Hit points and statuses

The capture formula in Pokémon Gen 3 was revamped from Gen 1 and 2, and is now straightforward. In order to have the best chances of a successful capture, a Pokémon's hit points need to be as close to 1 HP as possible and its status Sleeping or Frozen.

The move False Swipe cannot KO a Pokémon, while Spore has a 100% chance to put the Pokémon to sleep. In Gen 3, the Parasect and Breloom evolution lines are the only two which can learn both moves at the same time. To get False Swipe, breeding Pokémon is required, as the move is not naturally learned by either lines. Additionally, Breloom cannot learn Spore, and has to know it before evolving. Fortunately, the Shroomish available in Pokémon XD already has False Swipe when purified, requiring only to level up to 54 to learn Spore.

Poké Balls

The third determining factor in capture is the Poké Ball used. Every Ball has a different multiplier used in the catching formula, with sometimes a condition to fulfill, and is not available in every game. Which Ball is best suited to catch depends on the situation. Here is the list of all the relevant Poké Balls that should be used for capture:

Ball	Multiplier	Condition
Ultra Ball	x2	N/A
Net Ball	x3	Water or Bug-type Pokémon
Timer Ball	x1 to x4	Increases strength every turn (+0.1 per turn) (multiplier x2.1 during turn 12)
Nest Ball	x3.9 to x1	Low-level Pokémon (multiplier x2.1 at level 19)
Repeat Ball	x3	Pokémon already caught in the Pokédex
Dive Ball	x3.5	Used Underwater
Luxury Ball	x1	Any friendship increase is boosted by 1

To encourage players to capture Pokémon and not exclusively fight, the original Gen 1 games included rewards for having 10, 30 and 50 Pokémon owned in the Pokédex. These rewards have been expanded in FireRed and LeafGreen and include several important items. Given these are de facto mandatory to complete a Living Pokédex, here are their locations:

There is theoretically no way to obtain Celebi in any of the NA or EU versions. Fortunately, Celebi was made available in the JP version of Colosseum's bonus disc. To get the Mythical, a JP savefile of Pokémon Colosseum with every Shadow Pokémon purified is required. This leaves 3 illegitimate ways to obtain the coveted Pokémon for non-Japanese players:

• Purify the 48 Shadow Pokémon in JP Colosseum - This will allow transfer using the JP bonus disc. This method requires a Japanese version of both Colosseum and one of the GBA games required for the transfer, as well a Japanese GameCube. The GameBoy Advance is not region locked, and Pokémon can be transferred freely between regions.
• Purify the 48 Shadow Pokémon in NA/EU Colosseum and hack the JP bonus disc - Some people have devised a way to change the region checked by the Japanese Colosseum bonus disc in order to obtain the Pokémon on savefiles from other regions. All the details can be found in this thread.
• Obtain one of the event Celebi - It is possible to find dumps of all the event cartridges on the internet with a little digging.

There exists several event islands accessible in Gen 3. While the graphics and layout may differ between versions, the contents remain the same. It is possible to obtain the event tickets or gain direct access to each area by using glitches, cheating devices or dumps of event cartridges. For convenience, here are the details of each event island: