That ASP seems too low, because it would imply that demand is almost exclusively concentrated in the Sport model. While demand is probably skewed toward the more affordable Sport model, but I doubt that it's that skewed.

Anecdotally, I've seen a handful of the stainless-steel models out and about, which start at $550. Combine that with prior reports that demand is also concentrated in the 42mm models. Noted Apple analyst Ming-Chi Kuo with KGI Securities estimated in May that 42mm models are accounting for 60% to 70% of production, with buyers predominantly being men (who prefer larger watches). Not including the gold models, the 42mm models carry a $50 premium.

Theoretically, even if all demand was exclusively for the Apple Watch Sport and there were zero sales of Apple Watch (stainless steel) or Apple Watch Edition (gold), then the ASP would still be greater than $375 because the pricing range for Sport models is $350 to $400. Clearly, Apple did sell at least some of the more expensive models.

The $10,000-and-up Apple Watch Edition was never destined to be a big seller in terms of unit volumes, but I'm sure Apple sold a handful of them. In hindsight, that Wall Street Journal article proclaiming that Apple was ordering 1 million Edition units per month during the second quarter sounds even more absurd. Sadly, Apple won't need to procure 560 metric tons (a fifth of global production) of gold each year.

Math doesn't lie

There's no way Apple sold 4 million Apple Watch units during the second quarter, since the implied ASP is unrealistically low. If we use a more realistic theoretical ASP of $500, then that would translate into $2 billion in revenue. But that would comprise the bulk of the entire Other Products category, which generated a total of $2.6 billion in revenue. Tim Cook acknowledged that iPod and accessories sales are shrinking, but it seems unlikely that they plunged by over 60%.

As it stands, the numbers simply don't add up.