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I.e.
Deoxys speed form becoming paralyzed v.s. ferrothorn. Who will move first? And who will move first if Deoxys uses extreme speed?

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Answering because the previous answer was incorrect.

>Additionally, its Speed is reduced to 25% of its previous value (except for Pokémon with the Quick Feet Ability, where this condition raises the Speed by 50%).

It's only 25%. Deoxys-S has a max Speed of 504. Let us see what it is after:

504 / 4 = 126.

If Ferrothorn was running 204 Spd EVs with a neutral nature, nature, or 160 Spd EVs with a +Spd nature, Ferrothorn would outspeed a paralyzed Max Speed Deoxys-S.

If Deoxys-S used ExtremeSpeed, it would go first, as it is a priority move.

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wth you go ferro
I'm confused; does it lower it TO 25% or BY 25%? If it lowers it TO 25% then yes, it would be 126. However, if it lowers it BY 25% then Deoxys-S Speed would be dropped to;
Doing the math - [504 - 126 = 378]
Deoxys-S would still be rocking 378 Speed.

Not sure if this is a stupid question or not, but I would like the clarification, thank you.