Smash hit

A Smash hit (stylized as ) is an event that multiplies a regular attack's damage output. It is the EarthBound series's equivalent to a critical hit, a common feature in role-playing games. This can only occur when using a character's normal attack, such as Bash. Upon landing one, the game displays on the screen as the damage is being dealt, while the screen flashes green (red when an enemy lands a smash hit from EarthBound onwards). Jeff never lands smash hits in EarthBound although in Mother 1+2 he is able to.

Overview
Smash hits are determined by the character's Fight stat (in EarthBound Beginnings) or Guts stat (in EarthBound). The damage that is dealt is not consistant output, rarely it can do less than 2× normal damage, but often times a smash hit can do nearly triple the average damage.

In EarthBound Beginnings
Smash hits are determined by the Fight stat of a character, in other words the higher the Fight stat the higher the chances of landing a smash hit.

In EarthBound
(Information courtesy of Starmen.net) With the Bash command or Bash-like enemy/NPC attacks, the probability of a smash hit is equal to guts/500 or 1/20, whichever is greater. If a smash hit is successful, it deals 4*offense-defense damage, and skip the remaining steps. (Yes, even step 5.) This damage is still affected by defending if applicable. If the target had a physical shield, it will be depleted.