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Including banned Pokemon from Smogon.

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Note: Banned Pokemon who either have greater than or equil to the best stat are shown in brackets [].

Here are the highest of each stat for each type:

Normal
HP: Munchlax
Atk: Munchlax
Def: Slackoth
SpA: Litleo
SpD: Munchlax
Spe: Meowth

Water
HP: Wailmer
Atk: Krabby
Def: Tirtouga
SpA: Omanyte
SpD: Mantyke
Spe: Poliwag

Grass
HP: Foongus
Atk: Cacnea
Def: Ferroseed
SpA: Cacnea
SpD: Lileep
Spe: Deerling

Fire
HP: Darumaka
Atk: Darumaka
Def: Litleo
SpA: Houndor
SpD: Ponyta
Spe: Ponyta

Electric
HP: Chinchou
Atk: Geodude(alola)
Def: Geodude(alola)
SpA: Magnemite
SpD: Chinchou
Spe: Voltorb

Ice
HP: Amaura
Atk: Sandshrew(alola) [Sneasel]
Def: Sandshrew(alola)
SpA: Smoochum
SpD: Vulpix(alola) [Sneasel]
Spe: Vulpix(alola)/Smoochum tie [Sneasel]
[Sneasel is banned]

Ground
HP: Phanphy
Atk: Trapinch/Mudbray tie
Def: Onix
SpA: Sandyghast
SpD: Baltoy
Spe: Diglett

Rock
Hp: Rhydon
Atk: Cranidos
Def: Onix
SpA: Omanyte
SpD: Nosepass
Spe: Anorith

Fighting
HP: Timburr
Atk: Mienfoo
Def: Scraggy
SpA: Croagunk
SpD: Scraggy
Spe: Mankey

Flying
HP: Vulaby/Rufflet tie [scyther]
Atk: Archen
Def: Vulaby [scyther]
SpA: Archen
SpD: Mantyke
Spe: Wingull/Tailow tie [Scyther] [Scyther is banned]

Psychic
Hp: Wynaut
Atk: Slowpoke
Def: Bronzor
SpA: Abra/Solosis tie
SpD: Drowzee/Mime Jr. tie
Spe: Abra

Ghost
Hp: Pumpkaboo(Super)/Golett tie
Atk: Honedge
Def: Honedge
SpA: Ghastly
SpD: Duskull
Spe: Ghastly

Dark
HP: Grimer(alola)
Atk: Carvanha [Sneasel]
Def: Vulaby
SpA: Houndour/Zorua tie
SpD: Scraggy [Sneasel]
Spe: Meowth(alola) [Sneasel] [Sneasel is banned]

Steel
HP: Bronzor
Atk: Pawniard
Def: Shieldon
SpA: Magnemite:
SpD: Shieldon
Spe: Diglett(alola)

Poison
HP: Grimer/Grimer(alola) tie
Atk: Grimer/Grimer(alola) tie
Def:Koffing
SpA: Gastly
SpD: Tentacool
Spe: Gastly

Bug
HP: Venonat [scyther]
Atk: Anorith [Scyther]
Def: Skorupi/Pineco/Nincada tie
SpA: Joltik
SpD: Ledyba [scyther]
Spe: Wimpod [scyther] [Scyther is banned]

Dragon
HP: Gible/Tyrunt tie
Atk: Tyrunt
Def: Tyrunt
SpA: Goomy
SpD: Goomy
Spe: Axew

Fairy
HP: Igglybuff
Atk: Snubull
Def: Togepi
SpA: Mime Jr.
SpD: Mime Jr.
Spe: Cottonee

Source: Smogon

answered by
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calm, please. it took me 53 minutes to make that list
There, i included both
The asker specifically asked to include banned Pokemon.
and i included both so it would be good for the asker to know what it is withe the banned, as well as the banned pokemon tie with the nonbanned in certain cases.
Good enough.
Can you battle me right now?