I would love to hear some examples of either great trades, or great signings that were stats driven that were not obvious to most clubs. I would also like to hear examples of draft selection succeses driven by stats, either college or high school.
The problem I have is that Crane said Luhnow has one priority: build up the player selection and development. A stats-minded skillset doesn't mesh with that priority, at least the way I imagine talent is normally identified and developed.
I suspect that there are organizations who can identify talent, and those who can't, but I bet all of them rely on traditional scouting methods to evaluate the raw talent. This stats stuff is largely a myth. That is why there aren't many well known stats-driven success stories.
You'd be looking at the Moneyball model then, and your timeline would run roughly 1981 - 2011 for the real stat revolution. I don't have anything at hand that gives me anything like that. I don't remember the Abstracts going into anything like that.
It sounds like you are in favor of dismissing statistics, and all of the MLB teams make heavy use of very detailed statistics in their work. They also make heavy use of great scouts and their reports. The desire is to get as much possible information you have and to synthesize it well. Better if you can do it more efficiently than the other guys.
It's a bad comp, but an example of what you're looking for is sorta analogous to the Astros not being afraid to go after pitchers who weren't tall. The thought was that other teams were focusing on pitchers who were 6'1" or better and leaving the shorter guys behind. That resulted in players like Oswalt being in the Astro system and their line was that the large, ignored pool of shorter pitchers gave them a lot of choices of talented players to draft and follow.
They're not going to tell you how they do it, but I think it's very safe to assume that statistical analysis is used pretty sparingly for raw talent and much more often to make fine distinctions at higher levels. Just because we've got Harry Potter doesn't, in my opinion, mean that he's going to use his wand to open every Christmas present he gets. I think he's trying to use numbers and correlations to find some kind of combination, any combination, that he thinks is being ignored by other teams but may still yield good players.