Wait, to clear this up, the MIDA Multi Tool agility bonus is functional on both sprint and walk, but as far as I can feel walking is faster because lightweight is broken.
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If you walk it is marginally, ever so slightly faster than sprinting. Dunemarchers and Headstrong would even it out (if not break it entirely) once both are available.
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They may fix lightweight soon anyway
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And you never know, they may fix lightweight so its the same for both walking and sprinting