The basic premise being that the openers have 50 overs left in which to get out while a number six may have something like 20 or so.
I decided to check Dhoni's figures for those innings when he came in to bat in the first 25 overs of an odi innings. Since the data is not available for this I had to go through all his carreer innings list and see the over in which he came in to bat. To save time, I took only the innings since 1st Jan 2010 till date - a period of just over three years.
I 33 such innings where he came into bat before the 35th over was completed. Of these there were three innings where, although he went in early, there were only a handful of overs left for India to play since they were chasing a small total. I removed these three innings since this was not the kind of situation I was looking at. Here is what I found.
Innings : 30
Not outs : 4
Runs : 1103
Balls faced : 1524
Avg : 42.4
St Rt : 72
100's : 2
50's : 6
India lost 60 % (18) of these games.
If you take away the minnows (Bangladesh and Ireland) the average comes down to 39 and the strike rate to 70
The loss percentage goes up to 67 % (18 out of 27)
When he comes into bat after the 25th over his average is above 78 and the strike rate about 105.