If you truly understand the game, then you don't need statistics. Plus, the eye-test actually gives you both quantitative and qualitative data at the same whereas statistics only give you quantitative data without context.
You're arguing for the same test that people used to determine that the Sun revolved around the Earth instead of vice versa. We used numbers to learn the truth.
That's typically how it works.
As far as hockey, the eye-test is good for evaluating INPUTS. The hows and the whys. For example, stats can't tell us a player is FAST, but it can tell us he's great at controlled zone exits and puck retrievals. It takes the eye-test to determine it's because he out-skates his opposition, rather than muscling them off the puck or protecting the puck with his body.
But our brains are actually quite poor for measuring the 'how many' of anything over large quantities of data points. It's very easy for our brains to see something once, have it make an impression, then look for every piece of evidence that reinforces that impression while ignoring potentially vast amounts of of evidence that contradict it.
It's called confirmation bias. It's common, powerful phenomena.
The eye-test is a relatively good tool for evaluating what happened in one game.
It's a very poor tool for evaluating what happened over the course of many games.
