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Catch rate

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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× increase for sleep or freeze, and 1.5× for others).
  • 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 (catch rate 255).

Prior to Generation V, Transform changed a Pokémon's catch rate to that of the target, and was the primary purpose for the existence of catch rates for species that cannot be found in the wild.

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 following is performed:

  1. If a Master Ball is used, the Pokémon is caught.
  2. If a Poké Ball is used, generate a random number from 0 to 255. If a Great Ball is used, generate a random number from 0 to 200. Otherwise (i.e. an Ultra Ball or Safari Ball is used), generate a random number from 0 to 150.
  3. If the generated value is less than 25 and the Pokémon is asleep or frozen, the Pokémon is caught. If the generated value is less than 12 and the Pokémon is paralyzed, burned, or poisoned, the Pokémon is caught. If it is caught, skip all other steps.
  4. If the previous value (the generated value minus the status amount) is greater than the catch rate of the Pokémon, the Pokémon breaks free. Otherwise, generate a random value between 0 and 255. If f (defined below) is greater or equal to this value, the Pokémon is caught. Otherwise, the Pokémon breaks free. If the Pokémon breaks free, do the following:
    • Compute d as shown below. If d ≥ 256, the Ball shakes three times before it breaks free.
    • Otherwise, compute d × f / 255. Add 10 if the Pokémon is asleep or frozen, and add 5 if it is paralyzed, poisoned, or burned. If this value is less than 10, the Ball misses the Pokémon completely. If it is less than 30, the Ball shakes once before it breaks free. If it is less than 70, the Ball shakes twice before it breaks free. Otherwise, the Ball shakes three times before it breaks free.

The variables above are computed as follows:

  • d = Catch rate × 100 / Ball Factor, where the Ball Factor is 255 for the Poké Ball, 200 for the Great Ball, and 150 for all other balls.
  • f = (HPmax * 255 / Ball Factor) / (HPcurrent / 4), where all divisions are rounded down to the nearest integer (the denominator is set to 1 if it is 0 as a result). The Ball Factor is 8 if a Great Ball is used, and 12 otherwise. The resulting value is capped at a maximum of 255.

The formula 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. Furthermore, if a Pokémon breaks free after some number of shakes, and a subsequent attempt with all variables the same makes more shakes, the Pokémon is 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 can be caught in about six Ultra Balls in Generation I, but from Generation II onwards exactly the same circumstances would require about 64 Ultra Balls—ten times as many.

Capture formula (Generation I)

Using a simulation of the capture algorithm, a general formula for catch rates was found.

The formula to give probabilities of capture in Generation I is as follows:

Probability of Capture = p0 + p1

where

p0= statusAilment / (ballMod+1)
  • statusAilment = 12 if poisoned/burned/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.


(Please note that this probability is theoretical. Your own experiments may result in a different value, but over a large number of trials, any experimental probability will approach this theoretical value.)

Capture method (Generation II onwards)

The exact formula in Generation III and onwards are based on three parts: determining the modified catch rate, calculating the "shake probability" and then performing "shake checks". The formula in Generation II is similar, but the formula in Generation I is entirely different.

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.

Generation II

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

  • 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 have been previously modified from the use of the Heavy Ball modifiers),
  • bonusball is the multiplier for the Poké Ball used, and
  • bonusstatus is the multiplier for any status condition the Pokémon has (10 for sleep and freeze, and 0 otherwise).
    • bonusstatus was intended to equal 5 for paralyze, poison and burn, but due to a glitch, the game accidentally skips this check.

Note that in Generation II, if 3 × HPmax > 255, then both 3 × HPmax and 2 × HPcurrent are quartered (rounded down) for use in the formula; if the latter is 0, it is made to 1 instead in this case. Note that the subtraction itself may underflow, due to both values being unsigned 8-bit integers in Generation II.

Generation III-IV

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

Catch formula 1.png

Where

  • 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 have been previously modified from the use of the Heavy Ball or Safari Zone modifiers),
  • 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 and burn, and 1 otherwise).

Given this formula, the maximum value for a (if the Pokémon could have 0 HP) would be catch rate × bonusball × bonusstatus. The minimum value for a (for a Pokémon with full health) would be × catch rate.

Generation V

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:

  • bonusstatus is now 2.5 for sleep and freeze, instead of 2.
  • Capture Power factor: The catch rate is multiplied by 1.1 if the Pass Power Capture Power ↑ is active, 1.2 if Capture Power ↑↑ is active, and 1.3 if Capture Power ↑↑↑, Capture Power S, or Capture Power MAX is active, rounded down to the nearest multiple of 1/4096.
  • Dark grass factor: This factor is multiplied into the HP factor (3 × HPmax - 2 × HPcurrent above) and then rounded to the nearest multiple of 1/4096. It depends on whether or not the battle occurs in dark grass (where Double Battles may occur), and the number of Pokémon that have been caught in the Pokédex: if the battle is not in dark grass, this is 1. If it is, consult the table below.
Number Caught Multiplier
> 600 1
451-600 3686/4096 (90%)
301-450 3277/4096 (80%)
151-300 2867/4096 (70%)
30-150 2048/4096 (50%)
< 30 1229/4096 (30%)

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

Generation II

Consult the following table to determine b:

a 0-1 2 3 4 5 6-7 8-10 11-15 16-20 21-30 31-40 41-50 51-60 61-80 81-100 101-120 121-140 141-160 161-180 181-200 201-220 221-240 241-254 255
b 63 75 84 90 95 103 113 126 134 149 160 169 177 191 201 211 220 227 234 240 246 251 253 255

Generation III-IV

The shake probability is calculated as follows in Generation III and Generation IV:

Catch formula 2.png

Generation V

In Generation V, the formula is

b = 65536 / (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

A "shake check" is done to determine whether the Pokémon is caught, and, if the Pokémon breaks free, the number of shakes that occurs before it does so.

