I'm not sure why you take Botham's peak as from 77-84, his peak actually ended around his famous Ashes in 81/82,. After that, his performances ranged from inconsistent to finally mediocre, especially with the ball.
This is a fair point, perhaps not so much with the bat, but certainly with the ball. Inconsistent, from 82 - 84, and mediocre (at best) after 85.
However I take 1984 as such a statisical marker because, from recollection, in 1984 Botham had the second of his injuries. 1982 saw the first incidence of back trouble. After 1982, even though not as great as he had been, he was still a good/decent all-rounder. I agree though that his first peak was 1977 - 1982, while the second phase was a gradual descent, while after 1985 it became a steep slide. Either way, the total statistics rack up for that 1977 - 1984 period.
Its a fair point regarding the WI, but as I have argued before, I dont think that conclusive. Although I can see the counter-argument. In any case, Imran only did well against the WI with the ball, while Hadlee did better against WI with the bat and is equivalent with the ball. But that hardly establishes Hadlee as being the better all-rounder than Imran, does it? Its the same with Kapil, better than both Imran and Botham with the bat against the WI, and thereabouts or slightly behind with the ball than Hadlee or Imran, but again, it would be hard to argue that he is a better all-rounder than either of Imran or Botham.
My point was more about the validity of peaks in determining players, especially all-rounders. Certainly you could look at Botham's first peak from 1977 - 1982 where he played around 50 tests, iirc, and that would be enough, I think, as a statistical sample to judge him by. I chose the 73 test marker because he was still good upto then, it tracks to an important event in his career (his major back injury which kept him out of cricket until 1985), and it seemed a more fair and reasonable marker to set.