Marginal Goals

The underlying notion of a player contribution system is that a team’s results can be assigned individually to its players. Acceptance of this simple idea is necessary to accept the outcome of such a system. With Hockey Reference’s Point Shares methodology, the sum of the individual point shares for all of the players on a team will approximate that team’s point total. Each player is assigned a piece of the pie of the team’s overall results.

While Pittsburgh's Sidney Crosby is the face of the 2016 and 2017 Stanley Cup seasons, point shares try to appropriately assign credit to each player for their contributions in the regular season. "Captain Crosby" by brunkfordbraun is licensed under CC BY-SA 2.0

Consider the 2016-17 Pittsburgh Penguins. A 111-point team in the standings, this was the second of their back-to-back Cup-winning seasons. Sidney Crosby‘s team-leading 12.3 point shares suggest his on-ice contributions generated 12.3 points for Pittsburgh. This is the value assigned to Crosby’s performance as the runner-up for league MVP, third among NHL forwards. Matt Murray, bursting onto the scene with a .923 save percentage, is assigned 10.3 point shares, second on the team. Ian Cole, a dependable defencemen playing nearly 20 minutes a night, is credited 5.6 point shares. Matt Cullen, a bottom-six veteran forward, is assigned 2.9 point shares. Each skater and goaltender earn point shares based on their statistical contributions. The total point shares allocated to their roster that year is 111.3.

Point Shares #1:

One point share credited to an individual represents a contribution to the team equal to one point in the standings. 

But how did we arrive at these specific numbers, ranging from elite performances to bottom of the lineup impact? How will it form the basis for our evaluation of thousands of NHL players spanning a century-plus? Leveraging Hockey Reference’s approach, let’s bring this methodology to life and learn how point shares work.

Team Construction

First, we need to consider how a team is constructed in order to assign credit for its performance. Every hockey team places six players on the ice at even strength, including its goaltender. A team’s five skaters (i.e., three forwards, two defencemen) are tasked with playing both offence and defence, the fluidity of hockey mandating this requirement. A team’s goaltender makes no contribution to offence, at least not in a remotely meaningful way.

We’ll call our theoretical six-player lineup the Coniston Flames (after my first novice hockey team in 1993-94). Consider ordering the team a pizza pie after a game, with 12 slices available. The Flames’ five skaters rightfully snag two pieces each – one for their work on offence and one for their work on defence. The goaltender (in this case 8-year old me) is on the ice the same amount of time as the skaters, but earns both two slices for defence, the goalie’s only concern being goal prevention. So, we’ve split our pie with five of the slices going to offence and seven slices going to defence, replicating the contributions of the players in the game. This simple distribution, based on team construction, is factored into how point shares are allocated at the individual level within the point shares system.

Point Shares #2:

A hockey’s team composition results in contributions that consist of 5/12 offence, and 7/12 defence; 2/12 of the defence is attributed to goaltending.

Marginal Goals

Next, we need to understand how a team earns its points in the standings. By winning games and losing in overtime or a shootout, right? Well, yes, but each team’s performance is more accurately a function of two elements – offence and defence. A team can expect to perform in line with how it scores goals and how it prevents goals relative to the league; a clear correlation has long existed between a team’s point total and its goals for and against compared to the NHL average. A cursory look at any standings table shows the link between team goal differential (i.e. goals for less goals allowed) and a team’s place in the standings.

As a result of this relationship, point shares are driven by the notion of marginal goals for and marginal goals against. A team with zero marginal goals for and against would be made up of marginal players. A marginal player is a theoretical “replacement player.” Consider said player the first guy called up from the AHL that fills a roster spot. This player undoubtedly makes some contribution to the team, but the contribution is considered to be nil. A replacement player would earn zero point shares – not adding any value to a team’s results by virtue of being replaceable with a phone call or text. A team built exclusively of these players could perhaps win some NHL games, but adding value (i.e. point shares) starts with individual contributions beyond replacement.

40-year old Matt Cullen, the team "Dad", is credited 2.9 point shares for his 31 point season. "File:Matt Cullen 2017-06-08.jpg" by Michael Miller is licensed under CC BY-NC-ND 2.0

Let’s revisit the 2016-17 Penguins to apply our understanding to a real-life example, showing the strength of the relationship between marginal goals and standings points.


NHL Average8241311092.559223223
GP = Games Played; W = Wins; L = Losses; OTL = Overtime/Shootout Losses; PTS% = Points ÷ (2 x GP); GF = Goals For; GA = Goals Against

Pittsburgh was an excellent regular season team, second place in the NHL standings. Their success is largely driven by their league-leading offence (55 goals better than league average) rather than middle-of-the-pack defence (six goals worse than league average). Using marginal goals, we can convert the Pens’ performance by goals for and against to expected standings points. Sparing you the formulas, the team’s marginal goals should have resulted in 111.4 points, an exact match to the 111 points they earned in the standings.

This is not always the case. Why?

Teams typically do not get the exact number of points their marginal goals for and against warrant for many reasons. One of the main culprits is shootout and overtime results, easily proven to have little statistical repeatability year-over-year. Coupled with some element of randomness in frequent one-goal games, luck (both good and bad) has an inevitable impact on the link between goals for and against and team success. Per Kubatko on Hockey Reference, the relationship is normally within four or five points on average, across a full 82-game season.

Since the methodology relies on marginal goals to allocate point shares to players, it’s critical that we are confident that the concept of marginal goals is sound at the team level. Being within four or five points per team is accurate, a reliable correlation for our purposes. It allows us to go forward using marginal goals to assign credit to individual players without reservation.

Point Shares #3:

The relationship between marginal goals and standings points at the team level supports using marginal goals to assign point shares to individual players.

Before we take point shares any further, it is important to understand that they are estimates of individual value. In any player contribution system, the outputs are not designed to scream that Player A is conclusively better, or more talented, than Player B by virtue of a small difference in point shares. When we start creating a player evaluation system and setting Hall of Fame standards later in the project, we have to keep in mind that minor point share variances cannot be considered meaningful within a season or over a career.

Of course, point shares are hard numbers that inevitably produce a hierarchy. But at the end of an NHL season, the scoring leaders are not the definitive order of the league’s best players. Nor are point shares intended to be. As we’ll further discover, there are assumptions in the approach, different iterations of point shares based on available data, and constraints in allocating credit. We’ll even walk through some obvious flaws with the approach later for transparency.

The methodology is intended to approximate overall value across eras, not to unequivocally state what drives value. As we’ll see, the approach provides a reasonable, systematic way to assign credit at a team level. For this project, that’s all we want.

Data from