Catch rate: Difference between revisions

This article is incomplete. Please feel free to edit this article to add missing information and complete it. Reason: Generation VI

Each species of Pokémon has a catch rate that applies to all its members. Higher catch rates mean that the Pokémon is easier to catch, up to a maximum of 255. 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.

Approximately, the probability of catching a Pokémon starts with the species' catch rate divided by 255. Then it is multiplied by the following factors:

• The health of the Pokémon (relative to its full health), which can reduce the probability to ⅓× at full health.
• The type of Poké Ball, which can augment by some ×.
• Any status condition of the wild Pokémon (i.e. 2.5× increase for sleep or freeze, and 1.5× for paralyze, poison, or burn).
• Any active Pass Powers (in Generation V) or O-Power (in Generation VI).

The effects stack multiplicatively—for example, a 2× and a 3× will combine to be 6×. If the calculation ends up greater than 1, the wild Pokémon is assured to be caught.

The rarity of the Pokémon (i.e. how often it appears in the wild) is totally independent from its catch rate after it is encountered. Even rare Pokémon may have high catch rates, making them relatively easy to catch in battle, such as Nosepass, who has a catch rate of 255.

Poké Balls that guarantee capture (the Master Ball and Park Ball, and any ball used in the Entree Forest) bypass the catching formula entirely.

Capture method (Generation I)

The capture method in Generation I differs significantly from those of later generations. To determine whether a Pokémon is caught or not, the steps below are performed. If, at any point, the Pokémon is caught or breaks free, the steps following that point are not performed.

1. If a Master Ball is used, the Pokémon is caught.
2. Generate a random number, N, depending on the type of ball used.
   • For a Poké Ball: 0 to 255.
   • For a Great Ball: 0 to 200.
   • Otherwise (Ultra Ball or Safari Ball): 0 to 150.
3. The Pokémon is caught if...
   • It is asleep or frozen and N is less than 25.
   • It is paralyzed, burned, or poisoned and N is less than 12.
4. Otherwise, if N minus the status value is greater than the Pokémon's catch rate, the Pokémon breaks free.
5. If not, generate a random value, M, between 0 and 255.
6. Calculate f:
   • f = (HP_max * 255 * 4) / (HP_current * Ball), where all divisions are rounded down to the nearest integer. The minimum value of f is 1 and its maximum value is 255. The value of Ball is 8 if a Great Ball is used or 12 otherwise.
7. If f is greater than or equal to M, the Pokémon is caught. Otherwise, the Pokémon breaks free. In practical terms, lowering the target's HP to 1/3 of its maximum will guarantee capture with a Pokéball, while lowering it to 1/2 will guarantee capture with a Great Ball.

If the Pokémon broke free, the steps below are performed to determine how many times the ball will shake.

1. Calculate d:
   • d = Catch rate × 100 / Ball, where the value of Ball is 255 for the Poké Ball, 200 for the Great Ball, or 150 for other balls.
2. If d is greater than or equal to 256, the ball shakes three times before the Pokémon breaks free.
3. If not, calculate x = d × f / 255 + s, where s is 10 if the Pokémon is asleep or frozen or 5 if it is paralyzed, poisoned, or burned.
4. If...
   • x < 10: the Ball misses the Pokémon completely.
   • x < 30: the Ball shakes once before the Pokémon breaks free.
   • x < 70: the Ball shakes twice before the Pokémon breaks free.
   • Otherwise, the Ball shakes three times before the Pokémon breaks free.

This algorithm thus has several curious properties that do not apply in later generations:

• The amount of times a Poké Ball shakes before it breaks free (or not at all if it misses the Pokémon) is a rough approximation of the Pokémon's catch odds.
• If a Pokémon will break free, a given combination of ball plus status condition plus HP will always result in the same number of shakes. This means that, if a given number of shakes is observed before the Pokémon breaks free for a given combination of these values, if the ball is ever observed to shake more times with the same combination of values, the Pokémon will be caught.
• Under certain situations, a Great Ball is more effective than an Ultra Ball. In particular, Pokémon with high catch rates, no status, and above ½ HP may guarantee capture with a Great Ball but fail to do so with an Ultra Ball.
• The effect of reducing HP diminishes with lower catch rates, and the effect of inflicting status diminishes with higher catch rates. Regardless of catch rate, reducing the HP does not increase chances of capture at less than ½ HP with Great Balls, and ⅓ HP with other balls.
• Inflicting a status ailment gives the player a flat chance (from 4.6% to 16.6%) to catch the Pokémon regardless of all other factors, making certain Pokémon easier to catch in Generation I than they are in later generations: A sleeping Mewtwo with full HP may, on average, be caught in about six Ultra Balls in Generation I, but from Generation II onwards exactly the same circumstances would require an average of about 64 Ultra Balls—ten times as many.

