Uploaded December 2022 | Updated September 2026, 2 weeks ago
University of Oxford Mathematician Dr Tom Crawford breaks down the Pokémon Catch Rate Formula for the Generation I video games. Explore the formula for yourself using this FREE interactive worksheet from Maple Learn: learn.maplesoft.com/doc/5eumyykf94/pokemon-catch-rate
Check your working using the Maple Calculator App – available for free on Google Play and the App Store.
Android: play.google.com/store/apps/details?id=com.maplesoft.companion&hl=en
Apple: apps.apple.com/us/app/maple-companion/id1466659419
Find out more about the Maple Calculator App and Maple Learn on the Maplesoft YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ
The video begins with an explanation of the full catch rate formula, featuring maxima, minima and floor functions. This is then simplified to arrive at the more commonly used formula for the approximate probability of catching a wild Pokémon in the Generation I video games. Each variable is explained in turn, and the effects of status, HP, and ball type are discussed.
Next, the formula is derived using the catch algorithm for the game. This is outlined in detail on ‘Bulbapedia’ here: bulbapedia.bulbagarden.net/wiki/Catch_rate
Finally, using some visualisations from Maple Learn, the probability of success when using a great ball is compared to that for an ultra ball for a Pokémon with catch rate 45 (such as Butterfree) and a Pokémon with catch rate 3 (such as Zapdos). You can explore the formulae for yourself for FREE in the accompanying interactive Maple Learn worksheet here: learn.maplesoft.com/d/AKFPLNCOIOEUKQFKDNOHASGUGOJRMJGQIKJOFOLTFPKKMRAGGKGLCFBSJFBUORJLITJLCJGSNRJMBIOSCIAMBQFILTOJEOARIMJN
Full list of Pokémon catch rates on ‘Bulbapedia’ here: bulbapedia.bulbagarden.net/wiki/List_of_Pok%C3%A9mon_by_catch_rate
All in-game footage and images are copyright The Pokémon Company, Gamefreak and Nintendo. They are shown under a fair-use policy for the purposes of education and review.
Darkmurkrow video footage used under a Creative Commons licence.
Kangaskhan: youtube.com/watch?v=6tcL47jn_5o
Zapdos: youtube.com/watch?v=_zoyyYlja70
Snorlax: youtube.com/watch?v=WX7zwUps1dg
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: seh.ox.ac.uk/people/tom-crawford
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collections/tom-rocks-maths
With thanks to
Nintendo
The Pokémon Company
Gamefreak
Darkmurkrow
University of Oxford Mathematician Dr Tom Crawford breaks down the Pokémon Catch Rate Formula for the Generation I video games. Explore the formula for yourself using this FREE interactive worksheet from Maple Learn: learn.maplesoft.com/doc/5eumyykf94/pokemon-catch-rate
Check your working using the Maple Calculator App – available for free on Google Play and the App Store.
Android: play.google.com/store/apps/details?id=com.maplesoft.companion&hl=en
Apple: apps.apple.com/us/app/maple-companion/id1466659419
Find out more about the Maple Calculator App and Maple Learn on the Maplesoft YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ
The video begins with an explanation of the full catch rate formula, featuring maxima, minima and floor functions. This is then simplified to arrive at the more commonly used formula for the approximate probability of catching a wild Pokémon in the Generation I video games. Each variable is explained in turn, and the effects of status, HP, and ball type are discussed.
Next, the formula is derived using the catch algorithm for the game. This is outlined in detail on ‘Bulbapedia’ here: bulbapedia.bulbagarden.net/wiki/Catch_rate
Finally, using some visualisations from Maple Learn, the probability of success when using a great ball is compared to that for an ultra ball for a Pokémon with catch rate 45 (such as Butterfree) and a Pokémon with catch rate 3 (such as Zapdos). You can explore the formulae for yourself for FREE in the accompanying interactive Maple Learn worksheet here: learn.maplesoft.com/d/AKFPLNCOIOEUKQFKDNOHASGUGOJRMJGQIKJOFOLTFPKKMRAGGKGLCFBSJFBUORJLITJLCJGSNRJMBIOSCIAMBQFILTOJEOARIMJN
Full list of Pokémon catch rates on ‘Bulbapedia’ here: bulbapedia.bulbagarden.net/wiki/List_of_Pok%C3%A9mon_by_catch_rate
All in-game footage and images are copyright The Pokémon Company, Gamefreak and Nintendo. They are shown under a fair-use policy for the purposes of education and review.
Darkmurkrow video footage used under a Creative Commons licence.
Kangaskhan: youtube.com/watch?v=6tcL47jn_5o
Zapdos: youtube.com/watch?v=_zoyyYlja70
Snorlax: youtube.com/watch?v=WX7zwUps1dg
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: seh.ox.ac.uk/people/tom-crawford
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collections/tom-rocks-maths
With thanks to
Nintendo
The Pokémon Company
Gamefreak
Darkmurkrow
