Modelling the order of scoring in team sports

Kengo Hamada, Ken Ichi Tanaka

Research output: Contribution to journalArticlepeer-review


This paper considers sports matches in which two teams compete to score more points within a set amount of time (e.g. football, ice hockey). We focus on the order in which the competing teams score during the match (order of scoring). This type of order of scoring problem has not been addressed previously, and doing so here gives new insights into sports matches. For example, our analysis can deal with a situation that spectators find matches that involve comebacks particularly exciting. To describe such problems mathematically, we formulate the probabilities of (i) the favourite team leading throughout the match and (ii) the favourite team falling behind the opposing team but then making a comeback. These probabilities are derived using an independent Poisson model and lattice path enumeration, the latter of which involves the well-known ballot theorem. The independence assumption allows lattice path enumeration to be applied directly to the Poisson model and various scoring patterns to be addressed. We confirm that the values obtained from the proposed models agree well with actual sports data from football, futsal and ice hockey.

Original languageEnglish
Pages (from-to)283-301
Number of pages19
JournalIMA Journal of Management Mathematics
Issue number3
Publication statusPublished - 2021 Jul 1


  • ballot theorem
  • lattice path enumeration
  • order of scoring
  • probabilistic models
  • sports analysis

ASJC Scopus subject areas

  • Management Information Systems
  • Modelling and Simulation
  • Economics, Econometrics and Finance(all)
  • Strategy and Management
  • Management Science and Operations Research
  • Applied Mathematics


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