A Constraint Programming Approach for $n$-Day Lookahead Playoff Clinching

Computer Science > Artificial Intelligence [Submitted on 13 May 2026] A Constraint Programming Approach for n-Day Lookahead Playoff Clinching Gili Rosenberg, Kyle E. C. Booth, J. Kyle Brubaker, Ruben S. Andrist In professional sports, a team has clinched the playoffs if they are guaranteed a postseason spot, regardless of the outcomes of any remaining games. As the season progresses, sports fans and other stakeholders are interested in precisely when, and under what conditions, their team will clinch the playoffs. In this paper, we investigate playoff clinching in the context of the National Hockey League (NHL), where it is computationally challenging to produce clinching scenarios due, in part, to complex tie-breakers. We present an algorithm that determines under which combinations of game outcomes in the next n days a team will clinch the playoffs (i.e., "n-day lookahead clinching"). Our approach is a custom tree search which employs various preprocessing techniques, pruning strategies, and node ordering heuristics to efficiently explore the space of possible outcomes. The tree search leverages a constraint programming (CP)-based subroutine for inference that determines if a team has clinched the playoffs for some snapshot in time of the regular season (i.e., "0-day lookahead clinching"). This CP subroutine aims to find a counter-example in which the team being evaluated is eliminated, taking into account qualification rules and the NHL's extensive list of tie-breakers. We validate the efficacy of our algorithm using hundreds of scenarios based on public NHL data for the seasons 2021-22 through 2024-25. The methods introduced can be readily extended to other metrics of interest, including mathematical proof of playoff elimination, clinching the President's Trophy, as well as clinching (or being eliminated from clinching) any other seed in the standings. Comments: 18 pages, 5 figures, 4 tables. Accepted to CP 2026 Subjects: Artificial Intelligence (cs.AI); Optimization and Control (math.OC) Cite as: arXiv:2605.13142 [cs.AI]   (or arXiv:2605.13142v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2605.13142 Focus to learn more Submission history From: Gili Rosenberg [view email] [v1] Wed, 13 May 2026 08:09:58 UTC (170 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-05 Change to browse by: cs math math.OC References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)