status: gp checking 2/2
So, ete mentioned the lack of a capture mechanics article a while back so I decided to write one. All constructive criticism welcome.
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The likelihood of capture for wild Pokémon depends on a built-in formula. This formula relies on values such as CatchRate, BallRate, and MaxHP to determine whether a specific Pokémon will be easily caught or will require some effort and patience on behalf of the player. The information in this article focuses on this formula and its application in third and fourth generation Pokémon games.
The Capture Rate Formula
The Capture Rate Formula determines the probability of successfully capturing a Pokémon. The actual in-game formula is quite complex, so Community Member X-Act made a formula that produces nearly exact results:
Capture Rate = (( 1 + ( MaxHP * 3 - CurrentHP * 2 ) * CatchRate * BallRate * Status# ) / ( MaxHP * 3 )) / 256
The equation is based on five variables that depend on the Pokémon and the Poké Ball used to catch it. The +1 and division by 256 make the Capture Rate a decimal, which can be multiplied by 100% to produce a percentage of capture. A Capture Rate of 1 or more denotes a guaranteed capture. Since Pokémon games use integers, it is necessary to round down any numbers obtained while using the formula; this applies to all values obtained while calculating the final result (not just the final value). Therefore, you must remember to round down any non-integers before performing the next action to obtain accurate results. This equation is applicable to both third and fourth generation games.
Technical Information
The following is an analysis of the different variables involved in the Capture Rate equation along with some noticeable trends in the Capture Rate based on factors like MaxHP and the type of Poké Ball used on the Pokémon.
MaxHP
MaxHP refers to the maximum Hit Points (HP) of a Pokémon. This value varies depending on the Pokémon's IVs and level. Determining a Pokémon's maximum HP while battling is very difficult; however, thanks to RNG abuse, it's possible to calculate the MaxHP since the abuser knows the HP IV of the Pokémon they are attempting to catch.
At first glance it may not be apparent, but the greater the Pokémon’s maximum HP, the higher its Capture Rate. Converting the equation into the following makes it more noticeable:
Capture Rate = [(1/ MaxHP * 3) + (CatchRate * BallRate * Status#) – ((CurrentHP * 2 * CatchRate * BallRate * Status#)/( MaxHP * 3 ))]/256
Since the maximum HP is in the denominator of the expression ((CurrentHP * 2 * CatchRate * BallRate * Status#)/( MaxHP * 3 )), the larger its value, the smaller the result of the expression. Therefore, the expression's result will have less of an impact when it is subtracted from the rest of the values in the formula. For this to hold true, all other variables in the equation (BallRate, CatchRate, and Status#) must be kept constant when comparing Pokémon with different maximum HP. Furthermore, if the Pokémon is at full health, then the opposite occurs and the lower the MaxHP, the higher the Capture Rate. This is because the fraction ((CurrentHP * 2 * CatchRate * BallRate * Status#)/( MaxHP * 3 )) becomes a constant (all other values are set) when CurrentHP equals MaxHP. Consequently, the only value affecting the capture rate when comparing different MaxHP values is (1/ MaxHP * 3), which becomes greater as MaxHP decreases.
Current HP
CurrrentHP is the HP a Pokémon has at a point in time. This value changes as the Pokémon takes damage or recovers HP, and has a minimum value of 1 before the Pokémon faints. From the Capture Rate Formula, the greater the CurrentHP, the lower the capture rate, as the CurrentHP is subtracted from the other values in the formula. When the Pokémon's CurrentHP equals its MaxHP (when it is at full health), the equation becomes the following:
Capture Rate = [(1/ MaxHP * 3) + ((CatchRate * BallRate * Status#)/3)]/256
Essentially, a Pokémon's Capture Rate is given by the expression ((CatchRate * BallRate * Status#)/3)/256 since the value (1/ MaxHP * 3) /256 is negligible. Furthermore, the Capture Rate is equal to a third of the Pokémon's CatchRate when it is at full health and the BallRate and Status# are equal to 1. Alternatively, one could say that damaging a Pokémon will at most triple its capture rate.
CatchRate
The CatchRate is a numerical value that ranges from 1-255 and is assigned to each Pokémon to gauge the relative ease of catching that Pokémon. The CatchRate is set for each Pokémon, and as the CatchRate increases, so does the Capture Rate of a Pokémon.
Although the CatchRate is a set value, it can be modified with the effects of the Apricorn Balls in HeartGold and SoulSilver. Most of the Apricorn Balls modify the CatchRate by applying multipliers to it, which can be expressed as the BallRate. However, the Heavy Ball actually adds or subtracts from the CatchRate, which cannot be emulated by the BallRate. Furthermore, the Apricorn Ball modifier is applied before the game adjusts the CatchRate to a value in the range of 1 to 255, so at most an Apricorn Ball will have raised the CatchRate to 255; the BallRate doesn’t adhere to that restriction. If the CatchRate exceeds 255, the game brings it back down to 255 when calculating the capture rate. Additionally, if one tries to catch a Pokémon at full health with an Apricorn Ball, the chances of capturing it would not be greater than 1/3 due to the limit on the CatchRate. Mathematically, this can be illustrated by the expression ((CatchRate * BallRate * Status#)/3)/256, inserting values for the variables gives the following: (255*1*1)/3))/256 = (255/3)/256 = 0.332, which is about 33% or 1/3 chance of a successful capture. However, inflicting status or damaging the Pokémon improves the chances of a catching it and brings those odds well above a 1 in 3 chance. Due to the CatchRate's 255 maximum, the Apricorn Balls are best used on Pokémon with a low CatchRate, such as legendary Pokémon, to reap the complete benefit of the Apricorn Ball modifier; using them on Pokémon with high CatchRates would make their effects almost negligible, and their function comparable to a regular Poké Ball.
BallRate
The BallRate is a multiplier, for which the value changes depending on the Poké Ball used for the capture. Every Poké Ball has its own BallRate, though the value of the BallRate for an individual Poké Ball can change depending on the conditions of the battle, such as time of day or location. In HGSS, the Apricorn Balls apply their modifiers to the CatchRate, so their BallRate is considered to be 1. Finally, the BallRate is the only value in the Capture Rate Formula that can be a decimal and not rounded down. However, any value obtained by performing an action with the BallRate, such as CatchRate * BallRate * Status#, must be rounded down.
Status#
The Status# is a modifier that becomes significant when the Pokémon is inflicted with a status condition. The values for each condition are as follows:
Status#s:
Freeze : 2
Sleep : 2
Paralysis : 1.5
Burn : 1.5
Poison : 1.5
None : 1
Sleep and freeze are the most effective status conditions, though all status conditions increase the Capture Rate.
