Expected Reciprocal Rank for Evaluating Fingering Advice

We cast the computational modeling of musical fingering as an information retrieval (IR) problem in which the task is to generate an optimally ranked list of fingering suggestions for each phrase in a score. The audience for this list is a set of performers with potentially diverse fingering preferences. Specifically, we adapt the expected reciprocal rank (ERR) metric—proposed by Chapelle and associates as an improved evaluation metric for retrieving documents with graded relevance—to develop a set of novel metrics tailored to the piano fingering IR task. ERR, as originally described, relies on a heuristic function to estimate the probability that a user will be satisfied by a document with a particular graded relevance. For musical fingering, we instead estimate the likelihood that a given performer will deem a suggested fingering sequence sufficient for arriving at a satisfactory solution. Finally, we attempt to validate our specific use of ERR by comparing how it judges several competing models.