Anybody that doesn't appreciate the value of stats is [going to avoid making any personal attacks but it's such an ignorant viewpoint I feel like I need to]
Just looking at a basic box score, you can get a great feel for who the best players in the game are. In fact, I'd be willing to wager that a basic box score is far more accurate than anybody using the eye test.
Now ideally, you want to use objective and subjective analysis. But anybody ignoring stats out of fear or ignorance is missing out on a lot of knowledge about the game.
I'll agree with this. Statistics go together with watching the game to make the experience better after the fact. And it doesn't mean that you need to look at the game any differently*--I love watching Monta Ellis, for example, even though I know he's an inefficient gunner that takes way too many long 2's.
There's enough space in my brain to appreciate the beauty of a sweet 18 foot stepback and still acknowledge that it's the "worst" shot in the game of basketball--a long two, lowest percentage shot that still counts for the basic unit of points scored.
*what I really mean here is that if you're a fan of, say, Kendrick Perkins, you can still be a fan even after his stats don't wow you. That's ok.
As for best and worst stats, I've got a little bit of fluency--things like Assist Ratio, Pace, and Turnover ratio make sense to me, but I don't pay much attention to the "efficiency stats"--and not just because I like undersized gunners.