Catch rate/Examples

Most legendary Pokémon have a catch rate of 3. Assuming its HP is almost depleted and it is paralyzed, and Dusk Ball is used at night or in a cave, then the chance of catching the Pokémon with each Ball in Generation IV is approximated by 3 * 3.5 * 1.5 / 255 = 15.75/255 ~ 6.2%, resulting in about 16 Dusk Balls required to catch the Pokémon on average.

If an Ultra Ball were used instead, then the chance drops to 3 * 2 * 1.5 / 255 = 9/255 ~ 3.5%, which amounts to about 28 Ultra Balls on average.

Alternatively, if a Timer Ball were used after the tenth turn in Generation V or after the thirtieth turn prior to Generation V, the chance of capture is 3 * 4 * 1.5 / 255 = 18/255 ~ 7.1%, or about 14 or 15 Timer Balls required on average.