Arc enemies: Comparing a two-point arc in hockey to basketball’s three-point arc

 (Jim Rosvold/University of Minnesota)
If an arc was put in place to add scoring to college hockey, if shots were deflected, how would that affect outcomes of games? (photo: Jim Rosvold/University of Minnesota).

Efforts to grow the game of hockey have produced some innovative ideas, including how to increase scoring.

One idea is a “two-point” arc, similar to the three-point arc in basketball.

Details are fuzzy at this early stage, but the arc at last year’s Aurora Games (an international, multi-sport women’s tournament/festival) bent from the outer hashes to behind the faceoff circles, with an apex well inside the blue line.

A recent quantitative study has even analyzed how such an arc might affect scoring in the NHL, and where it might be placed on the ice.

But before the novelty gains any more traction, fans of the game might want to seriously consider its pitfalls.

Some concerns would be surmountable — the officiating headache, for example — while others would be more structural.

This article considers the potential effects of a two-point arc in hockey by contrasting it with its hugely successful predecessor, basketball’s three-point arc. As we will see, a scoring arc in hockey would have different effects than the arc in basketball, for three reasons.

The first reason is historical and involves the roles of different position groups. Since basketball’s modern era, the tallest players have clustered near the basket, grabbing most of the rebounds and the scoring opportunities.

Before the invention of the three-point arc, smaller guards found themselves stuck on the periphery of the action — literally — on both offense and defense. The three-point arc solved this imbalance by incentivizing shooting farther from the basket, where smaller, quicker guards can be more effective. The allure of three points from the perimeter helped reestablish offensive and defensive roles for smaller guards in the game.

Hockey does not have this problem.

In hockey, of course, defensemen are nearest the goal in their own zone, while forwards are nearest the goal in the offensive zone. This means that no position group is marginalized the way that guards were in basketball—each group plays in the high-traffic area where the most scoring occurs, albeit on opposite ends of the ice.

The three-point arc in basketball was invented in part to correct a problem of balance of gameplay between position groups, but this is a non-problem in hockey.

A second consequence of the three-point arc in basketball is on-court spacing. By luring shooters and their defenders away from the basket, the three-point arc unclogged the middle of the offense. We would probably not see the same effect in hockey, at least to the same degree.

The reason? Geometry.

Basketball is a more three-dimensional game than hockey, owing largely to the height of the basket and the trajectory of the shots. Because shots in basketball are launched high into the air, any shot-blocking must occur very near the shooter. (Of course, blocking a shot during its descent to the basket is “goaltending,” which is discouraged by simply counting the basket.)

In basketball, then, failure to defend shooters tightly on the perimeter can amount to a failure to guard them at all. Also, drawing defenders away from the basket opens up interior-passing lanes near the basket, which further boosts scoring.

An arc in hockey would probably have a less profound effect on defensive spacing. Of course, shooters at the point in hockey must be defended, and being closer to a shooter does cut down shooting angles.

That said, the fact remains that a hockey shot can be blocked at any point on its trajectory to the goal. (In hockey, goaltending is … encouraged.) Defensive players in hockey would not be forced to guard perimeter shooters as tightly as we see in basketball, because they could still block shots while staying closer to the goal.

Therefore, a two-point arc in hockey would not necessarily translate to increased defensive spacing, nor the resultant interior-passing lanes, at least to the extent that we see in basketball.

The final contrast between scoring arcs in the two sports involves simple arithmetic.

Actually, there are two considerations, one major and one minor.

The minor point is that hockey is a low-scoring sport. To vary the number of points available for each scoring opportunity in a low-scoring sport would inject an even stronger element of unpredictability, or maybe chance, than already exists.

In a high-scoring sport like basketball, whether a player’s foot was “on the line” for a three-point shot might mean the difference of one point among fifty or one hundred, depending on the level of play.

In hockey, whether the puck was “on the line” for a single goal might swing the total scoring in the game by a significant percentage, or even double it.

The more major point involves strategy, particularly involving scoring at the end of games. A quick glance reveals that a two-point arc in hockey could have a greater impact on scoring than the three-point arc in basketball: shooting from behind the arc would yield double the usual score in hockey (two versus one), and only 50 percent more in basketball (three versus two).

The difference is actually greater than that. The reason involves basketball’s free throws.

Before the invention of the three-point arc in basketball, teams could already score three points on a single possession: by making a two-point basket, simultaneously getting fouled, and making a one-point free throw. In this sense, adding the three-point shot merely increased the number of ways a team could get three points on a single possession, but didn’t increase the number of points they could get on a possession outright.

(A technical point: of course, nowadays a player can earn a four-point play by getting fouled on a successful three-point shot. This isn’t particularly common — fouling is less common/inevitable that far from the basket.)

At the end of a basketball game, then, any deficit of three points or fewer can be erased in a single possession—hence the critical four-point lead, which creates a “two-possession game.” This was true before the invention of the three-point arc, and remains true today.

Of course, the arc makes it far easier to quickly earn three points near the end of a game, but any deficit of four, five, or six points remains a “two-possession game” in basketball.

Again, hockey is different.

Adding a two-point arc would fully redefine a “two-possession game” as it stands in hockey today. Such an arc wouldn’t simply provide another avenue to score the same number of points on a single possession, as in basketball.

Instead, it would double the number of points possible, as well as enable a single shot to wipe out today’s “two-possession” deficit entirely. The ability to tie any two-possession game with one shot would be comparable to adding a six-point arc in basketball.

Considering the comment above regarding low-scoring games, the ability to double the available points scored on a single possession would not merely change the game, as we’ve seen in basketball. Instead, it might result in… chaos, where virtually any scoring deficit could be erased in two mere possessions, or in mere seconds.

Further, teams could quickly jump out to 2-0 or 4-0 leads on only one or two shots, thereby transforming the rest of the game into a perimeter-shooting affair for the team playing catch-up. The effects of a two-point arc on scoring and game strategy would be seismic.

Which might be part of its appeal, at least to some. However, adding a two-point arc in hockey — a move that is undoubtedly inspired, at least in part, by the overwhelming popularity of the three-point arc in basketball — would more fully disrupt the sport, for reasons stemming from its game play and scoring structure.

Further, adding an arc would not solve problems within the game, like balance among position groups, as the three-point shot did in basketball decades ago.

There are undoubtedly several ways to increase scoring in the game of hockey, which may be a noble goal in itself. However, following basketball’s lead would mean that no lead is safe.

The game might arc toward madness.

P. A. Jensen (@PrideOnIceCream) is a freelance data analyst and a former basketball official. He is also editor of