Staying in the Ball
In addition to calculating a Pokémon's Capture Rate, the game also determines the probability of a Pokémon remaining inside any given Poké Ball or breaking out of it. The following equation is used to determine whether it stays inside or breaks out:
B = 1048560 / √(√(16711680 / Capture Rate))
B is the probability that the Pokémon will remain inside the Poké Ball. The Capture Rate used for this calculation is the unmodified Capture Rate and can be obtained from the following equation:
Capture Rate = (( MaxHP * 3 - CurrentHP * 2 ) * CatchRate * BallRate * Status# ) / ( MaxHP * 3 ))
Once the Capture Rate is calculated from the previous equation, it is inserted into the first equation and a value from 0 to 65535 is produced; 65535 is the maximum value of an unsigned 16-bit integer and is used often in computer systems. The Trainer ID is another value found in Pokémon games that has 65535 as its maximum. Now, once the result is obtained from the equation, it can be treated as the strength of the Poké Ball relative to the Pokémon. The Pokémon makes up to four attempts to break out of the Poké Ball, represented by the Poké Ball wobbling for the first three attempts and possibly sealing on the fourth. For every attempt a random integer between 0 and 65535 will be selected and compared to the value of B. If the random integer is greater than or equal to B, then the Pokémon will break out of the Ball. Conversely, if it is less than B then the Pokémon will remain trapped inside the ball after it wobbles. If all four of the random integers selected at each attempt are smaller than B, then the ball will seal at the fourth attempt and the Pokémon has been captured.
CatchRate Values
The CatchRate is a value between 1 and 255 assigned to each Pokémon that help gauge how difficult it is to catch a certain Pokémon. The following is a list of Pokémon that can be caught in third or fourth generation games, arranged by National Dex number and their respective CatchRate:
Kanto Dex (001-151)
Johto Dex (152-251)
Hoenn Dex (252-386)
Pokémon CatchRate
Poochyena 255
Mightyena 127
Zigzagoon 255
Linoone 90
Wurmple 255
Silcoon 120
Beautifly 45
Cascoon 120
Dustox 45
Lotad 255
Lombre 120
Seedot 255
Nuzleaf 120
Taillow 200
Swellow 45
Wingull 190
Pelipper 45
Ralts 235
Kirlia 120
Surskit 200
Masquerain 75
Shroomish 255
Breloom 90
Slakoth 255
Vigoroth 120
Nincada 255
Whismur 190
Loudred 120
Makuhita 180
Hariyama 200
Azurill 150
Nosepass 255
Skitty 255
Delcatty 60
Sableye 45
Mawile 45
Aron 180
Lairon 90
Meditite 180
Medicham 90
Electrike 120
Manectric 45
Plusle 200
Minun 200
Volbeat 150
Illumise 150
Roselia 150
Gulpin 225
Carvanha 225
Sharpedo 60
Wailmer 125
Wailord 60
Numel 255
Camerupt 150
Torkoal 90
Spoink 255
Spinda 255
Trapinch 255
Vibrava 120
Cacnea 190
Cacturne 60
Swablu 255
Altaria 45
Zangoose 90
Seviper 90
Lunatone 45
Solrock 45
Barboach 190
Whiscash 75
Corphish 205
Crawdaunt 155
Baltoy 255
Feebas 255
Castform 45
Kecleon 200
Shuppet 225
Banette 45
Duskull 190
Dusclops 90
Tropius 200
Chimecho 45
Absol 30
Wynaut 125
Snorunt 190
Spheal 255
Sealeo 120
Clamperl 255
Relicanth 25
Luvdisc 225
Bagon 45
Shelgon 45
Salamence 45
Beldum 3
Metang 3
Metagross 3
Regirock 3
Regice 3
Registeel 3
Latias 3
Latios 3
Kyogre 5
Groudon 5
Rayquaza 3
Deoxys 3
Sinnoh Dex (387-493)
Miscellaneous CatchRates for Pokémon only caught through Ditto using Transform
Pokémon CatchRate
Bulbasaur 45
Ivysaur 45
Venusaur 45
Charmander 45
Charmeleon 45
Charizard 45
Squirtle 45
Wartortle 45
Blastoise 45
Pidgeot 45
Raichu 75
Nidoqueen 45
Nidoking 45
Clefable 25
Ninetales 75
Wigglytuff 50
Vileplume 45
Arcanine 75
Alakazam 50
Machamp 45
Victreebel 45
Golem 45
Cloyster 60
Vaporeon 45
Jolteon 45
Flareon 45
Omanyte 45
Omastar 45
Kabuto 45
Kabutops 45
Aerodactyl 45
Chikorita 45
Meganium 45
Cyndaquil 45
Typhlosion 45
Totodile 45
Feraligatr 45
Crobat 90
Ampharos 45
Azumarill 150
Politoed 45
Espeon 45
Umbreon 45
Slowking 70
Scizor 25
Kingdra 45
Porygon2 45
Blissey 30
Celebi 45
Treecko 45
Grovyle 45
Sceptile 45
Torchic 45
Combusken 45
Blaziken 45
Mudkip 45
Marshtomp 45
Swampert 45
Ludicolo 45
Shiftry 45
Gardevoir 45
Slaking 45
Ninjask 120
Shedinja 45
Exploud 45
Aggron 45
Swalot 75
Grumpig 60
Flygon 45
Claydol 90
Lileep 45
Cradily 45
Anorith 45
Armaldo 45
Milotic 60
Glalie 75
Walrein 45
Huntail 60
Gorebyss 60
Jirachi 3
Turtwig 45
Grotle 45
Torterra 45
Chimchar 45
Monferno 45
Infernape 45
Piplup 45
Prinplup 45
Empoleon 45
Staraptor 45
Luxray 45
Roserade 75
Cranidos 45
Rampardos 45
Shieldon 45
Bastiodon 45
Wormadam 45
Wormadam-G 45
Wormadam-S 45
Mothim 45
Vespiquen 45
Cherrim 75
Drifblim 60
Lopunny 60
Mismagius 45
Honchkrow 30
Garchomp 45
Lucario 45
Weavile 45
Magnezone 30
Lickilicky 30
Rhyperior 30
Tangrowth 30
Electivire 30
Magmortar 30
Togekiss 30
Yanmega 30
Leafeon 45
Glaceon 45
Gliscor 30
Mamoswine 50
Porygon-Z 30
Gallade 45
Probopass 60
Dusknoir 45
Froslass 75
Phione 30
Manaphy 3
Poké Balls
The following is a complete list of all Poké Balls available in third and fourth generation games, their BallRates, and their effects:
Poké Ball
BallRate: 1
Great Ball
BallRate: 1.5
Ultra Ball
BallRate: 2
Safari Ball:
BallRate: 1.5
*Can only be obtained and used at the Safari Zone (FRLG, RSE, and HGSS) and at the Great Marsh in DPP.
