The Line Blender: Using GNN Embeddings for Player Rankings

2026-01-31

Throughout this series, we have explored how players interact within lines and teams. We’ve seen how to optimize a single roster and how to predict performance for unseen combinations. Here, we are inverting the logic: instead of asking how to build a team around players, we are asking which individual players provide the most value to any line they join.

To rank players, we can create a sample of hypothetical line and pairing combinations leaving an open spot for evaluation. Then, for every player in the league, we place them into the open spot across each sampled line. With the line or pairing now full, we can score the line using our model. Lastly, each player's performance in the line is compared against all other players.

This effectively measures a player's "portability"—the ability to drive play regardless of the system or quality of teammates.

Note, that for each season, players were limited to those who played at least ~600 mins of icetime over the season¹.

Forwards

Rank	Player	Team	Pos	GP
1	Nathan MacKinnon	COL	C	50
2	Nikita Kucherov	TBL	R	47
3	Connor McDavid	EDM	C	54
4	Artturi Lehkonen	COL	L	50
5	Andrei Svechnikov	CAR	R	52
6	Martin Necas	COL	C	50
7	Cutter Gauthier	ANA	L	52
8	Beckett Sennecke	ANA	R	53
9	Auston Matthews	TOR	C	46
10	Timo Meier	NJD	R	47
11	Dylan Guenther	UTA	R	52
12	Sam Bennett	FLA	C	51
13	Tage Thompson	BUF	C	51
14	Sidney Crosby	PIT	C	51
15	Brock Nelson	COL	C	50
16	Alex Ovechkin	WSH	L	53
17	Kirill Marchenko	CBJ	R	47
18	Anders Lee	NYI	L	52
19	Jason Robertson	DAL	L	52
20	David Pastrnak	BOS	R	48

Rank	Player	Team	Pos	GP
1	Nathan MacKinnon	COL	C	79
2	Sidney Crosby	PIT	C	80
3	Nikita Kucherov	TBL	R	78
4	Rickard Rakell	PIT	R	81
5	Auston Matthews	TOR	C	67
6	Filip Forsberg	NSH	L	82
7	Sam Bennett	FLA	C	76
8	Timo Meier	NJD	R	80
9	Brady Tkachuk	OTT	L	72
10	Anders Lee	NYI	L	82
11	Bryan Rust	PIT	R	71
12	Sebastian Aho	CAR	C	79
13	Zach Hyman	EDM	L	73
14	Pierre-Luc Dubois	WSH	L	82
15	Clayton Keller	UTA	R	81
16	Cole Caufield	MTL	R	82
17	Leon Draisaitl	EDM	C	71
18	Frank Vatrano	ANA	R	81
19	Seth Jarvis	CAR	C	73
20	Connor McDavid	EDM	C	67

Rank	Player	Team	Pos	GP
1	Nathan MacKinnon	COL	C	82
2	Auston Matthews	TOR	C	81
3	Sidney Crosby	PIT	C	82
4	Zach Hyman	EDM	L	80
5	Connor McDavid	EDM	C	76
6	Mikko Rantanen	COL	R	80
7	Brady Tkachuk	OTT	L	81
8	Nikita Kucherov	TBL	R	81
9	Filip Forsberg	NSH	L	82
10	Owen Tippett	PHI	R	78
11	Ross Colton	COL	C	80
12	Bryan Rust	PIT	R	62
13	Jesper Bratt	NJD	L	82
14	Trevor Moore	LAK	L	82
15	David Pastrnak	BOS	R	82
16	Warren Foegele	EDM	L	82
17	Timo Meier	NJD	R	69
18	John Tavares	TOR	C	80
19	Martin Necas	CAR	C	77
20	Jake Guentzel	CAR	C	67

Rank	Player	Team	Pos	GP
1	Matthew Tkachuk	FLA	L	79
2	Brady Tkachuk	OTT	L	82
3	Auston Matthews	TOR	C	74
4	Sidney Crosby	PIT	C	82
5	Nathan MacKinnon	COL	C	71
6	Tage Thompson	BUF	C	78
7	William Nylander	TOR	R	82
8	Carter Verhaeghe	FLA	C	81
9	Jeff Skinner	BUF	L	79
10	Mikko Rantanen	COL	R	82
11	Zach Hyman	EDM	L	79
12	Jake Guentzel	PIT	L	78
13	David Pastrnak	BOS	R	82
14	Rickard Rakell	PIT	R	82
15	Alex Ovechkin	WSH	L	73
16	Tim Stutzle	OTT	L	78
17	Connor McDavid	EDM	C	82
18	Jack Hughes	NJD	C	78
19	Jesper Bratt	NJD	L	82
20	Jason Zucker	PIT	L	78

