Stats can be argued all day long, one can argue that Botham raced to 1,000 and 100 wickets, 2,000 and 200 wickets and 3,000 and 300 wickets as well as the fact that no all-rounder has more hundreds and 5-fers. I would rate Botham as a much better batsman than Imran and the reverse is true for me when it comes to bowling.
For his peak, I'm considering his first 50 Tests, a period where he notched up 9 Test hundreds (one more than Imran scored in his whole career) and took 19 five-wicket hauls (just 4 less than Imran's whole career tally). Now I perfectly understand the circumstances and the context why Imran did not score a lot of hundreds and why he lost a lot of bowling peak years due to injury, and also I accounted for the Packer rejects against which Botham padded up his stats (I mentioned it before you brought it to the table), but in spite of considering all of this, I have my doubts over Imran's ability to influence the game with the bat in the same vein as Botham could in his peak.
After studying all the top all-rounders of that era in depth, I've come to the conclusion that no one topped Botham when it came to the ability to influence the game with both bat and ball at the same time like he did in his peak. I have my reservations regarding Imran's prowess as a batsman (again, taking all the factors into consideration) and I would rank him well below Botham with the bat and just a little below Kapil.
As far as bowling is concerned, he is well ahead of them all except Hadlee. Hence, one can say that Imran was the most complete all-rounder of that era when you take the whole career into account. Hadlee was not an ATG batsman, Kapil was not an ATG bowler while Botham (in his peak) and Imran were ATG all-rounders.
However, since we are only discussing peaks here, I am yet to see any convincing argument why I should consider a portion of Imran's career as superior to Botham's first 50 Tests when it comes to impacting the game with both bat and ball at the same time.
You see, you are putting a qualifier of 1st 50 Test as the peak, simply because that statistically fits your argument; otherwise in any career, peak is considered the best few years of a career. In that regard, ifI take 1st 100 ODI of Tendulkar ... you know. And that first 50 Test statistical superiority is only because Botham (no disrespect, 2nd best all-rounder ever, tied with 3 others) had lots of matches against sub-standard teams in that period. Even, in his peak days, apart from that 1981 Ashes (which Pom media blown out of proportion - truth is Greg Chappel, Thompson & Pascoe didn't tour, while Hogg played 1.5 Tests before injuring himself), he had 9 Series against WI - batting average ~10, bowling average 30+; 1982-83 Ashes down under - batting average ~27, bowling average ~40. He played 6 Tests in 1982 summer - 3 against IND (batting average 134), 3 against PAK - batting average ~25. Moreover, thinking of that head to head of 1982 made him chasing Imran for through out his life.
The 5 wicket theory I can take partially, with a foot note. 5 wicket hauls are a function of match duration & the amount of overs you are bowling - it's always good to have a 5 for, but it doesn't help much for 100 runs - it's like Walshi's 519 Test wickets. In many, many spells, Imran had 3/30, 4/40 & the match ended in draw, simply because of the duration of match - since you have analyzed the matches, I don't think I need to explain this. But, more or less, the bowling argument is settled.
Coming to batting, you are probably among 2/3 people who considers Botham as better bat than Imran (& first one, when it comes to Kapil - even, I have read & heard Indians for 25 years
. Every former cricketer that I have read or heard said that among 4 greats, Imran was the most proper batsman - technically most complete to play pace, spin, swing & bounce, who batted at No. 4 for Sussex, while Botham at 5/6 for Somerset & Kapil at 6 for Northants (?). The word "Impact" I understand, though it's a bit over used - but here I have to argue, because we are talking about Test batting.
Batting in Test is not about slogging or SR only & it's a misleading word - batting to win. I haven't read such qualifiers when we talk about Kapil's 4 SIX at Lord's or his 129 at St. Georges. In Test (Actually in cricket), batting is all about serving the purpose - be it aggressive or defensive when it matters. Saving a Test is equal to win a Test - Imran played most part of his career for a struggling batting unit - hence he had to bat for salvaging most times. I can categorically tell that, he could have played some quick fire innings, still would have averaged at least well above Kapil - BUT, you can't even think of Botham saving a Test like Multan (WI, '81), MCG (84), Adelaide (90), SCG (90), Madras, Eden, Jaypur, Karachi (WI), Pindi (WI), Birmingham (82, 87), Leeds. Or him batting in a low scoring Bangalore ('87) - these are not statistically stunning innings, but impactful indeed.
As I said, he played for a much weaker batting line-up hence often had to salvage something - BUT, few times, when he had the chance to bat with his top order standing firm - he damaged some career - ask the Indian spinners touring PAK in 1978, or the Indian bowlers in 82. The batting filter that you are using, by that logic Flintoff comes almost at per with Jaques Kallis .....
Any way, I appreciate your last line regarding ATG All-rounder - in fact, not for peak years (1st 50 Test); Sir Ian Botham was truly an outstanding all-rounder, one who could make the ENG team simply as a batsman or bowler for few years. And, he was probably among top 5 slip catchers I have seen, despite his "thirst" pushing his bread basket out.