Master Ball
BallRate: 255
*This Poké Ball catches Pokémon 100% of the time.
Sport Ball:
BallRate: 1.5
*Can only be obtained and used during the Bug Catching Contest held at National Park.
Premier Ball
Ball Rate: 1
Repeat Ball
BallRate: 3 (if used on a Pokémon that has been caught and registered in the PokéDex previously); otherwise, 1
Timer Ball
BallRate: 1 (increases by 1 every 10 turns for a maximum of 4)
Nest Ball
BallRate: (40 – Pokemon’s Level)/10, has a minimum of 1.
Net Ball
BallRate: 3 (if used on Bug- or Water-type Pokémon); otherwise, 1
Dive Ball
BallRate: 3.5 (if used on Pokémon found underwater in RSE and while Surfing or fishing in FRLG, DPP, and HGSS); otherwise, 1
Luxury Ball
BallRate: 1
*Adds an extra point to an event that raises the Happiness of a Pokémon in third generation games. In fourth generation games, it provides a separate boost in Happiness.
Cherish Ball
BallRate: 1
*Only seen on Nintendo Event Pokémon, otherwise, unobtainable.
Heal Ball
BallRate: 1
*Fully restores the captured Pokémon's HP and PP, and removes status.
Quick Ball
BallRate: 4 (becomes 1 after the first turn)
Dusk Ball
BallRate: 3.5 (when used at night between 20:00 and 4:00 or dark areas like caves); otherwise, 1
Park Ball
BallRate: 255
*This Ball catches a Pokémon 100% of the time. Furthermore, it can only be obtained and used at Pal Park during a Catching Show.
Apricorn Balls are obtained in HGSS and behave differently to the aforementioned Balls, as they affect the CatchRate of a Pokémon. The following is a list of all the Apricorn Balls available in HGSS and their modifier:
Fast Ball
CatchRate Modifier: *4 (if the Pokémon has base 100 or higher Speed); otherwise, 1
Friend Ball
CatchRate Modifier: *1
*A Pokémon caught in this Ball will have its Base Happiness set to 200.
Heavy Ball
CatchRate Modifier: +20 if the Pokémon weighs more than 451.5lbs, +30 if it weighs over 677.3 lbs, or +40 if it weighs more than 903.0lbs; otherwise, -20
*Although subtracting 20 from the CatchRate may result in a negative CatchRate, the game treats it as a CatchRate of 1. Furthermore, since there are no Pokémon with a CatchRate of 20 it is impossible to get 0 as the CatchRate.
The following lists show which Pokémon have the +20, +30, or +40 applied to them, for all others assume that the -20 modifier is applied (Pokémon with asterisks* on them can only be caught by having Ditto Transform into them in HGSS):
+20
+30
+40
Level Ball
BallRate: *2 if the level of the player's Pokémon is greater than the level of the opposing Pokémon, *4 if the level of the player's Pokémon divided by two and rounded down is greater than the level of the opposing Pokémon, or *8 if the level of the player's Pokémon divided by four and rounded down is greater than the level of the opposing Pokémon; otherwise, *1
Love Ball
CatchRate Modifier: *8 (when used on a Pokemon who is the same species and opposite gender of the opposing Pokémon); otherwise, *1
Lure Ball
CatchRate Modifier: *3 (when used on Pokémon encountered by fishing); otherwise, *1
Moon Ball
CatchRate Modifier: *4 (when used on a Pokémon that evolves with a Moon Stone, which include: Nidoran-M, Nidorino, Nidoking, Nidoran-F, Nidorina, Nidoqueen, Cleffa, Clefairy, Clefable, Igglybuff, Jigglypuff, Wigglytuff, Skitty, and Delcatty); otherwise, *1
Sample Calculations
Mathematical representations and explanations of trends found in the Capture Rate equation, as well as how to use the various equations presented in the article.
Effectiveness of 3 different Balls on Kyogre
Difference between Apricorn Balls and Poké Balls with a BallRate greater than 1 on Pokémon with high CatchRates
Demonstration of the use of the equation that determines the probability of a Pokémon breaking out of a specific Poké Ball using the unmodified Capture Rate.
So, ete mentioned the lack of a capture mechanics article a while back so I decided to write one. All constructive criticism welcome.
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The likelihood of capture for wild Pokémon depends on a built-in formula. This formula relies on values such as CatchRate, BallRate, and MaxHP to determine whether a specific Pokémon will be easily caught or will require some effort and patience on behalf of the player. The information in this article focuses on this formula and its application in third and fourth generation Pokémon games.
The Capture Rate Formula
The Capture Rate Formula determines the probability of successfully capturing a Pokémon. The actual in-game formula is quite complex, so Community Member X-Act made a formula that produces nearly exact results:
Capture Rate = (( 1 + ( MaxHP * 3 - CurrentHP * 2 ) * CatchRate * BallRate * Status# ) / ( MaxHP * 3 )) / 256
The equation is based on five variables that depend on the Pokémon and the Poké Ball used to catch it. The +1 and division by 256 make the Capture Rate a decimal, which can be multiplied by 100% to produce a percentage of capture. A Capture Rate of 1 or more denotes a guaranteed capture. Since Pokémon games use integers, it is necessary to round down any numbers obtained while using the formula; this applies to all values obtained while calculating the final result (not just the final value). Therefore, you must remember to round down any non-integers before performing the next action to obtain accurate results. This equation is applicable to both third and fourth generation games.
Technical Information
The following is an analysis of the different variables involved in the Capture Rate equation along with some noticeable trends in the Capture Rate based on factors like MaxHP and the type of Poké Ball used on the Pokémon.
MaxHP
MaxHP refers to the maximum Hit Points (HP) of a Pokémon. This value varies depending on the Pokémon's IVs and level. Determining a Pokémon's maximum HP while battling is very difficult; however, thanks to RNG abuse, it's possible to calculate the MaxHP since the abuser knows the HP IV of the Pokémon they are attempting to catch.
At first glance it may not be apparent, but the greater the Pokémon’s maximum HP, the higher its Capture Rate. Converting the equation into the following makes it more noticeable:
Capture Rate = [(1/ MaxHP * 3) + (CatchRate * BallRate * Status#) – ((CurrentHP * 2 * CatchRate * BallRate * Status#)/( MaxHP * 3 ))]/256
Since the maximum HP is in the denominator of the expression ((CurrentHP * 2 * CatchRate * BallRate * Status#)/( MaxHP * 3 )), the larger its value, the smaller the result of the expression. Therefore, the expression's result will have less of an impact when it is subtracted from the rest of the values in the formula. For this to hold true, all other variables in the equation (BallRate, CatchRate, and Status#) must be kept constant when comparing Pokémon with different maximum HP. Furthermore, if the Pokémon is at full health, then the opposite occurs and the lower the MaxHP, the higher the Capture Rate. This is because the fraction ((CurrentHP * 2 * CatchRate * BallRate * Status#)/( MaxHP * 3 )) becomes a constant (all other values are set) when CurrentHP equals MaxHP. Consequently, the only value affecting the capture rate when comparing different MaxHP values is (1/ MaxHP * 3), which becomes greater as MaxHP decreases.
