An innovative super-efficiency data envelopment analysis, semi-variance, and Shannon-entropy-based methodology for player selection: evidence from cricket

Abstract

The increasing interest in club cricket and online fantasy cricket league games raises the importance of player selection from the perspective of financial and sports performance. Most previous studies focus only on player efficiency and ignore consistency and the player’s importance in a team strategy. This scenario motivates us to design a holistic player selection method based on a player’s efficiency, consistency, and importance in a team strategy. For efficiency measurement, we apply a modified data envelopment analysis (DEA) method, namely, the non-increasing return-to-scale ‘super-efficiency DEA model,’ that provides improved results compared with the conventional Banker, Charnes, and Cooper DEA model in the presence of a higher number of efficient players. We design a modified consistency index based on the semi-variance approach. Unlike the existing methods that apply a player-specific reference frame to capture variability, we use a common reference frame that calculates the consistency in a more effective manner. We aggregate different consistency indices into a single consistency index using Shannon’s entropy concept and introduce a novel ‘value index’ to determine player importance, which can also be used as an indirect measure of the player’s fitness level. Finally, we design a player performance index by aggregating the efficiency and consistency scores using the Shannon-entropy method and incorporating the value index. We perform a rigorous numerical analysis to determine the all-time best one-day international Cricket XI team for the time span of January 5, 1971 to March 29, 2015. Next, we explain the advantages as well as rationale behind the improvement in the proposed measures compared with the existing methods and highlight the key insights. Finally, we perform a comparative analysis of the proposed team, the team announced by the ICC in 2011, and the team announced by the BBC in 2015.