This is basically an add on to a post from u/republicofplay, who also has more info in his OP including comparisons/analysis of Mortal Empires.https://www.reddit.com/r/totalwar/comments/th4g4c/player_numbers_for_tw_games_at_28_days_from/
Comparing IE to ME, Immortal Empires was not able to beat Mortal Empires 28 day drop.Mortal Empires
Day 1: 41,500
Day 28: 16,977
% Drop: -59.09%
IE had 3X the player count at launch compared to ME, so this is still quite impressive. WH2 ME player count was more a slow build anyway.
So, in summary Warhammer 2, ME, IE and to a lesser degree 3K are the most successful Total Wars in terms of Player Retention at launch with Thrones of Britannia and Warhammer 3 being the worst.