Current HP
CurrrentHP is the HP a Pokémon has at a point in time. This value changes as the Pokémon takes damage or recovers HP, and has a minimum value of 1 before the Pokémon faints. From the Capture Rate Formula, the greater the CurrentHP, the lower the capture rate, as the CurrentHP is subtracted from the other values in the formula. When the Pokémon's CurrentHP equals its MaxHP (when it is at full health), the equation becomes the following:
Capture Rate = [(1/ MaxHP * 3) + ((CatchRate * BallRate * Status#)/3)]/256
Essentially, a Pokémon's Capture Rate is given by the expression ((CatchRate * BallRate * Status#)/3)/256 since the value (1/ MaxHP * 3) /256 is negligible. Furthermore, the Capture Rate is equal to a third of the Pokémon's CatchRate when it is at full health and the BallRate and Status# are equal to 1. Alternatively, one could say that damaging a Pokémon will at most triple its capture rate.
CatchRate
The CatchRate is a numerical value that ranges from 1-255 and is assigned to each Pokémon to gauge the relative ease of catching that Pokémon. The CatchRate is set for each Pokémon, and as the CatchRate increases, so does the Capture Rate of a Pokémon.
Although the CatchRate is a set value, it can be modified with the effects of the Apricorn Balls in HeartGold and SoulSilver. Most of the Apricorn Balls modify the CatchRate by applying multipliers to it, which can be expressed as the BallRate. However, the Heavy Ball actually adds or subtracts from the CatchRate, which cannot be emulated by the BallRate. Furthermore, the Apricorn Ball modifier is applied before the game adjusts the CatchRate to a value in the range of 1 to 255, so at most an Apricorn Ball will have raised the CatchRate to 255; the BallRate doesn’t adhere to that restriction. If the CatchRate exceeds 255, the game brings it back down to 255 when calculating the capture rate. Additionally, if one tries to catch a Pokémon at full health with an Apricorn Ball, the chances of capturing it would not be greater than 1/3 due to the limit on the CatchRate. Mathematically, this can be illustrated by the expression ((CatchRate * BallRate * Status#)/3)/256, inserting values for the variables gives the following: (255*1*1)/3))/256 = (255/3)/256 = 0.332, which is about 33% or 1/3 chance of a successful capture. However, inflicting status or damaging the Pokémon improves the chances of a catching it and brings those odds well above a 1 in 3 chance. Due to the CatchRate's 255 maximum, the Apricorn Balls are best used on Pokémon with a low CatchRate, such as legendary Pokémon, to reap the complete benefit of the Apricorn Ball modifier; using them on Pokémon with high CatchRates would make their effects almost negligible, and their function comparable to a regular Poké Ball.
BallRate
The BallRate is a multiplier, for which the value changes depending on the Poké Ball used for the capture. Every Poké Ball has its own BallRate, though the value of the BallRate for an individual Poké Ball can change depending on the conditions of the battle, such as time of day or location. In HGSS, the Apricorn Balls apply their modifiers to the CatchRate, so their BallRate is considered to be 1. Finally, the BallRate is the only value in the Capture Rate Formula that can be a decimal and not rounded down. However, any value obtained by performing an action with the BallRate, such as CatchRate * BallRate * Status#, must be rounded down.
Status#
The Status# is a modifier that becomes significant when the Pokémon is inflicted with a status condition. The values for each condition are as follows:
Status#s:
Freeze : 2
Sleep : 2
Paralysis : 1.5
Burn : 1.5
Poison : 1.5
None : 1
Sleep and freeze are the most effective status conditions, though all status conditions increase the Capture Rate.
Staying in the Ball
In addition to calculating a Pokémon's Capture Rate, the game also determines the probability of a Pokémon remaining inside any given Poké Ball or breaking out of it. The following equation is used to determine whether it stays inside or breaks out:
B = 1048560 / √(√(16711680 / Capture Rate))
B is the probability that the Pokémon will remain inside the Poké Ball. The Capture Rate used for this calculation is the unmodified Capture Rate and can be obtained from the following equation:
Capture Rate = (( MaxHP * 3 - CurrentHP * 2 ) * CatchRate * BallRate * Status# ) / ( MaxHP * 3 ))
Once the Capture Rate is calculated from the previous equation, it is inserted into the first equation and a value from 0 to 65535 is produced; 65535 is the maximum value of an unsigned 16-bit integer and is used often in computer systems. The Trainer ID is another value found in Pokémon games that has 65535 as its maximum. Now, once the result is obtained from the equation, it can be treated as the strength of the Poké Ball relative to the Pokémon. The Pokémon makes up to four attempts to break out of the Poké Ball, represented by the Poké Ball wobbling for the first three attempts and possibly sealing on the fourth. For every attempt a random integer between 0 and 65535 will be selected and compared to the value of B. If the random integer is greater than or equal to B, then the Pokémon will break out of the Ball. Conversely, if it is less than B then the Pokémon will remain trapped inside the ball after it wobbles. If all four of the random integers selected at each attempt are smaller than B, then the ball will seal at the fourth attempt and the Pokémon has been captured.
