Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Quantitative Analysis in Sports

An official journal of the American Statistical Association

Editor-in-Chief: Steve Rigdon, PhD

CiteScore 2017: 0.67

SCImago Journal Rank (SJR) 2017: 0.290
Source Normalized Impact per Paper (SNIP) 2017: 0.853

See all formats and pricing
More options …
Volume 15, Issue 1


Volume 1 (2005)

A mathematical optimization framework for expansion draft decision making and analysis

Kyle E. C. Booth / Timothy C. Y. ChanORCID iD: https://orcid.org/0000-0001-6929-8042 / Yusuf Shalaby
Published Online: 2019-02-15 | DOI: https://doi.org/10.1515/jqas-2018-0024


In this paper, we present and analyze a mathematical programming approach to expansion draft optimization in the context of the 2017 NHL expansion draft involving the Vegas Golden Knights, noting that this approach can be generalized to future NHL expansions and to those in other sports leagues. In particular, we present a novel mathematical optimization approach, consisting of two models, to optimize expansion draft protection and selection decisions made by the various teams. We use this approach to investigate a number of expansion draft scenarios, including the impact of “collaboration” between existing teams, the trade-off between team performance and salary cap flexibility, as well as opportunities for Vegas to take advantage of side agreements in a “leverage” experiment. Finally, we compare the output of our approach to what actually happened in the expansion draft, noting both similarities and discrepancies between our solutions and the actual outcomes. Overall, we believe our framework serves as a promising foundation for future expansion draft research and decision-making in hockey and in other sports.

Keywords: expansion draft; mathematical programming; national hockey league; operations research; optimization


  • Amoros, J., L. F. Escudero, J. F. Monge, J. V. Segura, and O. Reinoso. 2011. “Team Aspar Uses Binary Optimization to Obtain Optimal Gearbox Ratios in Motorcycle Racing.” Interfaces 42:191–198.Web of ScienceGoogle Scholar

  • Beaudoin, D. and T. B. Swartz. 2010. “Strategies for Pulling the Goalie in Hockey.” The American Statistician 64:197–204.CrossrefGoogle Scholar

  • Becker, A. and X. A. Sun. 2016. “An Analytical Approach for Fantasy Football Draft and Lineup Management.” Journal of Quantitative Analysis in Sports 12:17–30.Web of ScienceGoogle Scholar

  • Bonami, P., A. Lodi, A. Tramontani, and S. Wiese. 2015. “On Mathematical Programming with Indicator Constraints.” Mathematical programming 151:191–223.CrossrefWeb of ScienceGoogle Scholar

  • Boon, B. H. and G. Sierksma. 2003. “Team Formation: Matching Quality Supply and Quality Demand.” European Journal of Operational Research 148:277–292.CrossrefGoogle Scholar

  • Chan, T. C. Y., J. A. Cho, and D. C. Novati. 2012. “Quantifying the Contribution of NHL Player Types to Team Performance.” Interfaces 42:131–145.CrossrefWeb of ScienceGoogle Scholar

  • Chan, T. C. Y. and D. Fearing. 2017. “Process Flexibility in Baseball: the Value of Positional Flexibility.” forthcoming in Management Science. https://doi.org/10.1287/mnsc.2017.3004.

  • Chan, T. C. Y. and R. Singal. 2016. “A Markov Decision Process-Based Handicap System for Tennis.” Journal of Quantitative Analysis in Sports 12:179–188.Web of ScienceGoogle Scholar

  • Dawson, D. and L. Magee. 2001. “The National Hockey League Entry Draft, 1969-1995: An Application of a Weighted Pool-Adjacent-Violators Algorithm.” The American Statistician 55:194–199.CrossrefGoogle Scholar

  • Dickson, G., T. Arnold, and L. Chalip. 2005. “League Expansion and Interorganisational Power.” Sport Management Review 8:145–165.CrossrefGoogle Scholar

  • Duran, G., M. Guajardo, and D. Saure. 2017. “Scheduling the South American Qualifiers to the 2018 FIFA World Cup by Integer Programming.” European Journal of Operational Research 262:1109–1115.Web of ScienceCrossrefGoogle Scholar

  • Franks, A. M., A. D’Amour, D. Cervone, and L. Bornn. 2016. “Meta-Analytics: Tools for Understanding the Statistical Properties of Sports Metrics.” Journal of Quantitative Analysis in Sports 12:151–165.Web of ScienceGoogle Scholar

  • Fry, M. J., A. W. Lundberg, and J. W. Ohlmann. 2007. “A Player Selection Heuristic for a Sports League Draft.” Journal of Quantitative Analysis in Sports 3, doi:10.2202/1559-0410.1050.Google Scholar

  • Gibson, M. R., J. W. Ohlmann, and M. J. Fry. 2010. “An Agent-Based Stochastic Ruler Approach for Stochastic Knapsack Problem with Sequential Competition.” Computers and Operations Research 37:598–609.CrossrefGoogle Scholar

  • Gramacy, R. B., S. T. Jensen, and M. Taddy. 2013. “Estimating Player Contribution in Hockey with Regularized Logistic Regression.” Journal of Quantitative Analysis in Sports 9:97–111.CrossrefGoogle Scholar

  • James, B. and J. Henzler. 2002. Win Shares. Stats Inc.Google Scholar

  • Kaplan, E. H., K. Mongeon, and J. T. Ryan. 2014. “A Markov Model for Hockey: Manpower Differential and Win Probability Added.” INFOR: Information Systems and Operational Research 52:39–50.Google Scholar

  • Kubatko, J. 2011. “Calculating Point Shares.” https://www.hockey-reference.com/about/point_shares.html, [Online; accessed 12-December-2017].

