I'm really concerned that many of the hardcore advanced stats advocates are too lost in the numbers to consider the bigger picture.
I have an advanced mathematics education. I am a huge proponent of analytics and metrics in almost every aspect of my professional life. I personally don't care to analyze hockey (which I watch for fun) the same way I do the things that I am responsible for at work, and the fanatic and smug adherence to a few of these stats has made this place significantly less enjoyable to visit.
The eye test is real. The reality you experience is real. Yes, your senses are prone to tons of subconscious biases, but you can make yourself aware of them and minimize their effects. I've read and love Kahneman/Tversky/Thaler - I'm a believer, seriously.
Statistics, in addition to being predictive, should also be descriptive. When the numbers don't match experience, it is entirely possible that your biases are clouding your experience, but it's also possible that the numbers are either ill-conceived or simply not applicable to the situation at hand. Good analysis is backed by data but is comprised of much more than JUST DATA.