From the Super Mario Wiki
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Speed occasionally shorted to SPD is an ability which appears in Super Mario RPG: Legend of the Seven Stars, as well as the Mario & Luigi series. It is the stat that increases the character's ability to attack first. The members of the party as well as enemies, all have a Speed stat. In battle, the character or enemy with the highest Speed attacks first, followed by the others in decreasing order. In the Mario and Luigi series, Speed is increased when leveling up and can be given a boost with the Bonus Wheel. In Super Mario RPG, Speed can only be increased by wearing certain armor and accessories. In Mario & Luigi: Partners in Time, the Blue Pepper can briefly increase speed. In Mario & Luigi: Dream Team and Mario & Luigi: Paper Jam, Speed Beans can boost the desired character's speed permanently by one and Speed Bean DXs can boost it by three.