As I said earlier, it would have been a simple choice to pick McGrath if their batting would have been close, but it isn't. McGrath's batting was really poor. Running out of partners argument assumes that imran is working with 9, 10, and 11. But doesn't think about his partnership with number 5,6, and 7. The expected number of runs far exceed the very marginal reduction in bowling quality.
I'm interested now, I would like to explore this a bit further and am willing to accept that I could change my mind at the end of this post.
Assuming Gilchrist is batting 7, McGrath never really held his run scoring back.
Assuming the following team (ave in brackets):
Gavaskar (51)
Hobbs (57)
Bradman (100)
Tendulkar (54)
Lara (53)
Sobers (58)
Gilchrist (48)
Hadlee (27)
Marshall (19)
Warne (17)
The team is already on average making 484 runs per match on average. So we look at Imran (38) vs McGrath (7). If the averages were unmoved in this hypothetical tournament vs the Martians, the extra 31 runs is worth an extra 6% to the batting total. This is ignoring the fact that by batting lower down the order, Marshall and Warne are not going to be averaging as much as they did batting at 8 and 9 like they did in real life.
Statistically, McGrath's bowling is 5% better than Imran's bowling on a pure numbers basis and takes 0.4 more wickets per match than Imran. So in this analysis, on average Imran comes out quite a bit further ahead since the extra economy that McGrath offers is roughly only contributing a 1.5% opposition run saving over Imran.
However, this is misleading since the game of cricket is not really played in averages. If it were so, wouldn't we simply play Miller, Imran, Kallis and Sobers as our four batsmen and pick Chappell and Border in our middle order instead?
No we wouldn't, because bowling is more important than batting in test matches. You need 20 wickets (well, at least 10 wickets in theory) to win a test.
But even just looking at batting, the problem with looking at averages for tail enders is that they're very misleading if you're trying to get an idea of how many runs they usually offer to the team. For the top 7, average is a decent approximation of how many runs they will score when they go out to bad. But the lower you go in the batting order, the less likely a batsman is to contribute runs. That's because they're far more likely to end not out. Runs per innings is a measure of what they *actually* output on average. The lower a batsman bats, the wider the gap between their RPI and their average.
Looking at Glenn McGrath's batting stats, he batted in 11th position in 128 innings. He scored 603 runs at 7.6. His runs per innings though was 4.7, giving a whopping 62% difference between his runs per innings and his average due to not outs. In the whole of history, number 11s have contributed 26962 runs at an average of 8.57. They have done so over 5998 innings giving an average RPI value of 4.5. So historically, a number 11 will only score 52.5% of their batting average.
A number 10 will score 76% of their average. A number 9 would score 84% of their average and a number 8 will score 87% of their average.
So let's look at the two tails and adjust based on their batting position:
Name (ave) (RPI based on historic averages)
Imran (38) (33)
Hadlee (27) (23)
Marshall (19) (14)
Warne (17) (9)
Total (101) (79)
Hadlee (27) (23)
Marshall (19) (16)
Warne (17) (13)
McGrath (7) (4)
Total (70) (56)
So the actual RPI difference between these two sides (assuming averages don't change shuffling players up/down the order) is 23 runs in total. Assuming that the top 7 make their averages, they make 421 the two average scores are 500 and 477. The side with Imran in theory makes around 4.8% more runs than the side with McGrath.
But it's not even that simple in Imran's case. He batted a significant proportion of his career in different batting positions. He batted mostly at 6, 7 and 8. Here are his stats in those positions:
Position - innings (ave) (rpi)
6 - 23 (62) (40)
7 - 63 (35) (29)
8 - 30 (27) (24)
All - 126 (38) (30)
Looking at Imran's overall record, his RPI is actually far lower than the average number 8 batsman despite spending a huge proportion of his career batting 6 and 7. Even if we use his career average RPI, we're still looking at the difference in scores between the two sides now being 20 runs in total, or 4% of the batting total.
If we assume that both bowlers take 25% of the wickets in a match, then that means McGrath saves his team a total of 3 runs per innings. Imran is therefore more valuable to this team on average by 17 runs per innings, or roughly 3.5% of the average score of this theoretical ATG side. In a real side Imran becomes even more valuable relatively.
For Imran to be worse for this side than McGrath, he would have to average around 30 with the ball, assuming that Imran bats to his average.
This is of course assuming that the tests that this team plays are all timeless. If they are not timeless and the team averages 477 runs per innings, are you really going to add a slightly inferior bowler for the sake of 20 extra batting runs per innings? I guess that's left to the reader to decide.
Between, for me, it was never between Imran and Mcgrath until Steven brought it up. Marshall and Warne are not 20+ average batsmen anyways. All I am doing is having my batting lineup as strong as possible while also picking some of the greatest bowlers ever, giving it as much cushion as possible against any batting collapses. We can agree to disagree. There was nothing better to do than this on a sunday 
