Sorry that one's way over my head as well. How do you reach that conclusion?
LOL, ok, because a large portion of the not-outs Imran secured were as a tailender/lower-order batsman. Most of those not-outs are single-digit/unimportant scores.
You're persistently falling into the trap of viewing a not-out as increasing an average. It doesn't. It just doesn't count against it in the way that a dismissal does.
If I get 100 runs at #5 in one innings, it is much different to, 10*, 10*, 10*, 10* at #8 and a 60 at #5. Essentially, it's the same average but it goes without saying which one is harder to do.
Getting a not out with a large score is much harder to do in the middle order than get a small score not out and a medium score out lower down.
Again, your argument seems to proceed on the basis that Imran was "benefitting" from the not-out. With respect, it's completely fallacious.
Put it this way: if he's left not-out on (say) 40, he's been deprived of the chance of scoring more runs, and perhaps adding to his tally of centuries. The fact that he didn't have that chance is no reflection on his ability. What defines his ability is his ability to score runs when given the chance to do so. And the batting average provides a gloriously pure way of demonstrating that (albeit that it needs to be read in context with regard to conditions, opposition, era, etc).
You're hypothesising, I am going by his actual not-outs. A lot of his not-outs are a) single-digit scores b) unimportant (in that it was maybe 10-30 and for whatever reason, other than the batsman's grit, the innings had to end)
They don't deprive him to show anything because as batsman that bats that low he is unlikely to score more. That's the whole reason he is there in the first place. If anything, him not getting out at the stage of his career adds better to the later stage in his career where he can actually hold a bat.
Miller has 7 not-outs which is roughly standard for a middle-order batsman, with respect to the amount of innings he has played. 2 of then are 50+ scores (in fact they are both almost 150 scores). Imran has 25 not-outs. To give you some perspective, Sachin Tendulkar has played almost double the amount of Tests as Imran and only has 27 not-outs. In 10 of them Imran has 50+ scores. We'll ignore the others as not-outs for both batsmen.
Miller averages 35 (actual: 37)
Imran averages 33 (actual: 38)
Even then, Miller is ahead. Think about this: even though Imran has played 39 more innings, he has only scored 849 more runs.
I would only buy your point if they both batted the same position for most of their career.