Analysis of the Physical Efficiency Index in football teams and correlation with goal events: A survey of the Italian Serie A Championship


  • Lorenzo Canapini University Carlo Bo of Urbino, Italy
  • Ciro Hosseini Varde’i University Carlo Bo of Urbino, Italy
  • Antonio Cejudo-Palomo University of Murcia, Spain
  • Riccardo Izzo University Carlo Bo of Urbino, Italy


Match analysis, Key performance indicators, Technical efficiency index, Performance model, Goal actions


This paper is centred on the Match Analysis (MA) of football that nowadays is a fundamental tool in the elite level. The MA is the objectively analysis of matches using hardware and software that help the coaching staff to evaluate the performance of the single athlete and the entire team in order to define the Performance Model (PM). Soccer is a nonlinear dynamical system that required a specific mathematical analysis to investigate the relevance of the main key performance indicators (KPIs). Following this issue in 2011, Mirko Marcolini the CEO of K-Sport Universal (Montelabbate, Italy) has registered a patent (IB2010/002593, approved on April 28, 2011 by World Intellectual Property Organization) proposing a new MA approach, based on probability theory, setting as independent variables some KPIs (passes; ball speed; ball trajectory; distance between the holder players, the teammates, the opponents and the fitness ability) provided by the video-tracking and gained using a specific software, in order to analyse the final outcome of a match. From Marcolini formulas is possible to define the technical efficiency index (TEI) and physical efficiency index (PEI), both two percentage parameters (considering as 0%, the worst efficiency and 100% the maximum efficiency). The aim of this study, was to analyse the TA-PEI during goal actions in order to objectively define if the physical performance is correlated with goal events. Where examined a full season of one team, using video-tracking on 38 games from the 2015/2016 Italian Serie A, and calculated the TA-PEI during goal events for both teams. During this survey, 92 goals were scored, and 184 TA-PEI were collected. For each realization, the TA-PEI was examined, both by the finalizing team and for the team that suffered the goal. On 38 Matches four, two from the first round and two from the second round, ended without goal, end were not considered in the research. The TA-PEI is a resultant variable of different parameters and is certainly a tool that facilitates the task of the match analyst. In this research, attention was focused on the TA-PEI in the goal event, and it establishes the reliability of this parameter. An important update to this study can be the complete analysis of all matches of a championship from different countries or league, in order to receive more different data less affected by causality and errors, and to study if between years or nations there are different or specific trends. Also analysing with the same method, the TA-PEI during all match and not only during goal events can be relevant and useful. In conclusion the TA-PEI is certainly an interesting and valid parameter, from which the results can be used to objectivate and to improve the performance of the team, in an accurate way following the real performance model and help the coaching staff to receive more specific information during crucial moments of matches.


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Canapini, L., Varde’i, C. H., Cejudo-Palomo, A., & Izzo, R. (2019). Analysis of the Physical Efficiency Index in football teams and correlation with goal events: A survey of the Italian Serie A Championship. Journal of Human Sport and Exercise, 14(5proc), S2390-S2399. Retrieved from

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