Generation II

In Generation II, a check occurs to determine whether the Pokémon is caught outright, and shake checks are only used if this check fails to determine the number of shakes before the Pokémon breaks free. To determine if the Pokémon is caught outright, generate a random number between 0 and 255. If this value is less than or equal to a, the Pokémon is caught. To perform a shake check, generate a random number between 0 and 255, and compare it against b. Do this three times or until the check fails, whichever comes first, to determine the number of shakes before the Pokémon breaks free.

Generation III-IV

Unlike Generation II, the shake checks themselves determine whether or not the Pokémon is caught, and, if it is not, the number of shakes a Poké Ball will make before the Pokémon breaks free. Four checks are performed, and all checks must pass in order for the Pokémon to be caught, and if the Pokémon breaks free, the number of times the Poké Ball shakes is equal to the number of passed checks. To perform a shake check, generate random numbers between 0 and 65535, inclusive, and compare it against b; the checks fail if the generated value is greater.

Note that as a result of the formula, 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 shake checks.

Generation V

Generation V's shake checks work identically to those of Generation III and IV, except that after the critical capture check only three checks are performed in a normal capture and one in a critical capture. In a normal capture, the Pokémon breaks free without shaking if the first check fails, while the Pokémon breaks free after one shake if the second check fails. The Pokémon breaks free after three shakes (not two) if the third check fails. In a critical capture, the Ball will always shake once, and the Pokémon will break free or be caught depending on the check.

Generation VI

Pokémon can break out after two shakes again.

Probability of capture

Therefore, the probability p of catching a Pokémon in Generation IV, given the values a and b calculated above, is:

Catch formula 3.png

The second expression for p may be expanded as follows:

Catch formula 3 expansion.png

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

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:

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:

Catch formula 5.png

Poké Ball effectiveness rates

Ball Rate Notes
Poké Ball Poké Ball
Great Ball Great Ball 1.5×
Ultra Ball Ultra Ball
Master Ball Master Ball 255× Never fails, except against unidentified ghosts, the ghost Marowak, and Kyurem when under Ghetsis's control
Safari Ball Safari Ball 1.5× only usable in Safari Zones
Level Ball 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 Lure Ball 1× or 3× 3× only if fishing
Moon Ball 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 Friend Ball
Love Ball 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 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 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 Sport Ball 1.5× only usable in the Bug-Catching Contest
Net Ball Net Ball 1× or 3× 3× only if the target is a Bug- or Water-type Pokémon
Nest Ball Nest Ball 1× to 4× ((40 - Pokémon's level) / 10)×, minimum 1×RSEFRLGDPPtHGSS
((41 - Pokémon's level) / 10)×, minimum 1×BWB2W2
Repeat Ball Repeat Ball 1× or 3× 3× only if target has been caught previously
Timer Ball Timer Ball 1× to 4× ((number of turns passed in battle + 10) / 10)×, maximum 4× (reached after 29 turns)RSEFRLGDPPtHGSS
(1× + 1229/4096×) (0.3×) per turn passed in battle, maximum 4× (reached after 10 turns)BWB2W2
Premier Ball Premier Ball
Luxury Ball Luxury Ball
Dive Ball Dive Ball 1× or 3.5× 3.5× only if divingRSE or surfing/fishingFRLGDPPtHGSSBWB2W2
Dusk Ball Dusk Ball 1× or 3.5× 3.5× only if inside a cave or night
Quick Ball Quick Ball 1×, 4×, or 5× 4× only on the first turn of the battleDPPtHGSS
5× only on the first turn of the battleBWB2W2
Heal Ball Heal Ball
Cherish Ball Cherish Ball
Park Ball Park Ball 255× Never fails, only usable in Pal Park
Dream Ball 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.

Critical capture

Since Generation V, there is a chance of a critical capture, where the Poké Ball will only shake on the ground once before capture, and is much more likely to catch the Pokémon in the process. 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.

The probability of a critical capture occurring depends of the number of Pokémon that have previously been caught in the Pokédex. First, compute the value of a (the modified catch rate), as above. Then, whether or not this value is less than 255 (i.e. whether the Pokémon would be caught anyway), multiply this value by the following:

Species Caught Multiplier
>600 2.5
451-600 2
301-450 1.5
151-300 1
31-150 0.5
<30 0

A random number between 0 and 2047 is generated, and if it is less than the modified value, a critical capture occurs. That means that critical captures have a probability of about ⅛ of the modified catch rate a with an assumed critical catch modifier of 1.

Critical captures make one shake check instead of three, thus it has a higher probability of catching the Pokémon compared to a normal throw -- for example, throwing an ordinary Poké Ball at a full-health Pokémon with a catch rate of 3 (such as Kyurem) normally has only a 0.39% chance of actually catching the Pokémon, but if a critical capture occurs, the chance of catching the Pokémon is a much higher 15.77% chance.

Note that contrary to its name, a critical capture is not guaranteed to actually catch the Pokémon; the catch is still determined by one remaining shake check, which may fail. In fact, a critical capture is only guaranteed to catch the Pokémon if the modified catch rate would guarantee its capture already.

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

References

External links

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