Rage
Rage is a new mechanic in Super Smash Bros. 4, where a character's attacks will deal increased knockback as their damage rises. The effect is similar to Lucario's aura mechanic, though the damage dealt by attacks does not increase, and the increase in knockback is much less significant. Rage begins to take effect at approximately 30% damage, and maxes out at approximately 150% damage. At maximum rage, attacks will deal approximately 1.15x the amount of knockback that would normally be dealt. Rage is visually denoted by characters flashing red and smoke rising out of them when they reach 100%, and the effect grows more visually intense as damage rises farther until the aforementioned approximate 150%; this visual effect making characters appear to be enraged is what led to the mechanic being named "rage" by the Smash community.
The obvious application of rage is that it allows players at higher damages to land KOs sooner than they would be able to otherwise, which can help aid a losing player staging a comeback. Rage is not necessarily a comeback-friendly mechanic however, as the increased knockback can prevent combos from working sooner than they normally would, especially if the combo involves a setup from a high base knockback throw, making it more difficult for a highly-damaged player to rack up damage on a lower-damaged player.
Generally, heavyweight characters such as Bowser benefit the most from rage, as their greater survivability allows them to both experience rage longer and to a greater degree, and the fact that heavyweights rely less on combos allows them to make greater use of the knockback increase, with little concern of it preventing vital combos.
Rage is not present in Training mode; as such, its effects cannot be tested in that mode, requiring the player to do battles in Versus mode instead.