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What is the Catch rate system? Also how do the special balls help?

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Ever since I started playing Pokémon, everyone talks about catch rate, what in the world does this mean, and how does it work? The other question I have is how do the balls help with catch rate? Also what is the math for this?

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Catch Rate

Catch rate is basically the initial calculation which determines the probability of catching a Pokemon. The higher the catch rate, the higher the probability of catching a Pokemon is. Basic Pokemon have higher catch rates than evolved Pokemon, and Legendaries generally have the lowest catch rates.
>When a Poké Ball is thrown at a wild Pokémon, the game uses that Pokémon's catch rate in a formula to determine the chances of catching that Pokémon. The formula also takes into account the Pokémon's current health, any status effect it may have, and the type of Ball being used.

You can easily view a Pokemon's catch rate on any of their respective pages on Bulbapedia, Serebii, Pokemon Wikia or even here o3o!

How do Balls help?

Different Pokeballs will modify the probability of catching the Pokemon depending on the conditions. For example, an Ultra Ball doubles the probability of catching the Pokemon. Dusk Balls will increase the probability by 3.5x the original amount, provided it is used in a cave or while it is dark.

You can check a full list of the rate changes and requirements of each ball here

Overall Formula

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>HPmax is the number of hit points the Pokémon has at full health,
HPcurrent is the number of hit points the Pokémon has at the moment,
rate is the catch rate of the Pokémon (which may be modified due to use of the Heavy Ball or actions in the Safari Zone),
bonusball is the multiplier for the Poké Ball used, and
bonusstatus is the multiplier for any status condition the Pokémon has (2 for sleep and freeze, 1.5 for paralyze, poison, or burn, and 1 otherwise).
If a Pokémon could have 0 HP, the maximum value for a would be rate × bonusball × bonusstatus. For a Pokémon with full health and no status condition, and with a neutral ball used, the minimum value for a would be rate / 3.

Bulbapedia Page on Catch Rate

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The catch rate system is basically what the chances are of catching a Pokemon at full health with a Pokeball, for example, with Mewtwo the chances of catching it at full health with a regular Pokeball is o.4% or roughly 4/1000 or 1/250. In regards to how the Pokeballs help, each type has certain alterations that make them special. e.g. the regular Pokeball has a standard catch rate of 1x (or 1 times the catch rate of a regular Pokeball, you'll understand at the end) and the ultra ball has 2 times the catch rate of a regular Pokemon. there are also certain Pokeballs with special affects. e.g. the net ball has a times 3 but only when capturing water and bug types. for a full list of all the Pokeballs just click this link:

Hope I helped!

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The catch rate determines how easy a Pokemon can be caught.

Usually, the rarer the Pokemon, the harder the Pokemon is to catch. That's not always the case, but that's a general rule. Catch rates are listed by numbers, the highest catch rate is 255, while the lowest is 3.

Different balls have different multipliers.
The normal red & white Pokeball has a multiplier of x1. That means it'll have no extra added effect at catching a Pokemon.
The Ultra Ball has a multiplier of x2, meaning if a Pokemon has a catch rate of 100, the Ultra Ball will make that catch rate 200, causing the Pokemon to be easier to be caught.
The Quick Ball has a multiplier of x5, but only if used on the first turn of battle.
The Masterball has a multiplier of x255, meaning that it will always succeed in catching a Pokemon (as long as that Pokemon is catchable).

So, lets start with an example like Caterpie.

Caterpie has a catch rate of 255. That's the highest catch rate possible, so you can throw any ball at a Caterpie and it will be caught. It's really common, so that's why its catch rate is so high.

Lets move on to a Pokemon like Pelipper. Pelipper has a surprisingly low catch rate of only 45. That means even with an Ultra Ball, its catch rate is only 90. If you use a Quick Ball on a Pelipper on the first turn of battle, it'll have a catch rate of 225.

There are other things in addition to Pokeballs that help catch a Pokemon, such as HP and status conditions.

The lower the HP, the easier the Pokemon is to catch. That's why the move False Swipe is so useful, because it'll always leave the target with 1 HP, meaning you can accurately get a wild Pokemon down to 1 HP to make it easier to catch.

Statuses like freeze and sleep will have a multiplier of x2, while paralyse, poison and burn will have a multiplier of x1.5. Generally, sleep and paralysis moves are the best because freeze is very hard to happen, and burn & poison will decrease the wild Pokemon's HP every turn, meaning it could faint before you catch it.

Catch rate
List of Pokemon by catch rate

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