Catching Legendaries in Modern Emerald: Rates, Balls and How Many Throws

Every legendary in Modern Emerald sits at a base catch rate of 3 out of 255 in the game's data — the vanilla Gen 3 legendary rate. The trouble is not the rate, it is the ball, the HP and the status you bring, because a rate-3 Pokémon at full health is one of the worst catches in the game.

The short version

Never throw at full HP. Get the target to 1 HP and put it to sleep, and you roughly quadruple your per-throw odds (and with an Ultra Ball, five times) compared to full HP with the same ball.
The Timer Ball is the best ball in a long fight. Its multiplier climbs with the turn count, reaching its cap at turn 30 — better than an Ultra Ball from turn 20 onwards.
In Hard mode, ten legendaries drop to a rate of 2, which removes the low-effort options entirely: at full HP an Ultra Ball is a 0.39% throw.

The real odds

Assuming a level 70 legendary with around 300 HP — so Kyogre, Groudon, Rayquaza, Mewtwo and the birds — and the Gen 3 catch formula the game uses. "Expected throws" is the average number of balls you should budget; the 50% column is how many for a coin-flip chance:

Mode	Ball	Target state	Per throw	Expected throws	Throws for a 50% chance
Normal (rate 3)	Poké Ball	full HP	0.39%	255	176
Normal (rate 3)	Ultra Ball	full HP	0.78%	128	88
Normal (rate 3)	Timer Ball (turn 30)	full HP	1.57%	64	44
Normal (rate 3)	Poké Ball	1 HP + sleep	1.57%	64	44
Normal (rate 3)	Ultra Ball	1 HP + sleep	3.92%	26	17
Normal (rate 3)	Timer Ball (turn 30)	1 HP + sleep	8.63%	12	8
Hard (rate 2)	Ultra Ball	full HP	0.39%	255	176
Hard (rate 2)	Ultra Ball	1 HP + sleep	2.35%	43	29
Hard (rate 2)	Timer Ball (turn 30)	1 HP + sleep	5.49%	18	12

The pattern is consistent: a sleep + 1 HP target with a Timer Ball at turn 30 is about twenty times better than an Ultra Ball thrown at full health.

Which balls exist here

Modern Emerald is a Gen 3 engine, so the later-generation balls (Dusk, Quick, Repeat-in-bulk) are not all present. The balls in the item data are Poké, Great, Ultra, Premier, Nest, Net, Dive, Timer, Repeat, Luxury, Safari and Master. Notable multipliers: Net Ball is the specialist for Water and Bug types (Kyogre), Dive Ball is strong underwater, Nest Ball works on low-level targets, Repeat Ball for species you already own, and the Timer Ball for everything that drags on.

What Hard mode changes

Hard mode lowers the catch rate of Mewtwo, Mew, Ho-Oh, Lugia, Celebi, Kyogre, Groudon, Rayquaza, Deoxys and Regigigas from 3 to 2, and boosts their stats while you are fighting them — Regirock's Defence hits 999, Registeel sits at 350/350 defences, Regieleki reaches 999 Speed. Some of them are only realistically catchable with a status-and-1-HP setup.

Practical setup

Bring a False Swipe or fixed-damage attacker to leave exactly 1 HP without risking a knock-out.
Bring sleep, not paralysis — sleep doubles the catch value, paralysis and poison only multiply by 1.5.
Stall to turn 30 if you are using the Timer Ball; it is worth losing a few turns.
Save before the encounter. These are static battles, so nothing is lost by resetting.
If it roams or chases — Entei, Raikou and Suicune — the level changes between encounters, so the HP pool changes with them. Entei goes 40 → 50 → 60 and Suicune drops 90 → 80 → 70, so Suicune is easiest on the final encounter.

Catch rates read from the extracted Pokémon data (pokemon/*.json); the throw odds are computed with the Gen 3 catch algorithm at 300 max HP. Hard mode rate changes and stat boosts from the hack's official documentation.