You didn't move slow as shit in Reach. In Halo 3 you moved slow as shit
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Player base movement was slower than Halo 3 and you did not jump as high. You did not move faster in Reach unless you had sprint.
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I felt faster in Reach even without sprint
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Albeit, you personally may have, base movement speed and jump height were decreased in Reach from 3. If you played as an Elite in Reach, the movement was basically the equivalent as playing as your character in Halo 3.