Can you see any flaws in your logic?
I've invited any suggested improvements to the math. So far all you have said is that you dont like averages, maths and stats but you read and watched some games, and rank Sobers batting higher than Imran's bowling without an expressed objective or logical measure that I or anyone else can use. I like a more objective measure than that so as to compare batting to bowling. So I use the runs per wicket average of their eras to find how far above or below par that any given cricketer was. Sobers' bowling improves his par score by 5 runs per match, he is about 40 runs ahead of par per match on average, that is brilliant which it should as he was better than average bowler and an outstanding batsman and a true match winner, but he was no "front line" or "strike" bowler. He was a very good or excellent 5th bowler. He was a better than average bowler overall. That's what the math confirms. Could he have bowled more? Possibly, but the West Indies captains and Sobers chose not to for whatever reason. I doubt it was to help the opposition make more runs. So we are limited to what actually did happen in a career in terms of wickets taken. I find that measure quite objective. If Sobers was not such a master batsman, he wouldn't have played much as a specialist bowler at 2 odd wickets per test. That is not a difficult conclusion for anyone to accept. So sticking to what he actually did on the field, he is 35 odd runs ahead of par for batting which is improves by another 5 runs for his bowling. The precise numbers are on the preceding page. I think you may be missing the point that to improve on par, a player actually has to score enough runs, or take enough wickets below the average, to have a better than par score. So a batsman must average 36 or so (depending on the era) before he starts improving your teams fortunes and carries the specialist bowler's runs per wicket. That makes sense because specialist batsman below that score are obviously a hinderance. A batsman averaging over 40 over a decent length career is typically referred to as a good batsman.
I think you should think about the runs per wicket average and understand how it works, and if you have suggestion for improvement, I am open to suggestions for improvement. But if you merely misunderstand it, please read around on it. It is an objective measure, that is used for teams regularly and widely by many cricketing writers and analysts. A team is merely the sum of its parts, so I am using it for the players themselves to see how individually they fared.
I accept maths and stats as a means of sports analysis. I understand the limitations thereof. Fielding is excluded. So is captaincy. Running between wickets. Just a record of batsman vs bowler and a comparison who is above and below par as a batsman, bowler and ultimately as a cricketer. Bad and good pitches, batting under pressure, batting under little pressure, bowling under pressure, bowling under little pressure, easy runs and hard runs, lucky wickets and unlucky wickets/non wickets will average out, not perfectly but appreciably.
What the stats reveal is interesting. The West Indies 81-89, who made them a great team? Their batting or their bowling? Well despite Richards (who I think was declining towards the end of his career), Lloyd (for half the period), Haynes and Greenege, the West Indies were only above merely average with the bat, but they had Gomes and Hooper and some average batsmen play a lot of matches in sum. But they were ridiculously ahead of par with the ball. Cricketers always talk highly of Viv and Greenidge, and the entire West Indies attack, so it makes sense. Their batting was average at 36.27 (35.86 being the exact average) with Marshall batting 8 in the absence of a Hadlee, Imran, Botham or Dev. But their bowling was exceptionally good at 26.13. That's like a 100 runs lead on average at the conclusion of the first innings. What does it lead to in real terms? A win loss ratio, 5.71 wins for every loss with 58% of test played won.
The Australian team of 2000-2007 - well their batting was way ahead of par at 44.39 per wicket when the average is 38, but their bowling was at 27.25, or similarly as dominant as the West Indian bowling when standardizing eras. So while both facets are match winning, the bowling contributed just a little bit more. That is utter destruction of opposition. That is like a 170 run lead on the average at the conclusion of the first innings. What does it lead to in real terms? A win loss ratio, 7.2 wins for every loss with 77.4% won. That is just ridiculous. Now not every player contributes the same to this winning advantage - surely that you can accept. So the player's individual performances can also be measured.
There is great objectivity in the wickets per runs average. It can be used for players and teams alike. By analogy, and I am not saying that you would, you could tell me and argue till your blue in the face that the 1980's WI dominant because of its batting. I would respond that the numbers tell me that they were merely just above average overall for batting, but they were amazing for bowling, which makes sense because they batted Marshall at 8 and played the likes of Logie and Gomes as well as well as someone like Viv Richards (who was in decline towards the end of his career).
If you were to try and tell me, and I'm not suggesting that you are, that the West Indies batting line up top to bottom was as strong for their era as the Australian team 1999-2007, top to bottom, I will respond that the statistics strongly suggest otherwise and that its probably not the case that the 1980's West Indies batting line up top to bottom was as strong as the Australian batting line up top to bottom for their respective eras. And then you think well Australia had Gilchrist at 7 with 6 brilliant batsmen ahead of him, and a strong tail bar McGrath, it makes sense, even with Warne at 8.
Batsman WI Ave Aus Ave
1&2 43.10 48.52
No.3 44.85 62.77
No.4 37.50 45.12
No.5 41.90 46.37
No.6 39.26 39.75
No.7 32.87
51.52
Era comparison is 35.86 average for the 1980s. 38.37 odd for the Australian era.
Just look at that "Gilchrist factor" in the Australian team. You must accept that statistic surely?