Statistical analysis of magnetic resonance imaging (MRI) can help radiologists to detect pathologies that are otherwise likely to be missed. Deep learning (DL) has shown promise in modeling complex spatial data for brain anomaly detection. However, DL models have major deficiencies: they need large amounts of high-quality training data, are difficult to design and train and are sensitive to subtle changes in scanning protocols and hardware. Here, we show that also simple statistical methods such as voxel-wise (baseline and covariance) models and a linear projection method using spatial patterns can achieve DL-equivalent (3D convolutional autoencoder) performance in unsupervised pathology detection. All methods were trained (N=395) and compared (N=44) on a novel, expert-curated multiparametric (8 sequences) head MRI dataset of healthy and pathological cases, respectively. We show that these simple methods can be more accurate in detecting small lesions and are considerably easier to train and comprehend. The methods were quantitatively compared using AUC and average precision and evaluated qualitatively on clinical use cases comprising brain atrophy, tumors (small metastases) and movement artefacts. Our results demonstrate that while DL methods may be useful, they should show a sufficiently large performance improvement over simpler methods to justify their usage. Thus, simple statistical methods should provide the baseline for benchmarks. Source code and trained models are available on GitHub (https://github.com/vsaase/simpleBAD).