(This is not a thread about flaming the system or how stuck someone is.)

These are the last three games played by a friend of mine. While no one outside Riot understands the system, I thought this was a curious sample and would like your thoughts on how it could work out like this. In the bottom game, he ranks up with a positive score for kda (+4) and actual round score (+5). Then loses with the same score (-5), maintaining a +6, and ranks back down immediately. And then in the most recent game he wins with a 1 round better round diff and a +9 (and 7 assists) without ranking up again.

What could the criteria be for rankup that works with this? What am I missing? It doesn't seem to be round score, and if weighted at all by personal stats I don't see how that wouldn't skew it in his favour. Can we figure it out?
Again, not looking to start a fire. Just academic interest I suppose.

Edit:
Top game is against i3, i2, i1, i1, d3.
Teammates are i3, i3, d3, unranked.
ACS is 291

Middle game is against i3, i3, i1, d3, d3.
Teammates are i3, i2, i1, d3
ACS is 323

Bottom game is against i1, d3, d3, d2, d2.
Teammates are i1, d3, d2, d1
ACS is 234