I'm beginning to come to the view that the batsman's individual score isn't quite as important as how many runs get made while he's batting. Pietersen wouldn't have been able to win the game yesterday if Jon Lewis and the other tailenders had got themselves out, to take an extreme example - but look at the way in which WI have recovered to good totals because Chanderpaul has hung around forever or England have been indebted to Thorpe for shepherding the tail as well as his own runs.
As has been pointed out already, no average can ever capture the impact of particular performances, especially when we are talking about great all-rounders like Miller, Botham, Sobers or Flintoff who can take superb catches as well as produce whirlwind innings or crucial bowling spells (apologies to fans of Kallis, Imran and so on, but I don't recall them being regarded as major stars in the field as well as with ball or bat).
I can see the idea behind the first-chance average, and it would indeed help to identify those who are nervous starters, for whatever that's worth. To use it on its own would be pretty limiting, and would undermine its overall logic: to use it as an overall measure, you would have to compile the every-chance average. The basic problem with that is that the figures would end up so small in most cases that it wouldn't really give you much help unless you're prepared to go to the barricades over the difference between 14.87 and 15.04.
Cheers,
Mike