Did iPad unit sales grow by 26% or 44% last quarter?

The first time was on Tuesday when CEO Tim Cook announced that Apple sold its 100 millionth iPad on Oct. 9 — only 15.88 million more than its cumulative sales through the June (Q3) quarter. Over the next two days, analysts scrambled to lower their Q4 iPad sales estimates from an average of 16.5 million to an average of 15.4 million.

Then they were disappointed again on Thursday, when Apple reported Q4 sales of only 14 million iPads. That’s 26% more than it sold in the same quarter a year earlier, but quite a come down from the 183%-to-53% unit sales growth the iPad had registered in the previous six quarters.

In his Q&A with analysts Thursday evening, Tim Cook gave several explanations for the shortfall that made sense to me, from customers waiting for the rumored iPad mini to K-12 administrators making their equipment purchases in the spring, not the summer.

But one explanation he gave — which Asymco’s Horace Dediu zeroed in on in a post on Saturday — went right over my head.

“On a year-over-year basis because of the year ago quarter having also a channel inventory build as we stocked the channel to the proper level,” Cook said, “the sell through year-over-year actually grew 44%.”

Whoa! Which was it? Did iPad sales grow 26% or 44%?

To answer that question, I finally had to wrap my head around the difference between sales as Apple reports them and what the accountants call “sell-through.”

If you’re like me, you probably think of a sale as a purchase by an end user. You go into an Apple Store, hand someone a credit card and walk away with an iPad. That’s a sale.

But much of what Apple calls “sales” are actually bulk shipments to resellers — Best Buy, AT&T, Carphone Warehouse etc. — collectively known as the retail channel. For accounting purposes, those pallets of iPads are booked as sales by Apple when they leave the factories in China because the burden of paying for them has shifted to the retailers, also known simply as “channel.”

The great mass of product in transit or piled up in resellers’ warehouses is known as “channel inventory.”

If channel inventory were constant, we could ignore it. But it changes every quarter as Apple fills or draws down inventory by an amount that Apple COO Peter Oppenheimer dutifully reports every quarter during the conference call with analysts, and which I invariably tune out.

But this time it mattered. Because in Q4 2011, when Apple reported sales of 11 million iPads, the company had increased channel inventory by 1.45 million units. That meant actual sell-through — the difference between reported sales and the change in channel inventory — was 9.7 million.

In Q4 2012, when Apple reported sales of 14 million iPads, the company had increased channel inventory by only 200,000 units. Sell through for the quarter was 13.8 million.

So while sales increased only 26% from 11 million to 14 million, sell-through increased, by my calculation, 43% from 9.673 million to 13.836 million. (Tim Cook got 44% when he did the math; we won’t quibble.)

The point is, Wall Street was looking for iPad sales to grow 48% year over year before Tuesday and 38% year over year after Tuesday.

The truth turned out to be somewhere in between.