A Meta-Evaluation of C/W/L/A Metrics: System Ranking Similarity, System Ranking Consistency and Discriminative Power

Recently, Moffat et al. proposed an analytic framework, namely C/W/L/A, for offline evaluation metrics. This framework allows information retrieval (IR) researchers to design evaluation metrics through the flexible combination of user browsing models and user gain aggregations. However, the statistical stability of C/W/L/A metrics with different aggregations is not yet investigated. In this study, we investigate the statistical stability of C/W/L/A metrics from the perspective of: (1) the system ranking similarity among aggregations, (2) the system ranking consistency of aggregations and (3) the discriminative power of aggregations. More specifically, we combined various aggregation functions with the browsing model of Precision, Discounted Cumulative Gain (DCG), Rank-Biased Precision (RBP), INST, Average Precision (AP) and Expected Reciprocal Rank (ERR), examing their performances in terms of system ranking similarity, system ranking consistency and discriminative power on two offline test collections. Our experimental result suggests that, in terms of system ranking consistency and discriminative power, the aggregation function of expected rate of gain (ERG) has an outstanding performance while the aggregation function of maximum relevance usually has an insufficient performance. The result also suggests that Precision, DCG, RBP, INST and AP with their canonical aggregation all have favourable performances in system ranking consistency and discriminative power; but for ERR, replacing its canonical aggregation with ERG can further strengthen the discriminative power while obtaining a system ranking list similar to the canonical version at the same time.