CatchRate Values
The CatchRate is a value between 1 and 255 assigned to each Pokémon that help gauge how difficult it is to catch a certain Pokémon. The following is a list of Pokémon that can be caught in third or fourth generation games, arranged by National Dex number and their respective CatchRate:
Kanto Dex (001-151)
Pokémon CatchRate
Caterpie 255
Metapod 120
Butterfree 45
Weedle 255
Kakuna 120
Beedrill 45
Pidgey 255
Pidgeotto 120
Rattata 255
Raticate 127
Spearow 255
Fearow 90
Ekans 255
Arbok 90
Pikachu 190
Sandshrew 255
Sandslash 90
Nidoran-F 235
Nidorina 120
Nidoran-M 235
Nidorino 120
Clefairy 150
Vulpix 190
Jigglypuff 170
Zubat 255
Golbat 90
Oddish 255
Gloom 120
Paras 190
Parasect 75
Venonat 190
Venomoth 75
Diglett 255
Dugtrio 50
Meowth 255
Persian 90
Psyduck 190
Golduck 75
Mankey 190
Primeape 75
Growlithe 190
Poliwag 255
Poliwhirl 120
Poliwrath 45
Abra 200
Kadabra 100
Machop 180
Machoke 90
Bellsprout 255
Weepinbell 120
Tentacool 190
Tentacruel 60
Geodude 255
Graveler 120
Ponyta 190
Rapidash 60
Slowpoke 190
Slowbro 75
Magnemite 190
Magneton 60
Farfetch'd 45
Doduo 190
Dodrio 45
Seel 190
Dewgong 75
Grimer 190
Muk 75
Shellder 190
Gastly 190
Haunter 90
Gengar 45
Onix 45
Drowzee 190
Hypno 75
Krabby 225
Kingler 60
Voltorb 190
Electrode 120
Exeggcute 90
Exeggutor 45
Cubone 190
Marowak 75
Hitmonlee 45
Hitmonchan 45
Lickitung 45
Koffing 190
Weezing 60
Rhyhorn 120
Rhydon 60
Chansey 30
Tangela 45
Kangaskhan 45
Horsea 225
Seadra 75
Goldeen 225
Seaking 60
Staryu 225
Starmie 60
Mr. Mime 45
Scyther 45
Jynx 45
Electabuzz 45
Magmar 45
Pinsir 45
Tauros 45
Magikarp 255
Gyarados 45
Lapras 45
Ditto 35
Eevee 45
Porygon 45
Snorlax 25
Articuno 3
Zapdos 3
Moltres 3
Dratini 45
Dragonair 45
Dragonite 45
Mewtwo 3
Mew 45
Caterpie 255
Metapod 120
Butterfree 45
Weedle 255
Kakuna 120
Beedrill 45
Pidgey 255
Pidgeotto 120
Rattata 255
Raticate 127
Spearow 255
Fearow 90
Ekans 255
Arbok 90
Pikachu 190
Sandshrew 255
Sandslash 90
Nidoran-F 235
Nidorina 120
Nidoran-M 235
Nidorino 120
Clefairy 150
Vulpix 190
Jigglypuff 170
Zubat 255
Golbat 90
Oddish 255
Gloom 120
Paras 190
Parasect 75
Venonat 190
Venomoth 75
Diglett 255
Dugtrio 50
Meowth 255
Persian 90
Psyduck 190
Golduck 75
Mankey 190
Primeape 75
Growlithe 190
Poliwag 255
Poliwhirl 120
Poliwrath 45
Abra 200
Kadabra 100
Machop 180
Machoke 90
Bellsprout 255
Weepinbell 120
Tentacool 190
Tentacruel 60
Geodude 255
Graveler 120
Ponyta 190
Rapidash 60
Slowpoke 190
Slowbro 75
Magnemite 190
Magneton 60
Farfetch'd 45
Doduo 190
Dodrio 45
Seel 190
Dewgong 75
Grimer 190
Muk 75
Shellder 190
Gastly 190
Haunter 90
Gengar 45
Onix 45
Drowzee 190
Hypno 75
Krabby 225
Kingler 60
Voltorb 190
Electrode 120
Exeggcute 90
Exeggutor 45
Cubone 190
Marowak 75
Hitmonlee 45
Hitmonchan 45
Lickitung 45
Koffing 190
Weezing 60
Rhyhorn 120
Rhydon 60
Chansey 30
Tangela 45
Kangaskhan 45
Horsea 225
Seadra 75
Goldeen 225
Seaking 60
Staryu 225
Starmie 60
Mr. Mime 45
Scyther 45
Jynx 45
Electabuzz 45
Magmar 45
Pinsir 45
Tauros 45
Magikarp 255
Gyarados 45
Lapras 45
Ditto 35
Eevee 45
Porygon 45
Snorlax 25
Articuno 3
Zapdos 3
Moltres 3
Dratini 45
Dragonair 45
Dragonite 45
Mewtwo 3
Mew 45
Johto Dex (152-251)
Pokémon CatchRate
Bayleef 45
Quilava 45
Croconaw 45
Sentret 255
Furret 90
Hoothoot 255
Noctowl 90
Ledyba 255
Ledian 90
Spinarak 255
Ariados 90
Chinchou 190
Lanturn 75
Pichu 190
Cleffa 150
Igglybuff 170
Togepi 190
Togetic 75
Natu 190
Xatu 75
Mareep 235
Flaaffy 120
Marill 190
Sudowoodo 65
Hoppip 255
Skiploom 120
Jumpluff 45
Aipom 45
Sunkern 235
Sunflora 120
Yanma 75
Wooper 255
Quagsire 90
Murkrow 30
Misdreavus 45
Unown 225
Wobbuffet 45
Girafarig 60
Pineco 190
Forretress 75
Dunsparce 190
Gligar 60
Steelix 25
Snubbull 190
Granbull 75
Qwilfish 45
Shuckle 190
Heracross 45
Sneasel 60
Teddiursa 120
Ursaring 60
Slugma 190
Magcargo 75
Swinub 225
Piloswine 75
Corsola 60
Remoraid 190
Octillery 75
Delibird 45
Mantine 25
Skarmory 25
Houndour 120
Houndoom 45
Phanpy 120
Donphan 60
Stantler 45
Smeargle 45
Tyrogue 75
Hitmontop 45
Smoochum 45
Elekid 45
Magby 45
Miltank 45
Raikou 3
Entei 3
Suicune 3
Larvitar 45
Pupitar 45
Tyranitar 45
Lugia 3
Ho-Oh 3
Bayleef 45
Quilava 45
Croconaw 45
Sentret 255
Furret 90
Hoothoot 255
Noctowl 90
Ledyba 255
Ledian 90
Spinarak 255
Ariados 90
Chinchou 190
Lanturn 75
Pichu 190
Cleffa 150
Igglybuff 170
Togepi 190
Togetic 75
Natu 190
Xatu 75
Mareep 235
Flaaffy 120
Marill 190
Sudowoodo 65
Hoppip 255
Skiploom 120
Jumpluff 45
Aipom 45
Sunkern 235
Sunflora 120
Yanma 75
Wooper 255
Quagsire 90
Murkrow 30
Misdreavus 45
Unown 225
Wobbuffet 45
Girafarig 60
Pineco 190
Forretress 75
Dunsparce 190
Gligar 60
Steelix 25
Snubbull 190
Granbull 75
Qwilfish 45
Shuckle 190
Heracross 45
Sneasel 60
Teddiursa 120
Ursaring 60
Slugma 190
Magcargo 75
Swinub 225
Piloswine 75
Corsola 60
Remoraid 190
Octillery 75
Delibird 45
Mantine 25
Skarmory 25
Houndour 120