Approximated probability

Using a simulation of the capture algorithm, a general formula for the probability of catching a Pokémon was found.

Probability of Capture = p0 + p1

where

p0 = statusAilment / (ballMod+1)

• statusAilment = 12 if poisoned, burned, or paralyzed, 25 if frozen or asleep, 0 otherwise.
• ballMod = 255 if using a Poké Ball, 200 if using a Great Ball, and 150 otherwise.

and

p1 = ( (catchRate+1)/(ballMod+1) ) * ( (f+1)/256 )

• f is defined in the above section for the capture method.
• catchRate (given as an integer value) is stated on each individual Pokémon's article.

General capture method (Generation II onwards)

The capture algorithms in Generation II and onwards have three essential components: the modified catch rate, the "shake probability", and the "shake checks". Generation II handles shake checks slightly differently than the later generations.

Modified catch rate

The modified catch rate, a, is the catch rate after various factors such as weakening the Pokémon and using stronger Poké Balls are taken into consideration. A modified catch rate may never fall to 0 (that is, render a Pokémon impossible to capture), but it may cause the modified rate to fall below its original unmodified catch rate (such as from high health, Heavy Balls, Baiting in the Safari Zone, or the dark grass penalty in Generation V). In Generation III and Generation IV, the modified catch rate may never fall below 1.

Shake probability

The shake probability, b, is a value that determines the probability that a single shake check passes.

Shake checks

Shake checks are performed to determine whether the Pokémon will be caught or, if the Pokémon breaks free, the number of shakes that will occur before it does so.

In Generation II, whether a Pokémon will be caught is determined before any shake checks are performed, and shake checks are only performed if the Pokémon is not caught.

Capture method (Generation II)

Modified catch rate

The modified catch rate a is calculated in Generation II as follows:

a = (3 × HPmax - 2 × HPcurrent) × (rate × bonusball) / (3 × HPmax) + bonusstatus

with the final value rounded down to the nearest integer, where

• HP_max is the number of hit points the Pokémon has at full health,
• HP_current 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),
• bonus_ball is the multiplier for the Poké Ball used, and
• bonus_status is the multiplier for any status condition the Pokémon has (10 for sleep or freeze, 0 otherwise).
  • bonus_status was intended to equal 5 for paralyze, poison, or burn, but due to a glitch, the game skips this check.

If 3 × HP_max > 255, then both 3 × HP_max and 2 × HP_current are halved twice (and rounded down after each division) for use in the formula. If the latter product is 0, it is set to 1 instead.

Note that the subtraction may underflow, due to both values being unsigned 8-bit integers.

The maximum value of a is 255.

Shake probability

The shake probability b is determined from the table below, depending on the value of a.

Shake checks

First, a check is performed to determine whether the Pokémon is caught at all. A random number between 0 and 255 is generated, and if this number is less than or equal to a, the Pokémon is caught.

Shake checks are only performed if the Pokémon is not caught. A single shake check consists of generating a random number between 0 and 255 and comparing it to b. This is done at most three times, but if the number generated in a given shake check is greater than or equal to b, no further shake checks will be performed. The number of times the ball shakes is the same as the number of shake checks that were performed.

Capture method (Generation III-IV)

Modified catch rate

The modified catch rate, a, is calculated in Generation III and Generation IV as follows:

File:Catch formula 1.png

Where

• HP_max is the number of hit points the Pokémon has at full health,
• HP_current 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 apricorn balls or actions in the Safari Zone),
• bonus_ball is the multiplier for the Poké Ball used, and
• bonus_status 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 × bonus_ball × bonus_status. 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.

