The equation for the Timer Ball catch rate is: >(number of turns passed in battle + 10) / 10)×, maximum 4×)
[**Source**][2]
This means that it will take 30 turns for the Timer Ball to reach its most effective stage. 10 turns for a x2 effectiveness, and 20 turns for a x3 effectiveness.
I love Weird things ¯(°_o)/¯ Hail to the Mod [1]: http://cdn.bulbagarden.net/media/upload/3/3d/Bag_Timer_Ball_Sprite.png [2]: http://bulbapedia.bulbagarden.net/wiki/Poké_Ball