FanPost

waP/60 A new approach to looking at points

While I was running a correlation study for another project I’m working on, I decided to quickly measure the correlation of many individual statistics and their contribution to team points percentage (P%), and an even strength individual points per 60 time on ice (P/60) inter-year, that is between years.  Briefly looking over the list I noticed 2 interesting things.  First, goals (EV G/60) and first assists (EV A1/60) were well correlated with points, 0.859, 0.819 respectively.  However second assists (EV A2/60) lagged behind quite a bit limping in at 0.556. Given the substantial amount of emphasis everyone around the NHL places on the amount of points a player earns, I began to wonder if anyone had thought about how much each of these stats (G/60, A1/60, A2/60) should be weighted.  Currently the traditional points treats them as the same, but even intuitively one can probably conclude that a goal scored by a player is much more predictive of a good player than a 2nd assist.  In the next couple paragraphs I will outline the methods I used to reach my conclusions which you can skip ahead and read at the bottom.

Methods

Common abbreviations used

G/60 – even strength goals per 60 minutes ice time

A1/60 - even strength first assets per 60 minutes ice time

A2/60 - even strength second assists per 60 minutes ice time

P/60 - even strength points per 60 minutes ice time

AdjP/60 = G/60 + A1/60 even strength goals and first assists per 60 minutes ice time

waP/60 = G/60(1.44) + A1/60(1.32) + A2/60(.24) even strength goals, first assists, and second assists per 60 minutes ice time weighted by their predictive power.

I began with the hypothesis that totaling goals and first assists without 2nd assists would be a better predictor of future points than totaling goals, first assists, and second assists.  Ultimately I knew using split-half season reliability (ala JLikens- using even and odd # games to correlate 2 or more variables) would be the best method, but with limited time I decided to use inter-year data from the 2006-2007 season through this year (2010-2011) with a minimum of 20 games played.  This totaled 2040 player-seasons worth of data which I thought would be adequate.  This sample may skew the results as players that are capable of 4 consecutive years of 20+ games played are probably above average NHL players.

My first thought was the throw out second assists completely, and see if that correlated with the previous and next year’s points.  As is obvious when I looked at the data, it was hard to compare this new stat, I call Adj P/60 (adjusted by subtracting second assists) and points because I was reducing the point totals.  Consequently I knew I needed to find a fudge factor to rectify this, and at the same time I decided to run a least squares regression with second assists thrown back in to see how much variance it accounted for.  This gave me a new look at the data, with some interesting results. Shown below

Regression Statistics

Multiple R

0.761289354

R Square

0.57956148

Adjusted R Square

0.578941973

Standard Error

0.452955371

Observations

2040

ANOVA

 

df

SS

MS

F

Significance F

Regression

3

575.818501

191.9395003

935.5209835

0

Residual

2036

417.7232041

0.205168568

Total

2039

993.5417051

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.462361512

0.024887892

18.57776918

2.72626E-71

0.413553124

0.511169899

0.413553124

0.511169899

G/60

0.866300528

0.03124301

27.72781923

7.8447E-144

0.80502893

0.927572127

0.80502893

0.927572127

A1/60

0.819312773

0.041444731

19.76880413

1.03059E-79

0.738034275

0.900591272

0.738034275

0.900591272

A2/60

0.201343384

0.055619987

3.619982582

0.000301818

0.092265369

0.3104214

0.092265369

0.3104214

 

What I really found interesting is the coefficient column.  This describes in general how much a variable influences points.  That is if we ran the same regression with inter year data, each variable (goals, assistis) would be equal to 1 because every time you record a goal, you increase your points by 1.  However here we see that simply isn’t the case.  Goals and first assists seem to be much more predictive of points than second assists. 

Following this data I decided to come up with a different stat.  Instead of throwing out second assits completely, I would weight each variable accordingly to give the best R^2 to points.  Thus the waP/60 (weight adjusted points per 60 minutes ice time) was born.  Below you can find the regression statistics for its predictive power as well as for completeness I included points itself, and Adj P/60.

Regression Statistics

Multiple R

0.761146137

R Square

0.579343443

Adjusted R Square

0.579137036

Standard Error

0.452850439

Observations

2040

ANOVA

 

df

SS

MS

F

Significance F

Regression

1

575.6018717

575.6018717

2806.807394

0

Residual

2038

417.9398334

0.20507352

Total

2039

993.5417051

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.477112683

0.020184502

23.63757518

2.2774E-109

0.437528277

0.516697089

0.437528277

0.516697089

waP/60

0.614606873

0.011600885

52.979311

0

0.591856045

0.6373577

0.591856045

0.6373577

 

 Image001_medium

 

Regression Statistics

Multiple R

0.759490712

R Square

0.576826141

Adjusted R Square

0.576618499

Standard Error

0.454203396

Observations

2040

ANOVA

 

df

SS

MS

F

Significance F

Regression

1

573.1008278

573.1008278

2777.987466

0

Residual

2038

420.4408773

0.206300725

Total

2039

993.5417051

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.514341646

0.019667806

26.15144984

3.0988E-130

0.475770548

0.552912745

0.475770548

0.552912745

Adj P/60

0.867287228

0.016454997

52.70661691

0

0.835016861

0.899557595

0.835016861

0.899557595

 

Image003_medium

 

Regression Statistics

Multiple R

0.746660459

R Square

0.55750184

Adjusted R Square

0.557284717

Standard Error

0.464458265

Observations

2040

ANOVA

 

df

SS

MS

F

Significance F

Regression

1

553.901329

553.901329

2567.668872

0

Residual

2038

439.6403761

0.21572148

Total

2039

993.5417051

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.355996698

0.023118934

15.3984912

1.0701E-50

0.310657494

0.401335902

0.310657494

0.401335902

P/60

0.746660459

0.014735119

50.67217059

0

0.717762994

0.775557923

0.717762994

0.775557923

 

Image006_medium


You may notice that the first regression shows a slightly better correlation coefficient, and you would be right.  When taking this data into account I also wanted it to be reliable (inter-year correlatability). I modified the formula slightly by again running R^2 values to derive the best weight.  This adjustment didn’t alter the waP/60 predictive power of future points very much; it just boosted its reliability as a stat, which I thought to be very important.

