Researchers are increasingly using machine learning to study physiological markers of emotion. We evaluated the promises and limitations of this approach via a big team science competition. Twelve teams competed to predict self-reported affective experiences using a multi-modal set of peripheral nervous system measures. Models were trained and tested in multiple ways: with data divided by participants, targeted emotion, inductions, and time. In 100% of tests, teams outperformed baseline models that made random predictions. In 46% of tests, teams also outperformed baseline models that relied on the simple average of ratings from training datasets. More notably, results uncovered a methodological challenge: multiplicative constraints on generalizability. Inferences about the accuracy and theoretical implications of machine learning efforts depended not only on their architecture, but also how they were trained, tested, and evaluated. For example, some teams performed better when tested on observations from the same (vs. different) subjects seen during training. Such results could be interpreted as evidence against claims of universality. However, such conclusions would be premature because other teams exhibited the opposite pattern. Taken together, results illustrate how big team science can be leveraged to understand the promises and limitations of machine learning methods in affective science and beyond.