How should we calculate expected points in the NHL?

Huffington Post

Huffington Post

In the next week, I will be posting four articles previewing each division for the 2013-2014 NHL season. Like any hockey fan, I am very excited to see how each division builds a style, a characteristic and/or a brand within the next handful of seasons.

So to give you guys a sneak peak of how the format should be, I will be writing how each team will do on offense, defense and special teams as well as how their front offices performed during the offseason. While writing about these topics, I will be showing you guys projected line combinations and projected stats for each player on their respective teams, every team usage chart from Rob Vollman’s hockey abstract website at, and many team statistics from last season.

I know I threw a lot of Vollman-ology at your face during the trade value columns this month without any advanced warning, but for those that do not know what the charts mean, let me take this opportunity to tell you what these show.

Each chart’s x-axis and y-axis contains a player’s offensive zone start% and Corsi Relative to Quality of Competition (or Corsi Rel QoC for short), respectively. Offensive zone start% is simply what percentage does a player’s coach have him start his shift on the ice when the team is on the offensive side of the rink. If a player’s offensive zone start% is over 50%, it usually means that he is being used to join the offensive rush of his team and has an objective to help the team score goals. The complete opposite can be said if a player’s offensive zone start% is below 50%. For Corsi Rel QoC, it is the average Corsi (a player’s difference in shots for (for Corsi, it is shots on goal, off goal and blocked shots) to a player’s shots against) a player’s opponents are that is relative to their oppenents’ teammates.  A positive Corsi Rel QoC indicates that a hockey player is always facing great competition while the opposite can be said otherwise.

After understanding the x and y-axis of each graph, we need to understand each player’s bubble. The size of each bubble represents a player’s playing time compared to the rest of his teammates. The bigger the bubble, the more minutes that player has played. The next thing you’ll see is a player may sometimes have a blue bubble or an orange bubble. This indicates whether a player has a positive Relative Corsi (shown in blue) or negative Relative Corsi (shown in orange). Relative Corsi (or Corsi Rel for short) is a player’s Corsi relative to his teammates. The purpose of the of the statistic is to make sure a player’s Corsi is a particular amount thanks to himself and not thanks to the help of the teammates around him. The farther that player’s Relative Corsi is from 0, the darker and more prominent the color of the bubble is. Does everyone understand? Awesome.

Now that we have that out of the way, let’s introduce a brand new statistic!!!

For some reason, the NHL does not have “expected points (or wins)” like all the other popular North American professional sports do. For those not familiar with expected wins, it is also known as Pythagorean winning percentage as the formula looks almost like trying to use the Pythagorean theorem when trying to figure out the length of a triangle. The formula goes as follows:

Pretty simple math, right? Now, if you were to look at the Wikipedia article, there is mention that Clay Davenport and David Smyth tried to find a better exponent for figuring out expected wins in baseball. We will not delve into that for this post as I do not have a masters or doctorate degree in the material these guys bring up (yet?). However, football has not deviated from this formula and has been used as a reliable guide to figure out future success. For example, from 1988 to 2004, 11 of the 16 Super Bowl Champions were won by the team that led the league in Pythagorean wins, not regular season wins.

For basketball however, the exponent had to change in order to emphasize the point differential relative to the number of points scored throughout the basketball season. As a result, Daryl Morey, currently the General Manager of the Houston Rockets, decided to use 13.91 as the exponent to project expected wins.

For me, I started with the simple exponent of 2 to figure out the expected wins amongst all NHL teams. I did add a twist to the formula: only non-shootout goals count. We will get to that topic in a second, but let’s use the Washington Capitals as an example. In 2013, the Capitals scored 146 non-shootout goals and gave up 130 non-shootout goals. With this data, we can predict that the Capitals should have had 51.6 standings points.

Wins = (146)2/(1462+1302)*96 = 51.6 points

That is 5.4 points, or 2.7 wins less than what they ended up receiving during the regular season. So this makes them a lucky hockey team, right? Actually, not really. When using 2 as the exponent for Pythagorean points, only one team ended having more Pythagorean points than actual standings points. Also, compared to the rest of the professional sports leagues in North America, the NHL is not suited to use solely Pythagorean wins to calculate expected wins.

