Capturing Pokémon

Capturing Pokémon is the most important thing in the Pokémon Games. Without it you wouldn't be able to obtain any Pokémon. There's numerous factors involved here, with each Pokémon having a specific catch rate which goes into the calculation in order to determine whether or not the Pokémon is caught. The calculation runs through various different variables before finally determining whether or not the Pokémon is captured

The first element involved is the Pokémon's Hit Points. The Pokémon's Hit Points are factored in to the calculation with the lower the HP being from its maximum possibly Hit Points, so the lower the ratio of Hit Points, the better the chance of catching. A good thing to use here is a move like False Swipe which will always leave a Pokémon with 1 HP

CatchChance = floor((3 * MaxHP - 2 * CurrentHP) * 4096 + 0.5)

After this, the species catch rate is factored in. Each species and form has got a specific rate, which can be seen in the Pokédex throughout the site. The Heavy Ball effect is also factored in here, adding a value to thecatch rate straight out if the Heavy Ball is used

Heavy Ball
CatchChance = (SpeciesRate + HeavyBallModifier) * CatchChance

Standard
CatchChance = SpeciesRate * CatchChance

PokéBalls

After that calculation is done, then the Poké Ball you used is factored in. Each Poké Ball has got a special factor that alters the catch rate in certain circumstances, or just as standard. This ranges from the location caught, the type of Pokémon and more

CatchChance = PokeBallModifier * CatchChance

Icon	Name	Effect	Approx. Rate	Fig.
	PokéBall	Standard ball used to capture Pokémon	* 1	4096
	Great Ball	A Ball with a better catch rate than a PokéBall	* 1.5	6144
	Ultra Ball	A Ball with a better catch rate than a Great Ball	* 2	8192
	Master Ball	A Ball that never fails at capture	---	---
	Safari Ball	A Ball that only exists in the Safari Zone	* 1.5	4096
	Net Ball	A Ball that works better on Bug or Water Types. If they aren't Bug/Water then * 1. If they are then * 3 As of Pokémon Sun & Moon, the multiplication is *3.5	* 1 * 3 *3.5	4096 14336
	Dive Ball	A Ball that works better on the ocean floor and on Pokémon on water If used out of water then * 1. If battle field is water then * 3	* 1 * 3	4096 14336
	Nest Ball	A Ball that works better on Pokémon of a lower level The Opponent's Level is put into the following formula: (40 - Level)/10. The higher number at the end the better From Sun & Moon, it works through this formula: (8-0.2*(Level - 1)) with a minimum of 1 Scarlet & Violet runs it on the formula of floor(((41 - Level) * 4096 + 0.5) / 10)	* 1 to 3	4096
	Repeat Ball	A Ball that works better on Pokémon previously captured. If the Pokémon hasn't been in your Pokédex then * 1. If it has then * 3.	* 1 * 3	4096 14336
	Timer Ball	A Ball that works better the longer the battle has run Runs off a formula based on how long the Pokémon has been in battle: (Turn + 10) / 10. The longer the better (Maximum of 40 turns to count) In Sun & Moon it runs off the formula (1+.3*Turn Number), but with 4 as a maximum In scarlet & Violet the formula is (1229 * Turns + 4096) with maximum being 16384	* 1 - 4	4096 - 16384
	Luxury Ball	A Ball that can make a Pokémon like you easier. The Pokémon gains an extra Happiness Value for each Happiness Value that has been obtained	* 1	4096
	Premier Ball	A Ball that is given at special events.	* 1	4096
	Dusk Ball	A Ball that makes it easier to catch wild in dark places like caves and at night	* 3.5 (Pre-SM) *3 (Post-SM) * 1	12288 4096
	Heal Ball	A remedial Pokéball that restores the caught Pokémon's HP and eliminates any status problem.	* 1	4096
	Quick Ball	A Pokéball that provides a better catch rate if it is used at the start of a wild encounter Capture Rate is at 4 for the first turn and 1 any other turn As of Pokémon Sun & Moon, the capture rate is now *5	* 4 - * 1	20480 4096
	Cherish Ball	A Pokéball used to signify special Pokémon	* 1	4096
	Park Ball	A Pokéball only available in Pal Park. Guarantees capture.	--	4096
	Dream Ball	A dream-like Pokeball that appears suddenly in your bag when you are in the Highlink Forest. It can catch any Pokemon. (BW) A somewhat different Poké Ball that makes it easier to catch wild Pokémon while they're asleep. (SWSH)	-- (BW) *4 (SWSH)	16384 4096
	Fast Ball	A Ball that catches Fast Pokémon GSC If the Pokémon does not flee from battle then * 1. Else * 4 HGSS If the Pokémon has a Base Speed stat of less than 100 * 1. Else * 4	* 1 * 4	16384 4096
	Friend Ball	A Ball that makes Pokémon like you The Pokémon's Base Happiness is 200 instead of 70	* 1	4096
	Heavy Ball	A Ball that catches Heavier Pokémon Easier If the Pokémon weighs less than 451.1lbs, the value is -20. If the Pokémon weighs more than 451.1lbs, the value is +20. If the Pokémon weighs more than 677.3lbs, the value is +30. If the Pokémon weighs over 903lbs, the value is +40.	-20, +0, +20, +30, +40	-20, +0, +20, +30, +40
	Level Ball	The bigger the difference in level between your Pokémon and the Capture Target, the more likely the capture If the Pokémon's Level is greater than the opponent's level then * 2. If half your Pokémon's Level is greater than the opponent's Level then * 4. If a quarter of your Pokémon's Level is greater than the opponents Level then * 8	* 2, * 4, * 8	4096 8192 16384 32768
	Love Ball	This ball works better on Pokémon of the opposite Gender If the Pokémon is of the same species as yours and the Pokémon's Gender is not the same as the Opponent then * 8. If it is the same or either have no gender then * 1	* 1 * 8	32768 4096
	Lure Ball	This ball works better on Pokémon snagged with Fishing Rod If the Pokémon was obtained through Fishing then * 3, or *5 in Sun & Moon. If the Pokémon wasn't, then *1 In Scarlet & Violet, it was set to factor in when Pokémon were in water, but never actually activates	* 1 * 3 *5	4096
	Moon Ball	This ball works better on Pokémon that evolve with Moon Stone If the Pokémon evolves with Moon Stone then * 3. If the Pokémon doesn't, then *1	* 1 * 4	16384 4096
	Sport Ball	A Ball that only exists in the National Park	* 1.5	4096
	Beast Ball	A special Poké Ball designed to catch Ultra Beasts. It has a low success rate for catching others. If trying to catch an Ultra Beast (Nihilego, Buzzwole, Pheromosa, Xurkitree, Celesteela, Kartana, Guzzlord) it is *5 For all other Pokémon, it is *0.1	* 5 * 0.1	20480 410

