Is league even balanced?

I've returned to playing league for about a month now, and solidly for that time period, I've seen my win rate for ARAMs tank from the average 50-60% down to 20%, occasionally 25. I recognize the game is not balanced for ARAM at all, so there's bound to be some times where one side or the other decimates, but that liklihood is in theory just as possible for both sides to get/lose. Looking at the games played, especially where I did well (typically ezreal or lux due to poke factor and just feeling awesome for snipes or sheer damage output) I still did not have enough ability or power to overcome the enemy's sheer built-in capabilities which were augmented by the items bought. This game mode, to me, highlights the strengths and weaknesses of any given champion when it comes down to the core enjoyable experience of the game, the teamfights.

So, I ask, just how in the nine hells is this game balanced in that I am seemingly incapable of getting more than a 25% win rate in a 20 game history for a month despite clearly not being the weakest link of my team most of the time? Just what the hell am I missing or not doing or doing?