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Sheldon Jacobson: NHL general managers should study computer science

Ron Hextall, the general manager of the Pittsburgh Penguins, holds the 21st overall pick in the upcoming National Hockey League entry draft to be held on July 7. This selection gives him the opportunity to add to hockey’s unique prospects. Pittsburgh wasn’t particularly effective in its selections, with 2015 being the last time the team drafted a prospect to become an NHL regular.

Getting to know great hockey players isn’t as daunting as finding ways to pay for and save for it.

Salary caps are the limiting factor in building a championship team. If a small number of high-quality players are given high-paying contracts, then the rest of the team may have to be filled with role-playing players or high-quality players nearing the end of their careers. without asking for a high salary.

There are ways to avoid salary caps, at least temporarily. For example, teams may put injured players on long -injured reserve. These players ’salaries do not count against a team’s salary cap, until they return to play or if they only return during the playoffs.

What the salary cap does is create a knapsack problem for every general manager to solve.

The knapsack problem is a classic computer science problem. Given a set of items, each with a given weight and amount, what items need to fill a knapsack so that the total weight of these items does not exceed limit the weight of the knapsack and the total cost of these items as large as possible? One way to evaluate the usefulness of each item is to take the ratio of its value to its weight. The higher the ratio, the more benefits an object offers.

Clearly, the weights are the salary paid by the players, and the knapsack threshold is the salary cap. There is also a limit to how many players per team have a contract, which puts a second knapsack restriction.

More nuanced and subtle is the value each player brings to the team.

The value of a player is not his individual statistic. This is the team’s performance with him on the roster. This is where advanced analytics plays a role.

A good NHL goalie can be good with very good defensemen and strong backchecking forward playing in front of him. The value of each player will depend on all the other players on the team.

Entry level contracts offer a lot of value for general managers, so the entry draft is very important. That’s when the salary -to -salary ratio for the high draft pick is more attractive. However, once the entry -level contract expires, teams will have to pay for their best players, or they will be lost to free agency.

Given that assembling a team is a dynamic process, with players changing each season, and the resulting amount they bring to the team increasing or decreasing, long contracts are reasonable in a year can look terrible in six years, as a player. ages with injuries, or a synergistic linemate or defensive partner can be traded or transferred to another team.

After everything is drafted, and all the players are signed, a knapsack of players is collected, the amount of which will provide an indication of whether the team will advance to the Stanley Cup in the future. Computer science helps Hextall and every general manager fill their knapsacks.

Sheldon Jacobson is a professor of computer science at the University of Illinois at Urbana-Champaign. His specialty is data science, with applications to public policy and sports analytics.

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