The Speed stat (formerly Evasion) helps to determine whether an enemy attack will hit a vivosaur. Increasing Speed with support effects or Quicken will increase the chance of an enemy attack missing.
Small vivosaurs tend to have higher evasion than large or titanic vivosaurs.
Fossil Fighters: Champions
In Fossil Fighters: Champions, the Evasion stat is renamed to Speed. At the beginning of a fossil battle, the total sum of each team's Speed stat is added up, and whoever has the highest number goes first.