However when I met two people fighting each other in public, violently (blood and teeth), I was under a severe bystander effect I thought I wouldn't have
This is pretty rational actually, since you have no way of knowing who the instigator and who the victim (if any) is. A person who's been attacked for no reason will generally make it obvious, trying to escape or hang on property that's being taken from them or evincing other signs of distress. If you find two people actively going at each other and there isn't an obvious underdog, it's probably best not to intervene physically.
This is pretty rational actually, since you have no way of knowing who the instigator and who the victim (if any) is. A person who's been attacked for no reason will generally make it obvious, trying to escape or hang on property that's being taken from them or evincing other signs of distress. If you find two people actively going at each other and there isn't an obvious underdog, it's probably best not to intervene physically.