There is another factor involved. If a Pokémon is an Ultra Beast with the Beast Boost ability such as Nihilego, Pheromosa etc., if they have a non-Beast Ball Poké Ball thrown at them, their catch rate is multiplied by *0.6, reducing the effectiveness by 40%.

In Pokémon Scarlet & Violet, there's a new element factored in at this part, a badge penalty. For each Gym Badge you are missing, you have a reduction in catch rate, so if you have no badges, this is factored in to a power of 8. This is then multiplied by maximum Hit Points

BadgePenalty = 0.8^{BadgesMissing} * 4096

CatchRate = (BadgePenalty * CatchRate) / (3* Max HP)

Following this, there's a small bonus if the wild Pokémon is Level 13 or under. This makes it easier to catch the Pokémon when you are starting the game. If the target Pokémon's level is 14 or higher, this part is ignored

CatchRate = floor(((36-2* TargetLevel) * CatchRate)/10)

Status Conditions

Status Conditions have always been an element in the game that can help you turn the tide of battle. However, they also factor in to the capture calculations.

CatchRate = Status * CatchRate

After this, there's a Capture Value Coefficient. This is used for bonuses for things in Scarlet & Violet such as Backstrikes and Meal Powers. Backstrikes have an increase of *2 which activates if you start a battle by starting the battle with the Pokémon unaware. This lasts the entire of the battle.
Meal Powers ale also factored in here in a similar manner, with Catching Power giving an increase of 10%, 25% or 100% depending on the level. These stack.

This gives us the final catch rate which is capped at 1044480.

CatchRate = min((CVC * CatchRate),1044480)

Critical Capture

A totally new mechanic of capture is the Critical Capture. This feature works like Critical Hits in battle where there is a slight chance that this feature occurs. Critical Capture will be noticed when you throw the Pokéball. It'll make a metal noise, and pause in mid-air briefly. When it hits the Pokémon, it will shake once and capture. This cuts three of the four random calculations out of the overal capture mechanic making it more likely to capture the Pokémon. However, it can still fail.

The calculation is done by a simple factor depending upon the amount of Pokémon species you have captured. It will run this calculation based upon the capture value calculated above and will then have another random number based upon the Pokémon you have captured.

CriticalCatchRate = (715827883 * critical_catch_modifier * CatchRate / (4294967296*4096)

This value is then rounded down and then is determined if it will activate through a simple randomised number. If the number is less than the critical catch rate, then it will be a critical catch and it will only run a shake check once

When this is done, the game runs to the shake checks. It runs four of these checks and if all four are successful, then the Pokémon is captured.

Let's Go, Pikachu & Let's Go, Eevee

The Let's Go games run things a bit differently to the previous games.

Catch rate is a completely different situation to the previous and subsequent Pokémon games with the Pokémon's Catch Rate being modified through a variety of means.

65535 / (255/ModifiedCatchRate)^1/5.33

A number generator is then decided between 0 and 65535. If the number is less, then it's success. 4 shakes mean the capture is successful.

1.85√(SpeciesCatchRate * (Players x Berry) * 1.25)

There's another method that helps the catch rate. As you increase your catches of the same species of Pokémon, the capture rate will increase. This does not have to be within a combo.

4√(10000/((1000-TotalCaught)/100)*CP+1)

The final Species Catch Rate shown is showcased by the Ring

In addition to that, if you're playing in local co-op play and both players throw the ball and it hits at the same time, you'll get a boost due to the Synchronized capture.

NumberOfPlayers * (a*(√((Player1Ball + Player2Ball)/NumberofPlayers)*NewbieModifier)³)

Newbie Modifier is 1 as standard but 1.5 if you haven't reached Viridian Forest

Finally, there are three different berries that improve the rate of capture. Each Berry has a higher boost making capture a lot easier than standard. The technique also factors in, where if you hit the Poké Ball inside the circle as it goes down, you'll get a special bonus with an increase

Picture	Name	Effect
	Razz Berry	*1.5
	Silver Razz Berry	*2.25
	Golden Razz Berry	*4

Special thanks to Anubis for mechanic clarification