Note: All data correct as of April 15, 2018. The Test involving the ICC XI in 2005 is excluded.
We first look at the best averages in the third innings:
Bradman does not figure here, as he and his team-mates probably scored enough in the first and second innings so that they did not have to bat much in the third and fourth innings. So we have May, Kallis and Compton at the top of this table. There are also Amla and Azhar Ali from current players.
We now look at those who scored the most centuries in the third innings (5 and above):
Sangakkara and Cook lead with 12, followed by Tendulkar, Kallis and Hayden with 10. Perhaps Cook will add to his tally.
Now let see who disliked the third innings. These players made the most centuries without ever making one in the third innings:
SC Ganguly has the most (16) followed by AG Prince, M Vijay and TW Graveney with 11 each. Possibly Vijay, like Cook mentioned above, will be able to change his status.
Conversely, there are those who love batting in the third innings. Apart from May and his companions at the top of the table, there are those who scored all their centuries in the third innings:
R Subba Row (3). followed by ADR Campbell, GC White and JDB Robertson with 2 each.
Also WW Armstrong scored 5 of his 6 centuries in the third innings (which can be seen in the bottom of the above table).
To be continued with the fourth innings.