Houndoom 45
Phanpy 120
Donphan 60
Stantler 45
Smeargle 45
Tyrogue 75
Hitmontop 45
Smoochum 45
Elekid 45
Magby 45
Miltank 45
Raikou 3
Entei 3
Suicune 3
Larvitar 45
Pupitar 45
Tyranitar 45
Lugia 3
Ho-Oh 3
Hoenn Dex (252-386)
Pokémon CatchRate
Poochyena 255
Mightyena 127
Zigzagoon 255
Linoone 90
Wurmple 255
Silcoon 120
Beautifly 45
Cascoon 120
Dustox 45
Lotad 255
Lombre 120
Seedot 255
Nuzleaf 120
Taillow 200
Swellow 45
Wingull 190
Pelipper 45
Ralts 235
Kirlia 120
Surskit 200
Masquerain 75
Shroomish 255
Breloom 90
Slakoth 255
Vigoroth 120
Nincada 255
Whismur 190
Loudred 120
Makuhita 180
Hariyama 200
Azurill 150
Nosepass 255
Skitty 255
Delcatty 60
Sableye 45
Mawile 45
Aron 180
Lairon 90
Meditite 180
Medicham 90
Electrike 120
Manectric 45
Plusle 200
Minun 200
Volbeat 150
Illumise 150
Roselia 150
Gulpin 225
Carvanha 225
Sharpedo 60
Wailmer 125
Wailord 60
Numel 255
Camerupt 150
Torkoal 90
Spoink 255
Spinda 255
Trapinch 255
Vibrava 120
Cacnea 190
Cacturne 60
Swablu 255
Altaria 45
Zangoose 90
Seviper 90
Lunatone 45
Solrock 45
Barboach 190
Whiscash 75
Corphish 205
Crawdaunt 155
Baltoy 255
Feebas 255
Castform 45
Kecleon 200
Shuppet 225
Banette 45
Duskull 190
Dusclops 90
Tropius 200
Chimecho 45
Absol 30
Wynaut 125
Snorunt 190
Spheal 255
Sealeo 120
Clamperl 255
Relicanth 25
Luvdisc 225
Bagon 45
Shelgon 45
Salamence 45
Beldum 3
Metang 3
Metagross 3
Regirock 3
Regice 3
Registeel 3
Latias 3
Latios 3
Kyogre 5
Groudon 5
Rayquaza 3
Deoxys 3
Sinnoh Dex (387-493)
Pokémon CatchRate
Starly 255
Staravia 120
Bidoof 255
Bibarel 127
Kricketot 255
Kricketune 45
Shinx 235
Luxio 120
Budew 255
Burmy 120
Combee 120
Pachirisu 200
Buizel 190
Floatzel 75
Cherubi 190
Shellos 190
Gastrodon 75
Drifloon 125
Buneary 190
Glameow 190
Purugly 75
Chingling 120
Stunky 225
Skuntank 60
Bronzor 255
Bronzong 90
Bonsly 255
Mime Jr. 145
Happiny 130
Chatot 30
Spiritomb 100
Gible 45
Gabite 45
Munchlax 50
Riolu 75
Hippopotas 140
Hippowdon 60
Skorupi 120
Drapion 45
Croagunk 140
Toxicroak 75
Carnivine 200
Finneon 190
Lumineon 75
Mantyke 25
Snover 120
Abomasnow 60
Rotom 45
Uxie 3
Mesprit 3
Azelf 3
Dialga 30
Palkia 30
Heatran 3
Regigigas 3
Giratina 3
Cresselia 3
Darkrai 3
Shaymin 45
Arceus 3
Starly 255
Staravia 120
Bidoof 255
Bibarel 127
Kricketot 255
Kricketune 45
Shinx 235
Luxio 120
Budew 255
Burmy 120
Combee 120
Pachirisu 200
Buizel 190
Floatzel 75
Cherubi 190
Shellos 190
Gastrodon 75
Drifloon 125
Buneary 190
Glameow 190
Purugly 75
Chingling 120
Stunky 225
Skuntank 60
Bronzor 255
Bronzong 90
Bonsly 255
Mime Jr. 145
Happiny 130
Chatot 30
Spiritomb 100
Gible 45
Gabite 45
Munchlax 50
Riolu 75
Hippopotas 140
Hippowdon 60
Skorupi 120
Drapion 45
Croagunk 140
Toxicroak 75
Carnivine 200
Finneon 190
Lumineon 75
Mantyke 25
Snover 120
Abomasnow 60
Rotom 45
Uxie 3
Mesprit 3
Azelf 3
Dialga 30
Palkia 30
Heatran 3
Regigigas 3
Giratina 3
Cresselia 3
Darkrai 3
Shaymin 45
Arceus 3
Miscellaneous CatchRates for Pokémon only caught through Ditto using Transform
Pokémon CatchRate
Bulbasaur 45
Ivysaur 45
Venusaur 45
Charmander 45
Charmeleon 45
Charizard 45
Squirtle 45
Wartortle 45
Blastoise 45
Pidgeot 45
Raichu 75
Nidoqueen 45
Nidoking 45
Clefable 25
Ninetales 75
Wigglytuff 50
Vileplume 45
Arcanine 75
Alakazam 50
Machamp 45
Victreebel 45
Golem 45
Cloyster 60
Vaporeon 45
Jolteon 45
Flareon 45
Omanyte 45
Omastar 45
Kabuto 45
Kabutops 45
Aerodactyl 45
Chikorita 45
Meganium 45
Cyndaquil 45
Typhlosion 45
Totodile 45
Feraligatr 45
Crobat 90
Ampharos 45
Azumarill 150
Politoed 45
Espeon 45
Umbreon 45
Slowking 70
Scizor 25
Kingdra 45
Porygon2 45
Blissey 30
Celebi 45
Treecko 45
Grovyle 45
Sceptile 45
Torchic 45
Combusken 45
Blaziken 45
Mudkip 45
Marshtomp 45
Swampert 45
Ludicolo 45
Shiftry 45
Gardevoir 45
Slaking 45
Ninjask 120
Shedinja 45
Exploud 45
Aggron 45
Swalot 75
Grumpig 60
Flygon 45
Claydol 90
Lileep 45
Cradily 45
Anorith 45
Armaldo 45
Milotic 60
Glalie 75
Walrein 45
Huntail 60
Gorebyss 60
Jirachi 3
Turtwig 45
Grotle 45
Torterra 45
Chimchar 45
Monferno 45
Infernape 45
Piplup 45
Prinplup 45
Empoleon 45
Staraptor 45
Luxray 45
Roserade 75
Cranidos 45
Rampardos 45
Shieldon 45
Bastiodon 45
Wormadam 45
Wormadam-G 45
Wormadam-S 45
Mothim 45
Vespiquen 45
Cherrim 75
Drifblim 60
Lopunny 60
Mismagius 45
Honchkrow 30
Garchomp 45
Lucario 45
Weavile 45
Magnezone 30
Lickilicky 30
Rhyperior 30
Tangrowth 30
Electivire 30
Magmortar 30
Togekiss 30
Yanmega 30
Leafeon 45
Glaceon 45
Gliscor 30
Mamoswine 50
Porygon-Z 30
Gallade 45
Probopass 60
Dusknoir 45
Froslass 75
Phione 30
Manaphy 3
Poké Balls
The following is a complete list of all Poké Balls available in third and fourth generation games, their BallRates, and their effects:
Poké Ball
BallRate: 1
Great Ball
BallRate: 1.5
Ultra Ball
BallRate: 2
Safari Ball:
BallRate: 1.5
*Can only be obtained and used at the Safari Zone (FRLG, RSE, and HGSS) and at the Great Marsh in DPP.
