For supplier selection in the public sector, the Weighted Sum Model is often used in combination with relative scoring methods that allow rank reversal. With rank reversal we refer to a changed order in the ranking of bids leading to a new winner, after removing or adding a non-optimal bid that does not win the original tender. In practice, an important reason indicated by practitioners for using methods that allow rank reversal is that it would rarely occur in practice. Based on an analysis of 303 Dutch public tenders, this research shows this is not true. In about 1 out of 5 the tenders, rank reversal occurs after adding non-optimal fictional bids to tenders that do not have quality thresholds. After removing bids, the rate is about 1 out of 40 if a curved relative scoring method is used. In addition, the research shows that rank reversal rates increase when (i) there is no quality threshold, (ii) the number of bids increases, (iii) bid price variance increases, and (iv) price weights are not very low or high. We argue that relative scoring methods that allow rank reversal should not be used in public procurement, or otherwise only in exceptional cases, as it conflicts with public procurement principles and leads to reduced overall bid value.