Machine learning models are increasingly made available to the masses through public query interfaces. Recent academic work has demonstrated that malicious users who can query such models are able to infer sensitive information about records within the training data. Differential privacy can thwart such attacks, but not all models can be readily trained to achieve this guarantee or to achieve it with acceptable utility loss. As a result, if a model is trained without differential privacy guarantee, little is known or can be said about the privacy risk of releasing it. In this work, we investigate and analyze membership attacks to understand why and how they succeed. Based on this understanding, we propose Differential Training Privacy (DTP), an empirical metric to estimate the privacy risk of publishing a classier when methods such as differential privacy cannot be applied. DTP is a measure of a classier with respect to its training dataset, and we show that calculating DTP is efficient in many practical cases. We empirically validate DTP using state-of-the-art machine learning models such as neural networks trained on real-world datasets. Our results show that DTP is highly predictive of the success of membership attacks and therefore reducing DTP also reduces the privacy risk. We advocate for DTP to be used as part of the decision-making process when considering publishing a classifier. To this end, we also suggest adopting the DTP-1 hypothesis: if a classifier has a DTP value above 1, it should not be published.