Event-related potentials (ERPs) in the processing of grammatical violations typically investigate differences between natives and second language speakers by averaging the amplitude of a participant’s brain response in a pre-specified time window by condition. This approach suffers from the problem that time windows are defined arbitrarily, and that the result is sensitive to outliers as well as participant variation in latency. The latter is particularly problematic for studies on L2 processing. The size of the ERP response (i.e., amplitude difference) of an L2 speaker may not be the best indicator of near-native proficiency, either, with the consistency of the response potentially being a more valid indicator. We introduce a set of individual difference measures based on complete ERP waveforms using generalized additive modelling (GAM), extracted based on amplitude, area and peak effects. We illustrate the benefits of our method compared to the traditional Response Magnitude Index with data on the processing of grammatical gender violations in 66 Slavic L2 speakers of German and 29 German native speakers. One of our measures in particular appears to outperform the others in characterizing differences between natives and L2 speakers, and captures proficiency differences between L2 speakers: the ‘Normalized Modelled Peak’, reflecting the height of the (modelled) peak, normalized against the uncertainty of the modelled signal. This measure reflects peak robustness, that is, how reliable a P600 effect is found, largely independently of its latency in the P600 window. We discuss implications of our results and offer suggestions for future studies on L2 processing.