I'm pretty sure this hasn't done before, but I could be wrong.
This XI is made up completely of the best averaging batsman and bowlers in history. Only the two openers have been picked in terms of being the best at their position, while the rest of the middle order have been chosen purely on average. My team has two openers, four middle order batsman, one keeper (selected solely on batting average), and then the best averaging bowlers, three paceman and a spinner. The qualification for batsmen is 20 innings, while for bowlers it is at least 50 wickets.
1. H Sutcliffe, ENG (60.73, 54 games)
2. JB Hobbs, ENG (56.95, 61 games)
3. DG Bradman*, AUS (99.94, 52 games)
4. RG Pollock, RSA (60.97, 23 games)
5. GA Headley, WI (60.83, 22 games)
6. E Paynter, ENG (59.23, 20 games)
7. A Flower+, ZIM (51.55, 63 games)
8. W Bates, ENG, OB (27.33, 15 games, bowl 16.42)
9. W Barnes, ENG, RM (23.39, 21 games, bowl 15.55)
10. GA Lohmann, ENG, RFM (8.88, 18 games, bowl 10.76)
11. JJ Ferris, ENG, LFM, (8.76, 9 games, bowl 12.7)
So there it is. 7 Englishmen and one Australian, South African, West Indian and Zimbabwean. It should be noted that although I was planning on taking the best spinner and the best three seamers, it turned out that of the top four bowlers, one was a spinner while the rest where seamers. As you can see, there are no current players there. Were it not for his recent performances, I'm pretty sure Gilchrist would have been in there for Flower. Keep in mind the bowlers were selected in terms of averages; different teams could be made with strike rates or economy rates. Bradman is captain as he has the best captaincy record out of those in the team
Obviously, different people can have differing opinions in terms of make-up of sides (I have no allrounder, unless you count Bates and Barnes), different types of bowlers, and you may also have different ideas of what it takes for players to be qualified (Ferris only has 9 games). Feel free to post your own sides based on any different ideas.