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How does scoring affect NHL standings?
*February 2, 2016*

*Posted by tomflesher in Economics, Hockey, Sports.*

Tags: hockey, modeling points, NHL, parameter estimation

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Tags: hockey, modeling points, NHL, parameter estimation

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Patrick Kane (right) leads the league in goals and assists (and therefore total points). His Blackhawks are second in the league but lead the Western Conference, and are all but a lock to make the playoffs this season even with 29 games to go. Kane’s 30 goals (and 27.8 goals created) are a touch ahead of the second-place Jamie Benn and Alex Ovechkin, who each have 28 goals. Just how much, though, are those extra goals worth, and would it be better to focus on defense instead? In this entry, I’ll use some econometric modeling techniques to float an answer to that question.

When a team wins a game, they receive 2 points in the standings; a team that loses in regulation receives no points, but a team that loses in overtime or a shootout gets a consolation point for the tie after regulation. Since points, rather than direct win-loss records, are used to determine who makes the playoffs, it’s possible for a playoff team to have fewer points than a team that doesn’t make the playoffs. Though that didn’t happen in 2014-15, the Nashville Predators did finish ahead of the eventual Stanley Cup winning Chicago Blackhawks by having more points (104 to 102) despite having one win fewer (47 to 48). Nashville’s 10 overtime losses to Chicago’s 6 made the difference.

In a previous post, I calculated a pythagorean exponent useful for estimating a hockey team’s win-loss percentage and found a value of 2.11; a similar method to calculate the percentage of available points yields an exponent of 2.09. (That is, win-loss percentage and points percentage are really fairly close, in expectation terms.) Those models make the assumption that a goal against is worth the same as a goal for. Let’s try a couple of things to estimate the usefulness: first, let’s keep the same assumption, and fit a model of *Points = a + b*Goals For – b*Goals Against*. Using 2014-2015, that gives us an optimal model of *Points = 92.2 + .357*Goals For – .357*Goals Against*, with a sum of squared errors of 557.355.

Relaxing that assumption – allowing a goal for to be worth a different amount than a goal against – is theoretically justified by the fact that a losing team not only scores no points but loses the opportunity to score an overtime point, too. If we allow that flexibility, 2014-2015 gives us an estimated *Points = 88.2 + .366*Goals For – .347*Goals Against*, with a sum of squared errors of 555.594.

Since 88.2 points are expected in a season of 0-0 games, the expected points at the beginning of a game are approximately 88.2/82 = 1.076. Someone scores two, but the point given to the eventual losing team for a regulation tie pulls that average up a smidge.

The upshot of all of this? Defense is important, but since the expected points for a goal are higher than the expected penalty for allowing the other team to score, a team at the margin should consider signing a roving defenseman rather than a strictly defensive player – and it wouldn’t be crazy for a losing team to play four attackers and one defender for the last few minutes of the game, even before pulling the goalie.