CP and MIP approaches for soccer analysis

Abstract

<p style='text-indent:20px;'>Soccer is one of the most popular sports in the world with millions of fans that usually raise interesting questions when the competition is partially completed. One interesting question relates to the <i>elimination problem</i> which consists in checking at some stage of the competition if a team i still has a theoretical chance to finish first in a league or be within the first k teams in a tournament to qualify to the playoffs (e.g., become the champion if k = 1). Some other interesting problems from the literature are the <i>guaranteed qualification problem,</i> the <i>possible qualification problem,</i> the <i>score vector problem,</i> <i>promotion and relegation problem.</i> These problems are NP-complete for the actual FIFA pointing rule system (0 points-loss, 1 point-tie, 3 points-win). SABIO is an online platform that helps users discover information related to soccer by letting them formulate questions in form of constraints and go beyond the classical soccer computational problems. In this paper we considerably improve the performance of an existing constraint programming (CP) model and combine the use of mixed integer programming (MIP) and CP to answer general soccer queries in a real-time application.