If I were writing a course syllabus for an aspiring baseball analyst, this article by Phil Birnbaum would be one of the first lessons we’d cover. Bayesian methods and thinking don’t get enough use in baseball analysis.
As Phil summarized the situation (in regard to an example dealing with clutch hitting):
A good way to think of it: the result of the statistical test adds to the pile of evidence on whatever issue it’s testing. If you have no evidence, take the 70 points (or whatever) at face value. If you DO have evidence, use the 70 point difference to add to the pile, and it will move your conclusion one way or the other.
As Tango says, you are not entitled to assume that the difference is really 70 points just because the 70 is statistically significant. You have to make an argument. And, sure, your argument can be, “I don’t know anything about baseball, so 70 points is the most likely difference.” But it’s perfectly legitimate for Tango to turn around and say, “I DO know something about baseball, and 70 points makes no sense.”