The oldest definition of semi-presidentialism requires a president possessing considerable constitutional power. Subsequent research has listed presidential competences, but has not empirically set their respective weighting. In order to assess the relevant competences that determine presidential power, this article presents an indicator of relative turnout in 28 parliamentary democracies with a popularly elected president. The core hypothesis is that if presidents have considerable power, the turnout is higher for presidential elections than for legislative ones. The results show that presidents are deemed 'strong' when they play a central role in foreign policy. This finding is compatible with different analyses of presidential regimes and provides a clear and coherent criterion for identifying semi-presidential regimes.