Empirical theory (or Empirical probability) is when one predicts how many times something will happen based upon an actual collection of data. Essentially, this is where one states the predicted frequency of how many times a thing will happen based upon prior data.

Theoretical theory (or Theoretical probability) looks at random phenomenon. Prior data is not regarded in order to predict the outcome. essentially, probability theory examines phenomenon only.

That said, both empirical and theoretical probability are both branches of mathematics, and both are used to determine the outcome of specific events.

Contrastingly, each attempt to predict the outcome of any given scenario based upon very different ideas. Empirical theory uses prior data to predict an outcome, whereas theoretical theory does not. Instead, given data is not used, the hypothesis of the outcome is solely based upon random phenomenon.