PokéBase - Pokémon Q&A
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We know that Speed Boost increases the user’s speed by one stage. Not many Pokémon have this ability and most of them only have it as a hidden ability such as Torchic and Sharpedo so it’s quite rare. But what if a Pokémon was able to stay on the battlefield for a big amount of turns. Would the Pokémon be like god-fast. Can it exceed past 1000?

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Speed Boost will only boost Speed a maximum of six consecutive turns, for a total of four times the Pokemon's original Speed. It's very possible for Speed Boost Pokemon to exceed 1000 Speed, but there *is* a limit.

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Putting Amethyst’s comment in to account, it is possible to raise a Pokémon speed stat to over 1000.

For example, Ninjask’s Speed stat with Max Speed EV’s and IV’s and a beneficial nature, is 460 (Source) and since the stat can be boosted four times the amount, Ninjask, after 6 turns, will have a Speed stat of 1840

Here is a list of the it’s speed at each stage

Stage 1: 690
Stage 2: 920
Stage 3: 1150
Stage 4: 1380
Stage 5: 1610
Stage 6: 1840

(This is for Ninjask)

With the speed boosts, it is well and truly possible for a Pokémon to get a speed stat over 1000. Probably most of the Pokémon with Speed can reach that extent if they have had a good amount of speed. It’s not only limited to Pokémon with that ability

Hope I helped!

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insert dbz reference here