It isn't often that I disagree with Tango, but I would (albeit slightly) with this statement:
Sabermetrics is a process, a tool. It is not an ideology. Sabermetrics would say that a player’s RBI adds no new information, once you know all these other things. Sabermetrics would say that a pitcher’s wins, losses and saves adds no new information, once you know all these other things. This is not an ideology.
What sabermetrics says is: IF (that’s the start of a conditional clause) you are intent on using numbers, THEN (that’s the start of a main clause, dependent on the condition) you should use the numbers this way and that way but don’t use it the other way.
I would argue that it isn't simply a tool or process, like controlled experiments or case studies or econometrics. Rather, it is a philosophical mindset, a position one takes prior to leveraging the various tools and metrics that have been developed to support that mindset.
As I wrote a few weeks ago, ones has to buy in to the prior assumption that the world can be analyzed in an objective fashion and that outcomes in the world are the result of different distributions of individual, structural, and random causes.
You can't find FIP useful unless or until you buy in to this philosophical mindset. If you can't allow for some role of luck it's hard not to blame hitters entirely for long hit-less streaks or clutch performance in the playoffs.
The metrics and their application are secondary. They flow from the prior position that outcomes are a varied mix of various factors that can be objectively discovered, analyzed, and measured.