There are tons of metrics we use to rate a game we just finished, and a number of methods we use to determine its quality. Maybe its trying to assess how much fun we had with it, or maybe its a view of how compelling the narrative was. Perhaps you have a complex algorithm running on a super computer to define the absolute numerical rating of game quality(hint: the answer is always 42). But over the years, I've noticed that assessing how a game changed your expectations is an excellent metric for quality.
One of the greatest compliments you can give a game is "I don't normally enjoy games like that, but I loved this one!"
That single sentence right there is an enormous plus in the games favour. Here you had a game that was almost predestined to fail in your eyes. If there is a genre, gameplay mechanic, art style or narrative device that you're aware you don't like, then you are going to carry that predisposition with you as you play, there's just no avoiding it. That's a lot of factors stacked up against the game before you even press the Start button.
The problem with going into a game with such expectations is that you will always be looking for them to be met. If you know you don't like 3rd person shooters because of the control and aiming issues, then you will be looking for every single instance that the 3rd person perspective interferes with your gameplay, mentally adding them to your catalog of "Why I Don't Like 3rd Person Shooters".
It is incredibly difficult for a game to overcome that, because a single slip-up, a single point that reinforces your dislike of that genre/mechanic etc. will give you that "Aha!" moment, and may doom the game for good.
But a game that can push past your preconceived notions and expectations is usually something very special.
For me personally, I have always had a very 'meh' feeling when it comes to modern military shooters(what an original notion!). Generally I've avoided playing anything within that genre, simply because they don't appeal to me, and many of the shooters I've played have only reinforced that idea. But eventually I was convinced to play Spec Ops: The Line, intrigued enough by the word of a good story. What I wasn't expecting was one of the deepest and most mentally exhausting, but compelling games I've ever played, and a game that sits resolutely in my top gaming experiences of the year. I had gone in expecting another grey-brown shooter, perhaps with some interesting dialog and reasonably compelling characters. What I got was an experience that shook me to my core, and it was all the better for having worked against and shattered my expectations.
So, all in all, never rule a game out completely based on your preconceived notions. And if you ever hear someone utter the line "I don't normally like that sort of game...", give that title a second look, you might just be glad you did.