This is the second of a two part series looking at separating a skater from his teammates. In this second part I apply the methods described in the first part to separate a skater’s contribution from his teammates. For more details on the method I used check out part 1.

Introduction

In my first blog post, I quantified the expected goal differential for each skater while they were on the ice. However, this value will reflect not only the individual’s contribution to team goal differential but will be heavily influenced by the other player’s on the ice. While it is common to look at a skater’s performance in comparison to the rest of his team (e.g. CF% relative), this comparison can be misleading. This is because skaters do not play with all other teammates equally, thus simply comparing a skater with the rest of his team, or comparing his team’s performance while he is on the ice with that while he is off the ice will not accurately assess an individual skater’s contribution to this team performance.

In this post I will separate a skater’s contribution to his team from that of his teammates. I will do that by combining playing time, line deployment, and stats while a skater is on the ice for all the skaters on a team, to simultaneously solve for each skater’s individual contribution. This blog post is broken up into two parts. The first part used a simple example using simulated data to help explain the method, and to clearly see where the method led us astray. This second part presents the results of applying this method to all NHL teams.

Creating Linemate Tables

As described in part 1, to separate a skater from his teammates requires solving for all skaters’ contributions simultaneously. To do that, I formed a table, or matrix, of linemate usage and then multiplied the desired statistic by the inverse of this matrix. Linemate details were obtained from behindthenet.ca. However, the details provided were not sufficient to complete the table thus some adjustments needed to be made. I will outline these adjustments using the Chicago Blackhawks as an example.

Figure 1 shows the linemate table for the Chicago Blackhawks for 5-on-5 play derived from the data provided by behindthenet.ca. This site only provides playing time for each skater’s top 10 linemates, thus there are many holes in the linemate table as seen by the white squares.

If this table was in minutes instead of percentage of playing time, then the table must be symmetric, so we can fill in any unknown table entries if their transposed element is known. For example, Andrew Shaw is not one of Niklas Hjalmarsson’s top 10 linemates, however Hjalmarsson is one of Shaw’s top 10 linemates. We know that Shaw played 29.5% of his 759 minutes, or 197 minutes, with Hjalmarsson, which means that Hjalmarsson played 15.4% of 1278 minutes with Shaw. Filling in all these known entries results in the linemate table shown in Figure 2. Notice there are still numerous unknown entries.

The remaining entries were filled proportionally with the missing linemates’s total time-on-ice so that the sum of each skater’s linemates is 400%. The results of this procedure are shown with the final linemate table shown in Figure 3.

Computing Each Skater’s Individual Goal Differential

In my first blog post, I computed each skater’s on-ice expected goal differential. Now I will use the linemate table to compute each skater’s individual goal differential. Figure 4 shows the on-ice expect goal differential (blue) and the individual expected goal differential (red). For most skaters the individual component is approximately 2 to 3 times less than the on-ice component. However for some players their individual component can be near the same as their on-ice component (e.g. Duncan Keith), while for others their individual component can be completely different than their on-ice component (e.g. Brent Seabrook). Keith and Seabrook present a very interesting example. Keith and Seabrook play most of their ice-time together as can be seen in Figure 3, yet Keith’s on-ice xGD due to shot attempts is a fair bit larger than Seabrook’s. Thus the algorithm concludes that Keith is an extremely positive player while Seabrook is a negative player, but because of Seabrook playing so much time with Keith his on-ice xGD is still quite good.

Performing similar analyses for xGD due to blocked shots and penalties drawn gives individual expected goal differential (ixGD) for all skater’s in 5 on 5 situations, and the leaderboard for ixGD shown below.

Top 10 Bottom 5 Player ixGD Player ixGD Duncan Keith 10.3 Dennis Seidenberg -8.2 Nick Leddy 7.3 Andrew Ference -7.5 Pavel Datsyuk 7.2 Robyn Regher -6.8 Drew Doughty 7.1 Nick Holden -6.4 Kris Letang 7.0 Lauri Kopikorski -6.0 Tomas Tartar 6.5 Zach Bogosian -6.0 Joe Thornton 6.4 Andrew Desjardins -5.9 Eric Staal 6.2 Trevor Daley -5.9 Joe Pavelski 6.1 Jared Boll -5.9 Jake Muzzin 6.1 Jarome Iginla -5.8

A similar analysis can be run for power-play situations. Since the details of this analysis are nearly identical to the previous step, I will just present the best and worst individual power-play skaters.

