The emergence of SARS-CoV-2 variants stressed the demand for tools allowing to interpret the effect of single amino acid variants (SAVs) on protein function. While Deep Mutational Scanning (DMS) sets continue to expand our understanding of the mutational landscape of single proteins, the results continue to challenge analyses. Protein Language Models (pLMs) use the latest deep learning (DL) algorithms to leverage growing databases of protein sequences. These methods learn to predict missing or masked amino acids from the context of entire sequence regions. Here, we used pLM representations (embeddings) to predict sequence conservation and SAV effects without multiple sequence alignments (MSAs). Embeddings alone predicted residue conservation almost as accurately from single sequences as ConSeq using MSAs (two-state Matthew Correlation Coefficient – MCC - for ProtT5 embeddings of 0.596 ± 0.006 vs. 0.608 ± 0.006 for ConSeq). Inputting the conservation prediction along with BLOSUM62 substitution scores and pLM mask reconstruction probabilities into a simplistic logistic regression (LR) ensemble for Variant Effect Scoring without alignments (VESPA) predicted SAV effect magnitude without any optimization on DMS data. Comparing predictions for a standard set of 39 DMS experiments to other methods (incl. ESM-1v, DeepSequence, and GEMME) revealed our approach as competitive with the state-of-the-art (SOTA) methods using MSA input. No method outperformed all others, neither consistently nor in a statistically significant manner, independently of the performance measure applied (incl. two-state accuracy: Q2, MCC, Spearman and Pearson correlation). Lastly, we investigated binary effect predictions on DMS experiments for four human proteins. Overall, embedding-based methods have become competitive with methods relying on MSAs for SAV effect prediction at a fraction of the costs in computing/energy. Our method predicted SAV effects for the entire human proteome (~ 20k proteins) within 40 minutes on one Nvidia Quadro RTX 8000. All methods and data sets are freely available for local and online execution through bioembeddings.com, https://github.com/Rostlab/VESPA, and PredictProtein.