The formula is slightly different when applied to the apricorn balls in HeartGold and SoulSilver. The modifiers for these balls are applied directly to the Pokémon's catch rate, rather than in the formula as bonus_ball is always 1, and the catch rate can not go higher than 255. This means that for Pokémon whose catch rate is already 255, such as Rattata, the apricorn balls do not make the capture anymore likely than a regular Poké Ball.

Shake probability

The shake probability is calculated as follows:

File:Catch formula 2.png

Shake checks

To perform a shake check, a random number between 0 and 65535 (inclusive) is generated and compared to b. If the number is greater than b, the check "fails".

Four shake checks are performed. The Pokémon is caught if all four shake checks succeed. Otherwise, the Poké Ball will shake as many times as there were successful shake checks before the Pokémon breaks free.

Note that as a result of the formula for b, if a is 255 or greater then b will be at least 65535, and the Pokémon will be guaranteed to be caught. If a capture would be guaranteed, the game does not perform any shake checks.

Probability of capture

The probability p of catching a Pokémon, given the values a and b calculated above, is:

File:Catch formula 3.png

The second expression for p may be expanded as follows:

File:Catch formula 3 expansion.png

Since (2¹⁶ - 1)⁴ ≈ 2⁶⁴, we can approximate p with the following expression:

File:Catch formula 3 approximation.png

The percentage error in this approximation approaches 0 as a approaches 255, and does not exceed 21.2%.

For a constant probability p, the probability P that a player can capture the Pokémon with no more than r tries is:

File:Catch formula 4.png

Note that this is the cumulative probability function for a geometric distribution. The expected value of r is 1/p, that is to say, on average, a Pokémon that can be caught with probability p will be caught with 1/p tries.

The inverse problem, the number of tries, r, needed to have a probability P of capturing a Pokémon is:

File:Catch formula 5.png

Capture method (Generation V)

Modified catch rate

Generation V follows the formula in Generation III-IV, with all divisions above rounded down to the nearest multiple of 1/4096. However, there are three alterations:

• bonus_status is now 2.5 for sleep and freeze (instead of 2).
• Capture Power factor: if a Capture Power is active, the catch rate is multiplied by a factor and rounded down to the nearest multiple of 1/4096.
  • Capture Power ↑: ×1.1
  • Capture Power ↑↑: ×1.2
  • Capture Power ↑↑↑, S, or MAX: ×1.3
• Dark grass factor: This factor is multiplied into the HP factor (3 × HP_max - 2 × HP_current above) and then rounded to the nearest multiple of 1/4096. This factor is applied if the battle occurs in dark grass, and depends on the number of Pokémon that have been caught in the Pokédex, as shown in the table below, usually making it harder to catch a Pokémon.

If the modified catch rate is greater than 255, the Pokémon is guaranteed to be caught (but a critical capture check will be performed anyway).

Shake probability

The formula for b is

b = 65535 / (255/a)(¼)

where all divisions and the fourth-roots are rounded to the nearest 1/4096, and the final value is rounded down to the nearest whole number.

Shake checks

Generation V's shake checks work essentially the same as those of Generations III and IV.

Before any shake checks are performed, the game checks to see if a critical capture may happen. If not, three shake checks will be performed, otherwise, only one shake check will be performed.

In a normal capture, the Pokémon breaks free without shaking if the first check fails or after one shake if the second check fails. If the third check fails, the Pokémon breaks free after three shakes (not two).

In a critical capture, the ball will always shake once, and the Pokémon will break free or be caught depending on the result of the shake check.

Capture method (Generation VI)

Shake checks

Pokémon can break out after two shakes again.

Critical capture

Since Generation V, when a Poké Ball is thrown, a special type of capture that is much more likely to catch a Pokémon, called a critical capture, may occur. When a critical capture occurs, the Poké Ball will make a high-pitched whistling sound as it is thrown, then pause in mid-air, and shudder before it drops down to the ground, shaking only once on the ground before the Pokémon escapes or is caught.

The probability of a critical capture occurring depends of the number of Pokémon that have been caught in the Pokédex. First, compute the value of a (the modified catch rate) as shown in the appropriate section above. Then, multiply a by the appropriate multiplier from the table below.

Next, generate a random number between 0 and 2047. If this number is less than the product of a and the multiplier, a critical capture will occur. This means that, if the critical catch multiplier is 1, a critical capture has a probability of about ⅛ of the modified catch rate a.

