Moneyball is a good film, but it's real strength is as an example of a paradigm shift. The heart of the story is that "the game done change".
Against the backdrop of the dominant rationality, Billy Beane's rationality is non-rational. He trades excellent players and buys obscure players that don't fit into the present system. The Coach tries to merge the two rationalities together, but they do not mix, and Billy Beane looks like the fool that everyone thought him to be.
But when Beane's rationality is fully adopted rather than merely merged into the already existing one, the results begin to come. What is learned is that you cannot see the game of baseball the way you've always seen it, and then try to fit Beane into that picture. Your vision of the game, your perception of what makes sense and what doesn't, must be transformed.
Paradigm shifts are always resisted, but they are the stuff of life. In an ideal world, competing rationalities will not to be judged based on who has the most power to make their rationality the dominant one, but rather based on whose rationality leads to the telos, the goal.
In baseball, the goal is generally agreed upon - win the World Series. In life, however, the goal is not nearly so universally agreed upon, if the notion of a goal is even accepted in the first place.
To bring this down to the level of theology, this makes apologetics (or even evangelism) something more than what it is seen to be (though it often isn't even seen to be this) - a dialogue between competing rational paradigms whose intersections are largely trivial. Apologetics/evangelism is, at its heart, in the realm of desire and goal. If we do not want the same things from life, then the dialogue will produce more heat than light, or simply nothing at all.
This is the reason Christian proclamation to the world (and to the church) must begin with the word "repent": we say on the basis of the life of Jesus that what we want is not what is good for us, and so our desires must change.
How desires change is a question I cannot answer.