Even with AOBH, you haven't established a case other than perhaps enough to trigger an investigation but never enough to charge.
Player 1: He hit me. See my nose
Player 2: silence
Result? Nothing to see here
To build a case good enough to charge, you need corroborating evidence ie. witnesses (plural), CCTV of the incident, established date and time, corroborating medical evidence that was gathered as soon as possible after the event. You get all of that at a minimum and you have a start.
Then you have to eliminate all possible defences. You mentioned self defence. If the witnesses support that, you don't have a case. If the witnesses aren't sure who threw the punch ie Jezza or perhaps his evil twin, you don't have a case.
The hurdle you need to get over is quite a bit higher than you imagine.