What is the best time control for improvement?

Only time I have ever improved is by studying games from books. WHle games, move by move with the next move covered up and with the best annotations possible. It is funny, in other endeavours, snooker, golf, football, maths, swimming, training to get better does not involve actual full games, so I do not see why it should be different in chess.
Once read a book about improvement by Danny somebody. he worked out that the best US Football star trained incessantly every day and his actual playing time amounted to like 5% of his activity, the guy hardly played at all! That's pretty much what I get the impression the likes of Vishy and Fabby do and what Carlsen did when younger before on-line banter stuff came along.
Just a thought. 
I am addicted to bullet however!