It is interesting to note here that Viv Richards, who was rated as one of the best captains by the blog from where I got the idea of doing such an analysis, was a much better batsman when he wasn't captaining the side. His batting average as captain fell by more than 5 runs per innings as compared to his career average. Sir Richards averaged 53.64 in the 71 test matches he played while he wasn't captain, 8 runs higher than his average as captain. Moreover, in those 71 matches he managed 18 centuries, while in the next 50 as captain, he managed only 6. Finally, his case is similar to that of Pontings - he continued from where Lloyd left.
Brearley can easily be discarded from the list as his performance as captain or otherwise isn't much to speak of. I would also leave Mark Taylor out based on the numbers above.
This leaves us with Steve Waugh, Clive Lloyd, and Ian Chappell, the last of whom improves on his career batting performance the most when playing as a captain. Steve Waugh and Clive Lloyd have very similar records as captains, although Lloyd's improvement from his career average is much more than Waugh's. At this time, I still think Waugh has his nose slightly in front as he ranked #2 in part 1 and #1 here.
Watch this space for the final part where I analyze the 3rd criterion and reach a decision on who has been the best cricket captain in the last 40 years.