Master Ball
BallRate: 255
*This Poké Ball catches Pokémon 100% of the time.
Sport Ball:
BallRate: 1.5
*Can only be obtained and used during the Bug Catching Contest held at National Park.
Premier Ball
Ball Rate: 1
Repeat Ball
BallRate: 3 (if used on a Pokémon that has been caught and registered in the PokéDex previously); otherwise, 1
Timer Ball
BallRate: 1 (increases by 1 every 10 turns for a maximum of 4)
Nest Ball
BallRate: (40 – Pokemon’s Level)/10, has a minimum of 1.
Net Ball
BallRate: 3 (if used on Bug- or Water-type Pokémon); otherwise, 1
Dive Ball
BallRate: 3.5 (if used on Pokémon found underwater in RSE and while Surfing or fishing in FRLG, DPP, and HGSS); otherwise, 1
Luxury Ball
BallRate: 1
*Adds an extra point to an event that raises the Happiness of a Pokémon in third generation games. In fourth generation games, it provides a separate boost in Happiness.
Cherish Ball
BallRate: 1
*Only seen on Nintendo Event Pokémon, otherwise, unobtainable.
Heal Ball
BallRate: 1
*Fully restores the captured Pokémon's HP and PP, and removes status.
Quick Ball
BallRate: 4 (becomes 1 after the first turn)
Dusk Ball
BallRate: 3.5 (when used at night between 20:00 and 4:00 or dark areas like caves); otherwise, 1
Park Ball
BallRate: 255
*This Ball catches a Pokémon 100% of the time. Furthermore, it can only be obtained and used at Pal Park during a Catching Show.
Apricorn Balls are obtained in HGSS and behave differently to the aforementioned Balls, as they affect the CatchRate of a Pokémon. The following is a list of all the Apricorn Balls available in HGSS and their modifier:
Fast Ball
CatchRate Modifier: *4 (if the Pokémon has base 100 or higher Speed); otherwise, 1
Friend Ball
CatchRate Modifier: *1
*A Pokémon caught in this Ball will have its Base Happiness set to 200.
Heavy Ball
CatchRate Modifier: +20 if the Pokémon weighs more than 451.5lbs, +30 if it weighs over 677.3 lbs, or +40 if it weighs more than 903.0lbs; otherwise, -20
*Although subtracting 20 from the CatchRate may result in a negative CatchRate, the game treats it as a CatchRate of 1. Furthermore, since there are no Pokémon with a CatchRate of 20 it is impossible to get 0 as the CatchRate.
The following lists show which Pokémon have the +20, +30, or +40 applied to them, for all others assume that the -20 modifier is applied (Pokémon with asterisks* on them can only be caught by having Ditto Transform into them in HGSS):
+20
Camerupt*
Dragonite*
Glalie*
Golem*
Gyarados
Hariyama*
Hippowdon*
Lapras
Lugia
Mamoswine*
Mantine
Onix
Rayquaza
Regirock*
Registeel*
Rhyperior*
Dragonite*
Glalie*
Golem*
Gyarados
Hariyama*
Hippowdon*
Lapras
Lugia
Mamoswine*
Mantine
Onix
Rayquaza
Regirock*
Registeel*
Rhyperior*
+30
Aggron*
Arceus*
Kyogre
Palkia*
Probopass*
Steelix
Torterra*
Wailord*
Arceus*
Kyogre
Palkia*
Probopass*
Steelix
Torterra*
Wailord*
+40
Dialga*
Giratina*
Groudon
Heatran*
Metagross*
Regigigas*
Snorlax
Giratina*
Groudon
Heatran*
Metagross*
Regigigas*
Snorlax
Level Ball
BallRate: *2 if the level of the player's Pokémon is greater than the level of the opposing Pokémon, *4 if the level of the player's Pokémon divided by two and rounded down is greater than the level of the opposing Pokémon, or *8 if the level of the player's Pokémon divided by four and rounded down is greater than the level of the opposing Pokémon; otherwise, *1
Love Ball
CatchRate Modifier: *8 (when used on a Pokemon who is the same species and opposite gender of the opposing Pokémon); otherwise, *1
Lure Ball
CatchRate Modifier: *3 (when used on Pokémon encountered by fishing); otherwise, *1
Moon Ball
CatchRate Modifier: *4 (when used on a Pokémon that evolves with a Moon Stone, which include: Nidoran-M, Nidorino, Nidoking, Nidoran-F, Nidorina, Nidoqueen, Cleffa, Clefairy, Clefable, Igglybuff, Jigglypuff, Wigglytuff, Skitty, and Delcatty); otherwise, *1
Sample Calculations
Mathematical representations and explanations of trends found in the Capture Rate equation, as well as how to use the various equations presented in the article.
Effectiveness of 3 different Balls on Kyogre
Kyogre: MaxHP = 175, CurrentHP = 1, Status: asleep, CatchRate: 5
Net Ball (BallRate: 3)
Capture Rate = ((1 + (175 * 3 – 1 * 2) * 5 * 3 * 2) / (175 * 3)) / 256
= ((1 + 523 * 5 * 3 * 2) / (525)) / 256
= (15691 / 525) / 256
= 29 / 256
= 0.1133
= 11.33%
Dive Ball (BallRate: 3.5) *only applicable in RSE
Capture Rate = ((1 + (175 * 3 – 1 * 2) * 5 * 3.5 * 2) / (175 * 3)) / 256
= ((1 + 523 * 5 * 3.5 * 2) / (525)) / 256
= (18306 / 525) / 256
= 34 / 256
= 0.1328
= 13.28%
Heavy Ball (CatchRate Modifier: +30)
Capture Rate = ((1 + (175 * 3 – 1 * 2) * (5 + 30) * 1 * 2) / (175 * 3)) / 256
= ((1 + 523 * (5 + 30) * 1 * 2) / (525)) / 256
= ((1 + 523 * 35 * 1 * 2) / (525)) / 256
= (36611 / 525) / 256
= 69 / 256
= 0.2695
= 26.95%
Conclusion: Heavy Ball effectively doubles Kyogre's Capture Rate. The difference between the Net and Dive Balls is minimal.
