Various hyperpolarization methods are able to enhance the sensitivity of nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) by several orders of magnitude. Among these methods are para-hydrogen-induced polarization (PHIP) and signal amplification by reversible exchange (SABRE), which exploit the strong nuclear alignment of para-hydrogen. Several SABRE experiments have been reported but, so far, it has not been possible to account for the experimentally observed sign and magnetic-field dependence of substrate polarization. Herein, we present an analysis based on level anti-crossings (LACs), which provides a complete understanding of the SABRE effect. The field-dependence of both net and anti-phase polarization is measured for several ligands, which can be reproduced by the theory. The similar SABRE field-dependence for different ligands is also explained. In general, the LAC concept allows complex spin dynamics to be unraveled, and is crucial for optimizing the performance of novel hyperpolarization methods in NMR and MRI techniques.