2012-2013 season^exponent used for pythagorean wins total difference between pythagorean wins and actual wins games played difference/game
MLB^2 -6 162 -0.037
NHL^2 78.35 48 1.632
NFL^2 1.8 16 0.113
NBA^2 -0.9 82 -0.011
NBA^13.9 0.9 82 0.011
NBA^16.5 1.8 82 0.022

The comparisons were so stark, that even if the NBA were to use 2 as their exponent, their margin of error would still be more solid than the NHL’s. After experimenting with more exponents, I realized that this was going to get complicated to figure out a simple formula for expected wins. Some will argue I should increase the exponent to get more variety among NHL teams that were “lucky” or “unlucky”.

exponent 0-4 pts away from actual pt total less standings pts than pythagorean pts bottom ten teams amongst the ten luckiest teams
2 7 1 1
2.5 7 2 3
3 11 4 6
3.5 9 7 6
4 11 11 8

What happened was more variety of luck occurred when increasing the exponential value, but more teams that were amongst the worst in the NHL were considered “lucky” to have the standings points they received. Honestly, that can’t happen.

So what I came up with were two parts to create the expected standings points for an NHL team. First, we compare a team’s shutout wins to the league average. Personally, shootouts are not a hockey-related contest and any team that wins them should never have received a standings point in the first place. In the pre-shootout days, teams that finish overtime with a tie score only receives one standings point and calls it a day. Even if you lost in overtime, you would still receive a standings point as it is a skill for containing the eventual winning team to, at least, have them play into overtime to win the game. Some will argue that special teams percentage (percentage of time used on the power play and penalty kill per hockey game) could be used another category removed. However, I would not for now as I consider it a skill for a team to draw penalties and a weakness for a team to give up penalties.

First, we need the average number of shootout wins for an NHL team that season. For 2013, the average was 3.23 shootout wins per hockey team. Next, we subtract the team’s shootout wins to the league average and keep that total for future reference. For the 2012-2013 Capitals, they only won three shootouts. So three minus 3.23 will equal a negative 0.77 shootout reduced score.

Shootout Reduced Score = 3 shootout wins – 3.23 average shootout wins per team  = -0.77

Next, we will still calculate the Pythagorean point total, but this time we include shootout “goals for” and shootout “goals against”. This is only because we are taking shootouts into account for a separate category already. With this criteria in mind, the 2013 Capitals picked up 54.5 expected points, which is 2.5 points or 1.3 wins less than they actually received.

Wins = (149)2/(1492+1302)*96 = 54.5 points

However, the league-wide difference per team in Pythagorean standings points and actual standings points last NHL season was 5.223. So with that in mind, the luck reduced score is calculated is the team’s actual difference between actual and Pythagorean standings points minus league-wide difference per team. The 2013 Capitals had a luck reduced score of a negative 2.723 with this criteria.

Luck Reduced Score = (57 actual points – 54.5 Pythagorean points) – 5.223 league-wide difference per team = -2.723

With the Luck Reduced Score and the Shootout reduced score in hand, the last step to figure out a team’s expected amount of standings points is to remove the luck reduced score and shootout reduced score from the actual standings point total of a hockey team. This metric gives the 2013 Washington Capitals with 60.0 expected standings points.

Expected Standings Points = 57 actual points – (-0.23 shootout reduced score) – (-2.723 luck reduced score) = 60.0 points

That actually makes them a team an “unlucky” hockey team by 3.0 standings points. In general, the Caps were tied with the Carolina Hurricanes as the 7th unluckiest team in the NHL last year. The final results throughout all 30 teams brought me the following data from the last NHL season.

Most Expected Points Least Expected Points
Chicago 69.5 Florida 34.3
Pittsburgh 68.7 Colorado 41.8
Montreal 61.5 Buffalo 43.1
Boston 61.2 Nashville 43.9
Toronto 60.6 Carolina 45.0
Luckiest Teams Unluckiest Teams
Anaheim 16.4 Tampa Bay -14.9
Chicago 7.5 Edmonton -6.2
San Jose 5.3 Calgary -4.0
Vancouver 5.2 New York Rangers -3.6
Buffalo 4.9 Philadelphia -3.6
Toronto -3.6


  1. NFL is actually ^2.37

  2. and why are you multiplying by 96?

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