  • Light, J., A. Chernin, and J. M. Heffernan. 2016. “NHL Expansion and Fan Allegiance: A Mathematical Modelling Study.” Mathematics-in-Industry Case Studies 7.Google Scholar

  • Macdonald, B. 2011. “A Regression-Based Adjusted Plus-Minus Statistic for NHL Players.” Journal of Quantitative Analysis in Sports 7, doi:10.2202/1559-0410.1284.Google Scholar

  • Macdonald, B. 2012. “Adjusted Plus-Minus for NHL Players Using Ridge Regression with Goals, Shots, Fenwick, and Corsi.” Journal of Quantitative Analysis in Sports 8, doi:10.1515/1559-0410.1447.Google Scholar

  • MacDonald, B. and W. Pulleyblank. 2014. “Realignment in the NHL, MLB, NFL, and NBA.” Journal of Quantitative Analysis in Sports 10:225–240.Google Scholar

  • Mason, D. S. and W. M. Foster. 2007. “Putting Moneyball on Ice?” International Journal of Sport Finance 2:206.Google Scholar

  • NHL. 2016a. “Hockey Operations Guidelines.” http://www.nhl.com/ice/page.htm?id=26377, [Online; accessed 30-November-2016].

  • NHL. 2016b. “Rules for 2017 NHL Expansion Draft.” https://www.nhl.com/news/nhl-expansion-draft-rules/c-281010592, [Online; accessed 28-November-2016].

  • Pantuso, G. 2017. “The Football Team Composition Problem: A Stochastic Programming Approach.” Journal of Quantitative Analysis in Sports 13:113–129.Web of ScienceCrossrefGoogle Scholar

  • Pettigrew, S. 2015. “Assessing the Offensive Productivity of NHL Players Using in-Game Win Probabilities.” in Proceedings of 2015 Sloan Sports Analytics Conference.Google Scholar

  • Quinn, K. G. and P. B. Bursik. 2007. “Growing and Moving the Game: Effects of MLB Expansion and Team Relocation 1950-2004.” Journal of Quantitative Analysis in Sports, 3, doi:10.2202/1559-0410.1054.Google Scholar

  • Rigdon, S. E. 2011. “The Penalty Shot/Optional Minor Choice in Ice Hockey.” Journal of Quantitative Analysis in Sports 7, doi:10.2202/1559-0410.1271.Google Scholar

  • Riley, S. N. 2017. “Investigating the Multivariate Nature of NHL Player Performance with Structural Equation Modeling.” PloS One 12:e0184346.CrossrefWeb of ScienceGoogle Scholar

  • Schmidt, M. B. 2001. “Competition in Major League Baseball: The Impact Expansion.” Applied Economics Letters 8:21–26.CrossrefGoogle Scholar

  • Schuckers, M. and J. Curro. 2015. “Total Hockey Rating (THoR): A Comprehensive Statistical Rating of National Hockey League Forwards and Defensemen Based Upon All on-Ice Events.” in Proceedings of 2015 Sloan Sports Analytics Conference.Google Scholar

  • Schulte, O., M. Khademi, S. Gholami, Z. Zhao, M. Javan, and P. Desaulniers. 2017. “A Markov Game Model for Valuing Actions, Locations, and Team Performance in Ice Hockey.” Data Mining and Knowledge Discovery 31:1735–1757.Web of ScienceGoogle Scholar

  • Seravalli, F. 2016a. “Vegas isn’t Getting a Lot for $500M.” http://www.tsn.ca/vegas-isn-t-getting-a-lot-for-500m-1.615117, [Online; accessed 30-November-2016].

  • Seravalli, F. 2016b. “Viva Las Vegas! TSN Hockey’s Early Expansion Team Lineup.” https://www.tsn.ca/viva-las-vegas-tsn-hockey-s-early-expansion-team-lineup-1.614039, [Online; accessed 01-December-2016].

  • Shea, S. M. and C. E. Baker. 2012. “Calculating Wins Over Replacement Player (WORP) for NHL Goaltenders.” Journal of Quantitative Analysis in Sports 8, doi:10.1515/1559-0410.1358.Google Scholar

  • Thomas, A. C. 2006. “The Impact of Puck Possession and Location on Ice Hockey Strategy.” Journal of Quantitative Analysis in Sports 2, doi:10.2202/1559-0410.1007.Google Scholar

  • Thomas, A. C., S. L. Ventura, S. T. Jensen, and S. Ma. 2013. “Competing Process Hazard Function Models for Player Ratings in Ice Hockey.” The Annals of Applied Statistics 7:1497–1524.CrossrefGoogle Scholar

  • Trick, M. A., H. Yildiz, and T. Yunes. 2011. “Scheduling Major League Baseball Umpires and the Traveling Umpire Problem.” Interfaces 42:232–244.Web of ScienceGoogle Scholar

  • Van Voorhis, T. 2002. “Highly Constrained College Basketball Scheduling.” Journal of the Operational Research Society 53:603–609.CrossrefGoogle Scholar

  • Vincent, C. B. and B. Eastman. 2009. “Defining the Style of Play in the NHL: An Application of Cluster Analysis.” Journal of Quantitative Analysis in Sports 5, doi:10.2202/1559-0410.1133.Google Scholar

  • Washburn, A. 1991. “Still more on Pulling the Goalie.” Interfaces 21:59–64.CrossrefGoogle Scholar

About the article

Published Online: 2019-02-15

Published in Print: 2019-02-25

Citation Information: Journal of Quantitative Analysis in Sports, Volume 15, Issue 1, Pages 27–40, ISSN (Online) 1559-0410, ISSN (Print) 2194-6388, DOI: https://doi.org/10.1515/jqas-2018-0024.

Export Citation

©2019 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in