Focus on the residuals
Focus on what your models of the world get wrong. This is where the signal lies, and this signal can be used to update your mental models. Information is surprisal, so do not pay much attention to information sources whose output you could predict a priori. They do not yield much information (Highly likely events do not yield much information), nor are they useful in updating your models.
Further, many models can only be applied to residualized data, representing deviations from some expectation or trend (e.g. Autoregressive models, Real business cycles, etc).