Theories of non-equilibrium strategic thinking (e.g. Level-k and Cognitive Hierarchy) intend to describe how individuals actually behave. But how much of their descriptive accuracy is driven by being more permissive theories? We modify Selten  axiomaticmeasure of predictive success to ensure individual consistency. By applying restrictions over observables to the individual data (echoing the revealed preference literature), we test the necessary and sufficient conditions of these theories and quantify the economic losses for deviations from the theory. The non-parametric results are favourable for these theories and show that their predictive success is not mechanically due to their permissiveness.