The equation for the Timer Ball catch rate is:
(number of turns passed in battle + 10) / 10)×, maximum 4×)
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