Explanatory power is the ability of a hypothesis or theory to effectively explain the subject matter it pertains to. The opposite of explanatory power is explanatory impotence.
In the past, various criteria or measures for explanatory power have been proposed. In particular, one hypothesis, theory or explanation can be said to have more explanatory power than another about the same subject matter
if more facts or observations are accounted for; if it changes more "surprising facts" into "a matter of course" (following Peirce); if more details of causal relations are provided, leading to a high accuracy and precision of the description; if it offers greater predictive power, i.e., if it offers more details about what we should expect to see, and what we should not; if it depends less on authorities and more on observations; if it makes fewer assumptions; if it is more falsifiable, i.e., more testable by observation or experiment (following Popper).
Recently, David Deutsch proposed that the correct hypothesis or theory, the one that stands out among all possible explanations, is that specific explanation that
is hard to vary. By this expression he intends to state that the correct theory, i.e., the true explanation, provides specific details which fit together so tightly that it is impossible to change any one detail without affecting the whole theory.