Critical captures only make one shake check instead of three. This means they have a better chance of catching a Pokémon than a normal capture would. Whereas throwing an ordinary Poké Ball at a full-health Pokémon that has a catch rate of 3 (such as Kyurem) would only result in a 1.57% chance of capture (0.39% in Generation VI), if a critical capture occurs, the chance of catching the Pokémon will be a much higher 25.02%.

Poké Ball effectiveness rates

Ball	Rate	Notes
Poké Ball	1×
Great Ball	1.5×
Ultra Ball	2×
Master Ball	255×	Never fails, except against unidentified ghosts, the ghost Marowak, and Kyurem when under Ghetsis's control
Safari Ball	1.5×	only usable in Safari Zones
Level Ball	1×, 2×, 4× or 8×	1× if the player's Pokémon is the same level as or a lower level than the wild Pokémon 2× if the player's Pokémon is at a higher level than the wild Pokémon but less than double it 4× if the player's Pokémon is more than double but less than four times the level of the wild Pokémon 8× if the player's Pokémon is of a level four times or more than that of the wild Pokémon
Lure Ball	1× or 3×	3× only if fishing
Moon Ball	1× or 4×	Always 1× due to a glitchGSC 4× only if used on a Pokémon in the Nidoran♂, Nidoran♀, Clefairy, Jigglypuff or Skitty families HGSS
Friend Ball	1×
Love Ball	1× or 8×	8× only if used on a Pokémon of the same species and gender as the player's PokémonGSC 8× only if used on a Pokémon of the same species as, but opposite gender of, the player's PokémonHGSS
Heavy Ball	-20, 0, +20, +30 or +40	-20 if used on Pokémon weighing less than 220.6lbsGSC/451.5 lbsHGSS No modifier if used on Pokémon weight between 220.6lbs and 441.0 lbsGSC +20 if used on Pokémon weighing between 451.5 lbs and 677.3 lbs +30 if used on Pokémon weighing more than 661.5 lbsGSC +30 if used on Pokémon weighing between 677.3 lbs and 903.0 lbsHGSS +40 if used on Pokémon weighing more than 903.0 lbsHGSS
Fast Ball	1× or 4×	4× only if used on Magnemite, Grimer, or TangelaGSC 4× only if used on a Pokémon with a base Speed of at least 100HGSS
Sport Ball	1.5×	only usable in the Bug-Catching Contest
Net Ball	1× or 3×	3× only if the target is a Bug- or Water-type Pokémon
Nest Ball	1× to 4×	((40 - Pokémon's level) / 10)×, minimum 1×RSEFRLGDPPtHGSS ((41 - Pokémon's level) / 10)×, minimum 1×BWB2W2XY
Repeat Ball	1× or 3×	3× only if target has been caught previously
Timer Ball	1× to 4×	((number of turns passed in battle + 10) / 10)×, maximum 4× (reached at 30 turns)RSEFRLGDPPtHGSS (1 + number of turns passed in battle * 1229/4096)×, maximum 4× (reached at 10 turns)BWB2W2XY
Premier Ball	1×
Luxury Ball	1×
Dive Ball	1× or 3.5×	3.5× only if divingRSE or surfing/fishingFRLGDPPtHGSSBWB2W2XY
Dusk Ball	1× or 3.5×	3.5× only if inside a cave or night
Quick Ball	1×, 4×, or 5×	4× only on the first turn of the battleDPPtHGSS 5× only on the first turn of the battleBWB2W2XY
Heal Ball	1×
Cherish Ball	1×
Park Ball	255×	Never fails, only usable in Pal Park
Dream Ball	255×	Never fails, only usable in Entree Forest

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.

Quotes

Trivia

• Some people claim to have discovered button combinations that increase a Pokémon's catch rate. This was partly true in Generation I, as button input could slightly influence random number generation. This required frame-perfect timing; thus it is only used by tool-assisted speedruns.
• If used outside of the Entree Forest (which is not possible in regular gameplay), the Dream Ball has a catch rate of 1×.

See also

• List of Pokémon by catch rate

References

• ポケットモンスター情報センター　2号館 (Japanese)
• Generation I Capture Mechanics

External links

• Windows application to calculate catch rate as of Generation IV (includes source code)

This game mechanic article is part of Project Games, a Bulbapedia project that aims to write comprehensive articles on the Pokémon games.