The whole package matters. I believe the interview counts the most assuming all other things are equal to or better than the average accepted student. The thing is, it varies from year to year. A school might get three goalies or three first violin chairs or any combination. In that case, they are going to pick the one that fits best or can fill many buckets.
In terms of recommendations, they are looking for red flags. Private schools write much better recommendations than most public schools ( not all but most). Private schools have a paying clientele and have to be specific or the parents won’t be happy. I have heard from many and seen the difference and it’s vast. I have two similar kids and the private accolades are much stronger. Just like BS people who know what to say and how to coach their kids for interviews, private school teachers often know the buzzwords schools want to hear.
Athletics can also make a big impact. But so can a kid that is really outstanding in something.
SO you can’t really suss out where you stand because the AO doesn’t even know until all the applications are in. What they are telling you is how you/your kid compares to other candidates they have interviewed before.