Sheldon Jacobson: NHL general managers should study computer science

Ron Hextall, the Pittsburgh Penguins’ general manager, holds the 21st overall pick in the upcoming National Hockey League entry draft to be held July 7 . This pick gives him the opportunity to add outstanding hockey prospects. Pittsburgh has not been particularly effective with its selections, with 2015 the last time the team drafted a prospect who became an NHL regular.

Identifying great hockey players is not as daunting as finding ways to pay for and keep them.

Salary caps are the constraining factor when building a championship team. If a small number of high-quality players are given lucrative contracts, then the rest of the team might need to be filled with role players or quality players near the ends of their careers who might not demand high salaries.

There are ways to circumvent salary caps, at least temporarily. For example, teams can place injured players on long-term injured reserve. These player salaries are then not counted against a team’s salary cap, until they return to play or if they only return during the playoffs. The Tampa Bay Lightning used this loophole to their advantage in 2021, fielding a team during the 2021 playoffs that was $18 million above the salary cap limit. The team also won the Stanley Cup, much to the chagrin of the teams they defeated.

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

The knapsack problem is a classic problem in computer science. Given a set of items, each with a given weight and value, which items should fill a knapsack such that the total weight of these items does not exceed the knapsack’s weight limit and the total value of these items is as large as possible? One way to evaluate each item’s benefit is by taking the ratio of its value to its weight. The higher the ratio, the more benefit an item offers.

Clearly, the weights are the salaries paid to the players, and the knapsack threshold is the salary cap. There also is a limit on how many players each team can have under contract, which places a second constraint on the knapsack.

What is more nuanced and subtle is the value that each player brings to the team.

A player’s value is not his individual statistics. It is the team’s performance with him on the roster. This is where advanced analytics play a role.

A good NHL goalie can become great with superb defensemen and energetic backchecking forwards playing in front of him. The value of each player is then dependent on all the other players on the team, or at least the other players that share ice time with him.

Entry level contracts offer great value for general managers, which is why the entry draft is so important. That is when the ratio of value to salary for high draft picks are most attractive. However, once the entry level contract expires, teams must pay up for their best players, or lose them to free agency.

Given that assembling a team is a dynamic process, with players changing every season, and the resulting value that they bring to the team increasing or decreasing, long-term contracts that sound reasonable in year one might look awful in year six, as a player ages with injuries, or a synergistic linemate or defense partner gets traded or moves to another team through free agency.

After everyone is drafted, and all players are signed, a knapsack of players is assembled, whose value will provide a clue if the team will raise the Stanley Cup at some time in the future, something that the Penguins have not done since 2017. Computer science can help Hextall and every general manager fill their knapsacks.

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