A new approach for measuring productivity gaps across groups: an application with historic footballers from FC Barcelona and Real Madrid
提出一种不依赖基准技术且满足循环检验的生产率差距分解方法，并将其应用于分析巴塞罗那和皇家马德里历史球员按位置划分的生产率差异。
• Proposed a new method for measuring productivity gaps across groups. • Method decomposes the productivity gap into efficiency and technical components. • Approach is independent of base-reference technology and passes the circular test. • Analyzed productivity gaps between FC Barcelona and Real Madrid players. • Results show different productivity gaps by position between both clubs. The assessment of the productivity gap between two or more groups of production units that operate an equivalent production process in different settings is a common challenge in the field of production analysis. These groups need to determine whether they should keep operating in the same manner to sustain their better performance levels or decide which managerial practices should be altered to close the gap with respect to best practices in other groups. The aim of this paper is to propose a new tool for measuring the productivity gap across different groups based on the use of a synthetic reference group uniformly distributed within a unit hypercube. Besides, as the productivity gap can be decomposed into two components, efficiency gap and global technical gap, this method fulfills the circular test and is independent of a base-reference technology. Thus, it outperforms other traditional approaches. To illustrate the usefulness of this methodology, we analyze the productivity gap between Spanish football’s two biggest rival clubs: FC Barcelona and Real Madrid. We use data on the performance of the most important players in the history of both clubs, divided according to their position on the pitch. The period of analysis covers the last 70 years, from the beginning of European competitions to the present day, i.e., from the 1954/55 to the 2023/24 season. Results show that, to date, Real Madrid’s goalkeepers and midfielders were more productive than those playing for FC Barcelona, there is a tie for defenders, while the productivity of FC Barcelona’s forwards was higher than those playing for Real Madrid.