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Once we have obtained the data, the question is how much information is encoded in it and how we can extract it. Any framework with this purpose utilizes information-besides-data and mathematical and statistical tools. Bayesian statistics has the virtue that, by modeling the inner structure of the data, it allows us to inject prior information and its uncertainty as a catalyst to push out the information from the data. The framework also possesses tools to assess the results unbiasedness and its consistency with the data. We will show with examples at the LHC how to apply Bayesian tools in order to efficiently extract information about the physics inside. We discuss possible applications in improving data-driven methods, and in pp > hh > bbbb, however the generality of the results apply to rethinking a variety of observables. The method can exploit correlations at the event-by-event level and previously untapped strengths such as for instance continuity and unimodality of some distributions. We raise the question of whether there might be room for improvements in some of the current LHC analyses.