Best-worst scaling is a judgment format in which participants are presented with a set of items and have to choose the superior and inferior items in the set. Best-worst scaling generates a large quantity of information per judgment because each judgment allows for inferences about the rank value of all unjudged items. This property of best-worst scaling makes it a promising judgment format for research in psychology and natural language processing concerned with estimating the semantic properties of tens of thousands of words. A variety of different scoring algorithms have been devised in the previous literature on best-worst scaling. However, due to problems of computational efficiency, these scoring algorithms cannot be applied efficiently to cases in which thousands of items need to be scored. New algorithms are presented here for converting responses from best-worst scaling into item scores for thousands of items (many-item scoring problems). These scoring algorithms are validated through simulation and empirical experiments, and considerations related to noise, the underlying distribution of true values, and trial design are identified that can affect the relative quality of the derived item scores. The newly introduced scoring algorithms consistently outperformed scoring algorithms used in the previous literature on scoring many-item best-worst data.