Net Ball (BallRate: 3)
Capture Rate = ((1 + (175 * 3 – 1 * 2) * 5 * 3 * 2) / (175 * 3)) / 256
= ((1 + 523 * 5 * 3 * 2) / (525)) / 256
= (15691 / 525) / 256
= 29 / 256
= 0.1133
= 11.33%
Dive Ball (BallRate: 3.5) *only applicable in RSE
Capture Rate = ((1 + (175 * 3 – 1 * 2) * 5 * 3.5 * 2) / (175 * 3)) / 256
= ((1 + 523 * 5 * 3.5 * 2) / (525)) / 256
= (18306 / 525) / 256
= 34 / 256
= 0.1328
= 13.28%
Heavy Ball (CatchRate Modifier: +30)
Capture Rate = ((1 + (175 * 3 – 1 * 2) * (5 + 30) * 1 * 2) / (175 * 3)) / 256
= ((1 + 523 * (5 + 30) * 1 * 2) / (525)) / 256
= ((1 + 523 * 35 * 1 * 2) / (525)) / 256
= (36611 / 525) / 256
= 69 / 256
= 0.2695
= 26.95%
Conclusion: Heavy Ball effectively doubles Kyogre's Capture Rate. The difference between the Net and Dive Balls is minimal.
Difference between Apricorn Balls and Poké Balls with a BallRate greater than 1 on Pokémon with high CatchRates
Natu: MaxHP = 60, CurrentHP = 60, Status: none, CatchRate: 190
Level Ball (CatchRate Modifier: *8, maximum)
Capture Rate = ((1 + (60 * 3 – 60 * 2) * (190 * 8) * 1 * 1) / (60 * 3)) / 256
= ((1 + 60 * (190 * 8) * 1 * 1) / (60 * 3)) / 256
= ((1 + 60 * 1520 * 1 * 1) / (60 *3)) / 256
– CatchRate has a maximum of 255, value higher than 255 are set to 255.
= ((1 + 60 * 255 * 1 * 1) / (60 * 3)) / 256
= (15301 / (60 * 3)) / 256
= (15301 / 180) / 256
= 85 / 256
= 0.3321
= 33.21%
Quick Ball (BallRate: 4, assume used on turn 1)
Capture Rate = ((1 + (60 * 3 – 60 * 2) * 190 * 4 * 1) / (60 * 3)) / 256
= ((1 + 60 * 190 * 4 * 1) / (60 * 3)) / 256
= (45601 / (60 * 3)) / 256
= (45601 / 180) / 256
= 253 / 256
= 0.9883
= 98.83%
Conclusion: Apricorn Balls aren't effective in catching Pokémon with high CatchRates due to the 255 maximum. Poké Balls that have BallRate modifiers greater than 1 are best in these situations.
Level Ball (CatchRate Modifier: *8, maximum)
Capture Rate = ((1 + (60 * 3 – 60 * 2) * (190 * 8) * 1 * 1) / (60 * 3)) / 256
= ((1 + 60 * (190 * 8) * 1 * 1) / (60 * 3)) / 256
= ((1 + 60 * 1520 * 1 * 1) / (60 *3)) / 256
– CatchRate has a maximum of 255, value higher than 255 are set to 255.
= ((1 + 60 * 255 * 1 * 1) / (60 * 3)) / 256
= (15301 / (60 * 3)) / 256
= (15301 / 180) / 256
= 85 / 256
= 0.3321
= 33.21%
Quick Ball (BallRate: 4, assume used on turn 1)
Capture Rate = ((1 + (60 * 3 – 60 * 2) * 190 * 4 * 1) / (60 * 3)) / 256
= ((1 + 60 * 190 * 4 * 1) / (60 * 3)) / 256
= (45601 / (60 * 3)) / 256
= (45601 / 180) / 256
= 253 / 256
= 0.9883
= 98.83%
Conclusion: Apricorn Balls aren't effective in catching Pokémon with high CatchRates due to the 255 maximum. Poké Balls that have BallRate modifiers greater than 1 are best in these situations.
Demonstration of the use of the equation that determines the probability of a Pokémon breaking out of a specific Poké Ball using the unmodified Capture Rate.
Raikou: MaxHP = 134, CurrentHP = 1, Status: sleep, CatchRate: 3
Fast Ball (CatchRate Modifier *4)
Capture Rate = (134 * 3 – 1 * 2) * (3 * 4) * 1 * 2) / (134 * 3))
= (400 * (3 * 4) * 1 * 2) / (134 * 3))
= (400 * 12 * 1 * 2) / (134 * 3))
= (9600) / (134 * 3)
= 9600 / 402
= 23.8806
= 23 (Pokémon games round down values to integers)
Insert Capture Rate from the previous equation into the equation:
B = 1048560 / √(√(16711680 / Capture Rate))
The value of B gives a numerical representation of the probability that the Pokemon being caught will break out of the Ball (in this case the Fast Ball).
B = 1048560 / √(√(16711680 / 23))
= 1048560 / √(√726594)
= 1048560 / √852
= 1048560 / 29
= 36157
Conclusion: If the random value selected for each attempt Raikou makes to break out of the Fast Ball is lower than 36157, then the Fast Ball will shake, and Raikou will remain inside. However, if it is greater than 36157, then Raikou will break out. If the random value is lower on all four attempts, then the Fast Ball will seal on the fourth attempt and Raikou will be caught. Essentially, Raikou has less than a 50% chance per attempt of breaking out of a Fast Ball when it is asleep and down to 1 HP.
Fast Ball (CatchRate Modifier *4)
Capture Rate = (134 * 3 – 1 * 2) * (3 * 4) * 1 * 2) / (134 * 3))
= (400 * (3 * 4) * 1 * 2) / (134 * 3))
= (400 * 12 * 1 * 2) / (134 * 3))
= (9600) / (134 * 3)
= 9600 / 402
= 23.8806
= 23 (Pokémon games round down values to integers)
Insert Capture Rate from the previous equation into the equation:
B = 1048560 / √(√(16711680 / Capture Rate))
The value of B gives a numerical representation of the probability that the Pokemon being caught will break out of the Ball (in this case the Fast Ball).
B = 1048560 / √(√(16711680 / 23))
= 1048560 / √(√726594)
= 1048560 / √852
= 1048560 / 29
= 36157
Conclusion: If the random value selected for each attempt Raikou makes to break out of the Fast Ball is lower than 36157, then the Fast Ball will shake, and Raikou will remain inside. However, if it is greater than 36157, then Raikou will break out. If the random value is lower on all four attempts, then the Fast Ball will seal on the fourth attempt and Raikou will be caught. Essentially, Raikou has less than a 50% chance per attempt of breaking out of a Fast Ball when it is asleep and down to 1 HP.
