Some insurance coverage explicitly requires the loss to have resulted from an accident (see lessons on “occurrence”). But almost all policies exclude coverage for intentional injury.
The ISO CGL form (and others) make exception for intentional injury inflicted in self-defense.
In Michigan, the rule is that injury must be expected/intended, not just the action. So, if Adam intentionally throws a baseball to Bob, but the ball hits Casey, that should not be subject to the expected or intended injury exclusion.