It's the other way around for me.
I notice other teams' SSs making more great plays than Bogey, then I look at the metrics and stats, and it confirmed the observations.
No joke, I'm obsessed with watching the Sox. I have come very close to watching every possible play of every Sox game for over a decade. That does not make me an expert, and I'm not trying to sound like a know-it-all, but I love defense, especially up the middle and pay very close attention to it- both on our team and the teams we are playing.
I have loved man of our players' defense, and I have no bias against Bogey that would make me see what is not there. I can understand the fact that others watch a lot of games, too and don't see what I see. It's just my opinion.
The fact that most metrics and stats back up my opinion does make me feel more firmly entrenched in my position, but I do not think the fact that I am a stat freak makes me see things that are not there, delude myself into beliefs based on numbers or enjoy watching the game less than anyone who hates or could care less about metrics or stats.
I can think of only one time it worked the other way around. I remember when Ellsbury first came up, I felt he was a plus defender, but the numbers showed otherwise, so I started watching more closely, and started seeing late breaks, bad routes and a sub par arm. I changed my opinion based on stats and further observations, but then over time, Ellsbury improved his defense, and my opinion changed, again. Maybe somebody might think I let the numbers bias me into seeing what I wanted to see, but with Ellsbury, it actually meant I had to admit I was wrong.