Rank	Player	Team	Pos	GP
1	Auston Matthews	TOR	C	73
2	Timo Meier	SJS	R	77
3	Sam Bennett	FLA	C	71
4	Viktor Arvidsson	LAK	L	66
5	Jake Guentzel	PIT	L	76
6	Michael Bunting	TOR	L	79
7	Carter Verhaeghe	FLA	C	78
8	Aleksander Barkov	FLA	C	67
9	Nathan MacKinnon	COL	C	65
10	Matthew Tkachuk	CGY	L	82
11	Sidney Crosby	PIT	C	69
12	Vladimir Tarasenko	STL	R	75
13	Connor McDavid	EDM	C	80
14	Jonathan Huberdeau	FLA	L	80
15	John Tavares	TOR	C	79
16	Pierre-Luc Dubois	WPG	L	81
17	Nikolaj Ehlers	WPG	L	62
18	Mitchell Marner	TOR	R	72
19	Phillip Danault	LAK	C	79
20	Elias Lindholm	CGY	C	82

Rank	Player	Team	Pos	GP
1	Auston Matthews	TOR	C	52
2	Nathan MacKinnon	COL	C	48
3	Connor McDavid	EDM	C	56
4	Gabriel Landeskog	COL	L	54
5	Brady Tkachuk	OTT	L	56
6	Mikko Rantanen	COL	R	52
7	Jonathan Marchessault	VGK	C	55
8	Patrice Bergeron	BOS	C	54
9	Max Pacioretty	VGK	L	48
10	David Pastrnak	BOS	R	48
11	Tyler Toffoli	MTL	C	52
12	John Tavares	TOR	C	56
13	Aleksander Barkov	FLA	C	50
14	Bryan Rust	PIT	R	56
15	Nazem Kadri	COL	C	56
16	Timo Meier	S.J	R	54
17	Evander Kane	S.J	L	56
18	Craig Smith	BOS	C	54
19	Andrei Svechnikov	CAR	R	55
20	Alex Tuch	VGK	R	55

Defense

Rank	Player	Team	Pos	GP
1	Sam Malinski	COL	D	50
2	Cale Makar	COL	D	50
3	Brent Burns	COL	D	50
4	Mattias Ekholm	EDM	D	54
5	Sean Walker	CAR	D	52
6	Zach Werenski	CBJ	D	47
7	Josh Manson	COL	D	50
8	Devon Toews	COL	D	40
9	Jakob Chychrun	WSH	D	51
10	Evan Bouchard	EDM	D	54
11	Jacob Trouba	ANA	D	52
12	MacKenzie Weegar	CGY	D	52
13	Alexander Nikishin	CAR	D	51
14	Rasmus Andersson	VGK	D	50
15	Jordan Spence	OTT	D	43
16	Darren Raddysh	TBL	D	45
17	Morgan Rielly	TOR	D	51
18	John Carlson	WSH	D	49
19	Darnell Nurse	EDM	D	54
20	Mikhail Sergachev	UTA	D	52

Rank	Player	Team	Pos	GP
1	Brent Burns	CAR	D	82
2	Zach Werenski	CBJ	D	81
3	Erik Karlsson	PIT	D	82
4	Cale Makar	COL	D	80
5	Evan Bouchard	EDM	D	82
6	Darnell Nurse	EDM	D	76
7	Mattias Ekholm	EDM	D	65
8	Jaccob Slavin	CAR	D	80
9	Thomas Chabot	OTT	D	80
10	Devon Toews	COL	D	76
11	Rasmus Dahlin	BUF	D	73
12	Gustav Forsling	FLA	D	80
13	Sean Walker	CAR	D	82
14	Victor Hedman	TBL	D	79
15	Dougie Hamilton	NJD	D	64
16	Jake Walman	EDM	D	65
17	Noah Dobson	NYI	D	71
18	Dmitry Orlov	CAR	D	76
19	Thomas Harley	DAL	D	78
20	Alex Pietrangelo	VGK	D	71

