I find it rather strange that you are SO upset that you got placed in Bronze 4. You obviously think yourself as so much much better so then it wont take much time for you to climb to a more suitable rank.
And kills is not everything in the placement algorithm. First of all; placement matches is not supposed to mega boost you to the rankt that EXACTLY corresponds to your ELO. In all games that uses this method for the first ranked matches, it always heavily "rounds down". Ranked is still a climb where you need to prove that you actually are better than your current rank to be promoted.
Secondly; I kinda doubt that you got 5+ kills in all your 10 matches since people usually tend to over-exaggerate these kinds of claims to make a better argument. But whatever; lets assume that you had overall good games most of your 10 matches for the sake of the argument.. Then we still need to consider other things like what matches you performed well in and what matches you performed less good, more specially your teammates and enemies individual elos and ranks.
Example: Lets say you had a banger game but in that match, your two teammates had 30% higher individual ELO than all your enemies, and everyone was around Bronze. Ofc such match wont count as much in the placement algoritm, compared to a match where you literally hard carries two teammates, both with lower ELO than all the enemies players, to a 3-0 win. Also, lets say that you stomped in a couple of bronze, low elo matches so the placement algoritm decides to "test" you in a like low Gold match the next match, in which you have a very bad game. Then this would tell the placement algoritm that your final rank after the placement matches need to be placed far below Gold etc etc..
The entire ranked system for arena seems to be quite broken TBH, maybe much due to how relatively unpopular the mode is among the Apex player base. I think it messes up the individual ELO vs rank system when the player ELO distribution isnt "evenly" distributed etc.
But in your case, perhaps your cousin had a slightly higher individual ELO than you, coming into the placement matches? There is alot of stuff under the hood of every system that isnt that obvious. I played very few games of arena when ranked was released and ended up in Diamond and the next split I played arena (dont even know if it was one or two splits in between) , I performed quite average in the placement matches but ended up in low Plat.
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