Top 5 Bottom 5 Player PP ixGDAA Player PP ixGDAA Nicklas Backstrom 5.2 Marcus Johansson -3.8 Erik Karlsson 4.5 Mark Stone -2.7 Ryan Kessler 4.0 Oliver Ekman-Larsson -2.7 Patrice Bergeron 3.8 Milan Lucic -2.5 Joe Thornton 3.7 Jack Johnson -2.5

Unfortunately, at this time, linemate information is not available for short-handed situations. Thus short-handed ixGDAA, as well as 4 on 4 ixGD, will be computed simply by dividing on-ice xGDAA by 4.

Adding up the iXGDAA in all situations results in an overall ixGDAA, which quantifies each skater’s individual contribution to the team’s expected goal differential. Here are the top and bottom 10:

Top 10 Bottom 5 Player ixGD Player ixGD Duncan Keith 10.7 Dennis Seidenberg -8.8 Joe Thornton 10.2 Rasmus Ristolainen -8.5 Erik Karlsson 9.7 Nick Holden -7.6 Patrice Bergeron 9.6 Andrew Ference -7.4 Eric Staal 8.6 Jack Johnson -7.1 Pavel Datsyuk 8.5 Lauri Kopikorski -7.1 Nicklas Backstrom 8.5 Chris Stewart -7.1 Brent Burns 8.2 Robyn Regher -7.0 Claude Giroux 7.9 Peter Holland -7.0 Jonathan Toews 7.6 Brad Stuart -6.9

The complete list of NHL players and their ixGDAA can be found here.

Plotting all player’s on-ice overall xGDAA and their individual xGDAA shows that most players’ individual component is approximately 0.36 of their on-ice component (Fig. 5).

However, there are players who do not fall as close to the line of best fit as others. These players are those that are either dragged down by poor teammates or being propped up by superior teammates. Here are the top and bottom 5 players whose individual components vary the most from their scaled on-ice component.

Top 5 Bottom 5 Player ixGDAA difference Player ixGDAA difference Matt Moulson 5.5 Robyn Regher -6.1 Erik Karlsson 5.2 Marcus Johansson -5.2 Scott Hartnell 5.2 Dennis Seidenberg -5.1 Zemgus Girgenson 4.4 Zach Bogosian -4.7 Jaromir Jagr 4.4 Mark Streit -4.6

Conclusion

One of the goals of hockey analytics is to assess each individual skater’s contribution to team success. This is an especially challenging problem due to the tendency of coaches to stick with certain line combinations. While some metrics are already in use that present relative estimate of a skater to that of his team, these metrics are not very good at estimating each skater’s true contribution. Here I have presented the results of using advanced analytical methods to separate each individual contribtions to their team’s expected goal difference. The leaders for highest individual expected goal differential are filled with players who most regard as elite player, providing some anecdotal validation of this method.

Despite the advance over the status-quo methods of separating a player’s individual contribution from that of his linemates, improvements can still be made. The data set used for this analysis was limited to at most 10 linemates, thus missing values had to be predicted based on relative playing time. Furthermore, some players have played on multiple teams, resulting in stats that are not dictated by teammates from a single team, but from multiple teams, a scenario that cannot be handled by the current method. In the first part of this post, I mentioned that regression would be another method to find individual contributions to xGDAA, however I do not have easy access to the needed compiled data set. Not only would such a data set overcome the previously mentioned limitations, but may provide additional advantages such as providing confidence intervals on the ixGDAA, and allowing for cross-validation of the method. Thus, if someone has access to such a data set, please contact me as I would love to collaborate.

In my first blog post, I outlined a method to compute the team’s and each player’s on-ice expected goal differential based on shot attempts, blocked shots and penalties. In this blog post, I applied a method, presented in the first part of this post, that computed each player’s contribution to their team expected goal differential. With that information, in my next post I will then determine how many wins each player adds to their team above average, which is the final aim of all this work.