Faced with the choice between changing one’s mind and proving that there is no need to do so, almost everyone gets busy on the proof — John Kenneth Galbraith

When Apple announced iPad mini I wrote in GigaOm,

At the high end, Apple could sell as many as 58 million (full year), but those chances are very very slim (1 percent). Considering all the possible scenarios, the expected value of volume is 40 million.

Apple released its Q1FY13 earnings today, let us estimate how many iPad minis Apple most likely sold. The iPad mini numbers are based on the Apple‘s report.

They sold a total of 22.8 million iPads (new iPad, iPad2 and iPad mini), compared to 14.03 million in the previous quarter (pre iPad mini). If you were to attribute all incremental volume to iPad mini it comes to 8.77 million. I could stop here and say my model is correct.

If you compare the Average Selling Price (ASP) between two periods, in Q4FY12 the iPad ASP (iPad and iPad2) was $508 but it dropped to $467 this quarter (Q1FY13).

So let us plug in these numbers into the model I recently built to estimate the number of iPad minis Apple sold. We find that the 8.77 million is actually the lower limit. With the assumptions I have made, Apple likely sold 12.5 million iPad minis (all editions combined).

Apple put on some impressive iPad mini numbers. Did it cannibalize its full priced iPad? You bet it did. Last quarter Apple sold about 9.84 million full size iPad. (Again see the model.) That number dropped to 7.42 million units, thanks to iPad mini. So a cannibalization of 2.42 million units — that is 2.42 million people who would’ve chosen full size iPad chose iPad mini.

How did I do with my previous prediction of iPad mini numbers in my GigaOm article?

I predicted an annual expected volume (considering all possible scenarios) of 40 million. But Apple could end up selling at least 50 (4 times 12.5) million iPad minis in FY13.

What did my model say were the chances of selling 50 million (full year) units or more?

Mere 12%.

As Galbraith said I could get busy arguing that is still within my scenarios and I am still correct. Galbraith’s writings have influenced my thought process in many ways, I will note his warning and not get busy with my proof.

It indeed appears I had started with some overly conservative numbers on iPad mini uptake based on the survey results I had used. Hence my model underestimated the iPad mini volumes considerably as iPad mini yearly volume could be 50-60 million units.

Model is only as good as the informed input we start with. After all we are paid to make better hypotheses and make informed assumptions.