Abstract Routine scalp EEG is essential in the clinical diagnosis and management of epilepsy. However, a normal scalp EEG (based on expert visual review) recorded from a patient with epilepsy can cause delays in diagnosis and clinical care delivery. Here, we investigated whether normal EEGs might contain subtle electrophysiological clues of epilepsy. Specifically, we investigated (i) whether there are indicators of abnormal brain electrophysiology in normal EEGs of epilepsy patients, and (ii) whether such abnormalities are modulated by the side of the brain generating seizures in focal epilepsy. We analysed awake scalp EEG recordings of age-matched groups of 144 healthy individuals and 48 individuals with drug-resistant focal epilepsy who had normal scalp EEGs. After preprocessing, using a bipolar montage of eight channels, we extracted the fraction of spectral power in the alpha band (8–13 Hz) relative to a wide band of 0.5–40 Hz within 10-s windows. We analysed the extracted features for (i) the extent to which people with drug-resistant focal epilepsy differed from healthy subjects, and (ii) whether differences within the drug-resistant focal epilepsy patients were related to the hemisphere generating seizures. We then used those differences to classify whether an EEG is likely to have been recorded from a person with drug-resistant focal epilepsy, and if so, the epileptogenic hemisphere. Furthermore, we tested the significance of these differences while controlling for confounders, such as acquisition system, age and medications. We found that the fraction of alpha power is generally reduced (i) in drug-resistant focal epilepsy compared to healthy controls, and (ii) in right-handed drug-resistant focal epilepsy subjects with left hemispheric seizures compared to those with right hemispheric seizures, and that the differences are most prominent in the frontal and temporal regions. The fraction of alpha power yielded area under curve values of 0.83 in distinguishing drug-resistant focal epilepsy from healthy and 0.77 in identifying the epileptic hemisphere in drug-resistant focal epilepsy patients. Furthermore, our results suggest that the differences in alpha power are greater when compared with differences attributable to acquisition system differences, age and medications. Our findings support that EEG-based measures of normal brain function, such as the normalized spectral power of alpha activity, may help identify patients with epilepsy even when an EEG does not contain any epileptiform activity, recorded seizures or other abnormalities. Although alpha abnormalities are unlikely to be disease-specific, we propose that such abnormalities may provide a higher pre-test probability for epilepsy when an individual being screened for epilepsy has a normal EEG on visual assessment.