Building a score from a questionnaire to predict a binary gold standard is a common research question in psychology and health sciences. When building this score, researchers may have to choose between statistical performance and simplicity. A practical question is to what extent it is worth sacrificing the former to improve the latter. We investigated this research question using real data, in which the aim was to predict an alcohol use disorder (AUD) diagnosis from 20 self-reported binary questions in young Swiss men (n = 233, mean age = 26). We compared the statistical performance using the area under the ROC curve (AUC) of (a) a "refined score" obtained by logistic regression and several simplified versions of it ("simple scores"): with (b) 3, (c) 2, and (d) 1 digit(s), and (e) a "sum score" that did not allow negative coefficients. We used four estimation methods: (a) maximum likelihood, (b) backward selection, (c) LASSO, and (d) ridge penalty. We also used bootstrap procedures to correct for optimism. Simple scores, especially sum scores, performed almost identically or even slightly better than the refined score (respective ranges of corrected AUCs for refined and sum scores: 0.828-0.848, 0.835-0.850), with the best performance been achieved by LASSO. Our example data demonstrated that simplifying a score to predict a binary outcome does not necessarily imply a major loss in statistical performance, while it may improve its implementation, interpretation, and acceptability. Our study thus provides further empirical evidence of the potential benefits of using sum scores in psychology and health sciences.