Rank	Player	Team	Pos	GP
1	Roman Josi	NSH	D	82
2	Mattias Ekholm	EDM	D	79
3	Evan Bouchard	EDM	D	81
4	Brent Burns	CAR	D	82
5	Jaccob Slavin	CAR	D	81
6	Victor Hedman	TBL	D	78
7	Josh Morrissey	WPG	D	81
8	Erik Karlsson	PIT	D	82
9	Morgan Rielly	TOR	D	72
10	Rasmus Dahlin	BUF	D	81
11	Darnell Nurse	EDM	D	81
12	Zach Werenski	CBJ	D	70
13	Cale Makar	COL	D	77
14	Kris Letang	PIT	D	82
15	MacKenzie Weegar	CGY	D	82
16	Brady Skjei	CAR	D	80
17	Sean Walker	COL	D	81
18	Josh Manson	COL	D	76
19	Noah Dobson	NYI	D	79
20	Gustav Forsling	FLA	D	79

Rank	Player	Team	Pos	GP
1	Brent Burns	CAR	D	82
2	Dougie Hamilton	NJD	D	82
3	Brandon Montour	FLA	D	80
4	Kris Letang	PIT	D	64
5	Victor Hedman	TBL	D	76
6	Gustav Forsling	FLA	D	82
7	Roman Josi	NSH	D	67
8	MacKenzie Weegar	CGY	D	81
9	Erik Karlsson	SJS	D	82
10	Noah Hanifin	CGY	D	81
11	Travis Hamonic	OTT	D	75
12	Brady Skjei	CAR	D	81
13	Devon Toews	COL	D	80
14	Damon Severson	NJD	D	81
15	Darnell Nurse	EDM	D	82
16	Radko Gudas	FLA	D	72
17	Thomas Chabot	OTT	D	68
18	Aaron Ekblad	FLA	D	71
19	Rasmus Dahlin	BUF	D	78
20	Josh Morrissey	WPG	D	78

Rank	Player	Team	Pos	GP
1	MacKenzie Weegar	FLA	D	80
2	Brandon Montour	FLA	D	81
3	Morgan Rielly	TOR	D	82
4	Evan Bouchard	EDM	D	81
5	Gustav Forsling	FLA	D	71
6	Aaron Ekblad	FLA	D	61
7	Roman Josi	NSH	D	80
8	Noah Hanifin	CGY	D	81
9	Cale Makar	COL	D	77
10	Brady Skjei	CAR	D	82
11	Radko Gudas	FLA	D	77
12	Kris Letang	PIT	D	78
13	Charlie McAvoy	BOS	D	78
14	Darnell Nurse	EDM	D	71
15	Dougie Hamilton	NJD	D	62
16	Shea Theodore	VGK	D	78
17	Victor Hedman	TBL	D	82
18	Jaccob Slavin	CAR	D	79
19	Justin Faulk	STL	D	76
20	Alex Pietrangelo	VGK	D	80

Rank	Player	Team	Pos	GP
1	Darnell Nurse	EDM	D	56
2	Tyson Barrie	EDM	D	56
3	Shea Theodore	VGK	D	53
4	Dougie Hamilton	CAR	D	55
5	Alex Pietrangelo	VGK	D	41
6	Alec Martinez	VGK	D	53
7	Devon Toews	COL	D	53
8	Thomas Chabot	OTT	D	49
9	Jakob Chychrun	ARI	D	56
10	Roman Josi	NSH	D	48
11	Jake Muzzin	TOR	D	53
12	Ryan Graves	COL	D	54
13	Morgan Rielly	TOR	D	55
14	Brett Pesce	CAR	D	55
15	Radko Gudas	FLA	D	54
16	Seth Jones	CBJ	D	56
17	Mark Giordano	CGY	D	56
18	Nicolas Hague	VGK	D	52
19	Jaccob Slavin	CAR	D	52
20	Samuel Girard	COL	D	48

Across these posts, we have used optimization and machine learning to explore network effects in NHL lineups. The implementation here leaves a lot of potential for future work, including: utilizing disaggreated data, better representing the time-series data that comprises a player's career, and more.

All posts in this series:
1. The Line Blender: Optimizing Lineups Using MoneyPuck's Expected Goals Percentage (xG%)
2. The Line Blender: Embedding Line Performance Using a GNN
3. The Line Blender: Using a GNN To Produce Olympic Rosters
4. The Line Blender: Using GNN Embeddings for Player Rankings
5. The Line Blender: Olympic Lineups with Announced Rosters
6. The Line Blender: Hypothetical Russian Olympic Lineups

Credit to MoneyPuck lines/pairs and skaters data used in this series. ↩

← The Line Blender: Olympic Lineups with Announced Rosters

The Line Blender: Using a GNN To Produce Olympic Rosters →