As a reaction to the high infectiousness and lethality of the COVID-19 virus, countries around the world have adopted drastic policy measures to contain the pandemic. However, it remains unclear which effect these measures, so-called non-pharmaceutical interventions (NPIs), have on the spread of the virus. In this article, we use machine learning and apply drift detection methods in a novel way to measure the effectiveness of policy interventions: We analyze the effect of NPIs on the development of daily case numbers of COVID-19 across 9 European countries and 28 US states. Our analysis shows that it takes more than two weeks on average until NPIs show a significant effect on the number of new cases. We then analyze how characteristics of each country or state, e.g., decisiveness regarding NPIs, climate or population density, influence the time lag until NPIs show their effectiveness. In our analysis, especially the timing of school closures reveals a significant effect on the development of the pandemic. This information is crucial for policy makers confronted with difficult decisions to trade off strict containment of the virus with NPI relief.