The identification of abnormal electrographic activity is important in a wide range of neurological disorders, including epilepsy for localising epileptogenic tissue. However, this identification may be challenging during non-seizure (interictal) periods, especially if abnormalities are subtle compared to the repertoire of possible healthy brain dynamics. Here, we investigate if such interictal abnormalities become more salient by quantitatively accounting for the range of healthy brain dynamics in a location-specific manner. To this end, we constructed a normative map of brain dynamics, in terms of relative band power, from interictal intracranial recordings from 234 subjects (21,598 electrode contacts). We then compared interictal recordings from 62 patients with epilepsy to the normative map to identify abnormal regions. We hypothesised that if the most abnormal regions were spared by surgery, then patients would be more likely to experience continued seizures post-operatively. We first confirmed that the spatial variations of band power in the normative map across brain regions were consistent with healthy variations reported in the literature. Second, when accounting for the normative variations, regions which were spared by surgery were more abnormal than those resected only in patients with persistent post-operative seizures (t=-3.6, p = 0.0003), confirming our hypothesis. Third, we found that this effect discriminated patient outcomes (AUC = 0.75 p = 0.0003). Normative mapping is a well-established practice in neuroscientific research. Our study suggests that this approach is feasible to detect interictal abnormalities in intracranial EEG, and of potential clinical value to identify pathological tissue in epilepsy. Finally, we make our normative intracranial map publicly available to facilitate future investigations in epilepsy and beyond.