TSpace Research Repository tspace.library.utoronto.ca A mathematical optimization framework for expansion draft decision making and analysis K. E. C. Booth, T. C. Y. Chan, Y. Shalaby Version Published Version Citation K. E. C. Booth, T. C. Y. Chan, Y. Shalaby, “A mathematical (published version) optimization framework for expansion draft decision making and analysis,” Journal of Quantitative Analysis in Sports, Vol. 15, pp. 27-40, 2019. How to cite TSpace items Always cite the published version, so the author(s) will receive recognition through services that track citation counts, e.g. Scopus. If you need to cite the page number of the author manuscript from TSpace because you cannot access the published version, then cite the TSpace version in addition to the published version using the permanent URI (handle) found on the record page. This article was made openly accessible by U of T Faculty. Please tell us how this access benefits you. Your story matters. J. Quant. Anal. Sports 2019; 15(1): 27–40 Kyle E. C. Booth, Timothy C. Y. Chan* and Yusuf Shalaby A mathematical optimization framework for expansion draft decision making and analysis https://doi.org/10.1515/jqas-2018-0024 salary cap. Existing teams can mitigate their loss by care- fully choosing which players are exposed for selection and Abstract: In this paper, we present and analyze a mathe- by applying smart roster management leading up to the matical programming approach to expansion draft opti- expansion draft. mization in the context of the 2017 NHL expansion draft Expansion drafts in professional sports occur when involving the Vegas Golden Knights, noting that this a league decides to add new teams to its current pool of approach can be generalized to future NHL expansions teams. These drafts have been used to grow leagues across and to those in other sports leagues. In particular, we a variety of sports, including hockey, American football, present a novel mathematical optimization approach, con- baseball, and basketball. Although the detailed rules of sisting of two models, to optimize expansion draft protec- an expansion draft may differ across sports, its structure tion and selection decisions made by the various teams. remains largely consistent, involving: a protection process We use this approach to investigate a number of expan- where existing teams identify players that they wish to sion draft scenarios, including the impact of “collabora- shield from being selected by the expansion team, and a tion” between existing teams, the trade-off between team selection process where the expansion team selects players performance and salary cap flexibility, as well as opportu- from some or all of the existing teams to fill its roster. Con- nities for Vegas to take advantage of side agreements in a straints may be imposed in each of these processes, such “leverage” experiment. Finally, we compare the output of as limits on the number of players that can be protected by our approach to what actually happened in the expansion a team, and positional requirements that must be fulfilled draft, noting both similarities and discrepancies between by the expansion team’s selections. Together, the rules our solutions and the actual outcomes. Overall, we believe governing who can be protected and who can be selected our framework serves as a promising foundation for future form part of a decision making problem that is amenable to expansion draft research and decision-making in hockey rigorous, mathematical optimization. Thus, league expan- and in other sports. sion represents a perfect opportunity to apply optimiza- Keywords: expansion draft; mathematical program- tion in sports team management. ming; national hockey league; operations research; In this paper, we present and analyze a mathematical optimization. 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 1 Introduction be generalized to future NHL expansions and to those in other sports leagues. We develop two optimization mod- In 2017, the Vegas Golden Knights joined the National els: the first formulation models the existing teams’ pro- Hockey League (NHL) as the first expansion team since tection problem and the second formulation models the the Columbus Blue Jackets and the Minnesota Wild expansion team’s selection problem. The first model can joined in 2000. As newly introduced teams to the league, be used by each existing team to optimize the players it expansion teams have the unique opportunity to draft protects (or equivalently, exposes) in the draft. The sec- active, NHL-ready players directly from their opponents – ond model can be used by the expansion team to iden- essentially roster optimization from a clean slate with a tify a salary cap-compliant team of players given a list of exposed players by the existing teams. Together, these models form a novel framework to aid the expansion team *Corresponding author: Timothy C. Y. Chan, Mechanical and in evaluating and optimizing against different exposure Industrial Engineering, University of Toronto, Toronto, Canada, scenarios it may encounter during the expansion draft. e-mail: [email protected]. In the case of the 2017 NHL expansion draft, the https://orcid.org/0000-0001-6929-8042 expansion team, Vegas, had a short turnaround time Kyle E. C. Booth and Yusuf Shalaby: Mechanical and Industrial Engineering, University of Toronto, – 3 days from when the existing teams finalized their Toronto, Canada, e-mail: [email protected]; protection lists to when Vegas had to make their selections [email protected] on June 21, 2017 – amplifying the value of our optimization 28 | K.E.C. Booth et al.: Expansion draft decision making and analysis framework, which can evaluate a large number of possible decisions faced by the existing teams and the expansion selections very quickly. Indeed, Craig Button, a former team under the 2017 NHL expansion draft rules. The NHL general manager and a current broadcast analyst, framework is general and with simple modifications reiterated “Who you decide to select from one team has can be extended to future NHL expansion drafts, as well serial impact on what you do with every other one. There as those found in other sports with different expansion are lots of combinations and permutations” (Seravalli draft rules. Our selection model, with minor modi- (2016b)). Existing teams can also use this framework to fications, is also applicable to fantasy sports lineup guide their protection decisions and other personnel deci- optimization. sions leading up to the expansion draft such as trad- 2. We use our optimization framework to quantify Vegas’ ing players with other teams or signing free agents. Our team value under a variety of scenarios: model provides structure to the vast combinatorial deci- (a) We demonstrate that Vegas’ potential team value sions faced by the expansion team, which an existing team degrades by over 13% over the course of the 2016– can use to optimize their exposure list accordingly. 2017 season leading up to the expansion draft as a After presenting our optimization framework, we con- result of personnel decisions made by the existing duct several computational experiments aimed at shed- teams. ding light on the value of mathematical optimization in (b) By considering future financial flexibility, we show the context of the 2017 NHL expansion draft. First, our that Vegas can select a team that degrades in team baseline experiment tracks the quality of the team Vegas value by only 4.9% but with a 57.1% reduction in could have drafted, given optimized protection lists of the 2018–2019 salary commitments. other 30 teams, at four time points over the course of the (c) Our collaboration experiment shows that coordi- 2016–2017 season. Second, we illustrate how our model nated personnel decisions made by other teams can can be used to generate rosters for Vegas that trade off have significant impact on Vegas’ team quality. Our between performance and salary cap flexibility. Through- structured approach to investigating this concept out, we use the Point Shares metric as a measure of player shows that had teams focused on minimizing the value/performance, although our framework is general value of their exposed assets to Vegas, they had enough to accommodate any statistic. Third, we show how the potential to degrade Vegas’ team value by up to our framework can tractably investigate an important and 34%. realistic scenario that can hurt Vegas leading up to the (d) Our leverage experiment shows that the second best expansion draft. This “collaboration” experiment refers pick among the exposed players of any given team to teams making personnel decisions such as trades that may still lead to a high quality team for Vegas, after would minimize their exposure and the value of assets re-optimizing the other 29 selections. For the top lost in the expansion draft. Indeed, Vegas’ general man- 10 teams that had the most to gain from Vegas not ager George McPhee said he expected a “redistribution of selecting the optimal player suggested by the frame- players” to occur ahead of the draft (Seravalli (2016a)). work, Vegas’ team value only degraded by 1.9% For example, a team with valuable exposable assets could on average, suggesting that Vegas had leverage to make a trade with another team with more protection extract additional assets from those teams in return room, in return for future draft picks or prospects who for not selecting the suggested player, while giving would be exempt from selection. Fourth, we conduct a up little in terms of overall team value. series of experiments to show how optimization can sup- port Vegas in making side deals with teams to avoid pick- ing a particular player, but still create a team with high value.