 

I next thought to correlate this data with team points %, that is how likely players with high waP/60 are on good teams.  My initial hope was a better correlated number than P/60.  When the data came out and showed that it wasn’t, I was a bit disappointed, and thought that I might be stumbling into garbage in garbage out analysis.

 

Team P%

Team P%

1.000

+-ON/60

0.38955

CORSI ON

0.389077

Ozone%

0.224368

PDO

0.224032

Fin Ozone%

0.210028

Sv%

0.207835

P/60

0.099613

Sh%

0.095569

GP

0.092267

A2/60

0.089503

wP/60

0.08742

A1/60

0.077553

G/60

0.070729

CORSI REL

-0.00046

RATING

-0.00118

 

However I noticed that A2/60  correlates stronger with team P%, than goals and assists.  It made me realize that this stat again is providing mis-information.  It seems that the better team a player plays for is more that player is to have 2nd assists, that is to say 2nd assists are more correlated with team goals, and thus are highly influenced by the team a player plays for.

 

G/60

A1/60

A2/60

P/60

wP/60

Team GF

0.117348

0.128756

0.155427

0.167829

0.145492

 

Discussion

Now that we have a stat that can predict future points, to a minor degree reduce team influence, as well as improved reliability we can look at some data to find some interesting conclusions.  I decided to look at how players faired between the two stats, so I ranked them for each year accordingly. Here is the data.

Top 25 waP/60 players for 2007-2008

NAME

G/60

A1/60

A2/60

P/60

P/60 rank

Adj P/60

wP/60

wP/60 Rank

wP/60 Rank Chg

wP/60 - P/60

SIDNEYCROSBY

1.41

1.49

0.47

3.38

1

2.9

4.106

1

0

0.726

EVGENIMALKIN

1.48

1.18

0.54

3.2

2

2.66

3.814

2

0

0.614

ALEXANDEROVECHKIN

1.68

0.97

0.35

3

5

2.65

3.777

3

2

0.777

JASONSPEZZA

1.13

1.39

0.41

2.93

7

2.52

3.557

4

3

0.627

MARIANGABORIK

1.36

1.09

0.33

2.77

17

2.45

3.472

5

12

0.702

DANIELALFREDSSON

1.36

1

0.77

3.12

3

2.36

3.46

6

-3

0.34

ILYAKOVALCHUK

1.67

0.73

0.31

2.72

22

2.4

3.436

7

15

0.716

JAROMEIGINLA

1.52

0.83

0.51

2.85

12

2.35

3.402

8

4

0.552

JEAN-PIERREDUMONT

1.09

1.3

0.49

2.88

8

2.39

3.401

9

-1

0.521

MAREKSVATOS

1.87

0.45

0.27

2.59

25

2.32

3.344

10

15

0.754

ALEXANDERRADULOV

1.2

1.09

0.57

2.86

9

2.29

3.301

11

-2

0.441

ALEXANDERFROLOV

1.06

1.23

0.47

2.76

18

2.29

3.26

12

6

0.5

DANYHEATLEY

1.37

0.84

0.74

2.95

6

2.21

3.256

13

-7

0.306

MATSSUNDIN

1.22

1.05

0.47

2.74

21

2.27

3.252

14

7

0.512

JOETHORNTON

0.87

1.4

0.58

2.84

13

2.27

3.239

15

-2

0.399

MIKERIBEIRO

1.09

1.15

0.63

2.86

10

2.24

3.237

16

-6

0.377

JASONPOMINVILLE

1.29

0.95

0.5

2.75

20

2.24

3.228

17

3

0.478

PAVELDATSYUK

0.92

1.33

0.51

2.76

19

2.25

3.201

18

1

0.441

DEREKROY

1.23

0.95

0.67

2.86

11

2.18

3.183

19

-8

0.323

HENRIKZETTERBERG

1.44

0.72

0.67

2.83

15

2.16

3.181

20

-5

0.351

DREWSTAFFORD

1.25

0.91

0.66

2.83

16

2.16

3.157

21

-5

0.327

PAULSTASTNY

1.34

0.7

1.08

3.12

4

2.04

3.111

22

-18

-0.01

JUSTINWILLIAMS

0.99

0.99

0.86

2.84

14

1.98

2.938

23

-9

0.098

BRADBOYES

1.64

0.38

0.33

2.35

36

2.02

2.936

24

12

0.586

 

Not too much movement in the top 25 though you can see from the waP/60 rank change column (this is the waP/60 rank – P/60 rank; and thus how a player moves up and down in ranking well looking at waP/60 as compared to P/60) certain players can be well over-valued as compared to other players that are undervalued.  For example Marian Gaborik and Ilya Kovalchuk jumped of12 and  15 spots respectively, clearly indicating they were undervalued, as Dany Heatly and Paul Statsny were a bit overvalued.

Top 25 waP/60 players in 2008-2009

NAME

G/60

A1/60

A2/60

P/60

P/60 rank

Adj P/60

wP/60

wP/60 Rank

wP/60 Rank Chg

wP/60 - P/60

ALEXANDERSEMIN

1.76

1.25

0.15

3.16

3

3.01

4.213

1

2

1.053

PHILKESSEL

1.73

0.83

0.26

2.82

13

2.56

3.642

2

11

0.822

RENEBOURQUE

1.69

0.76

0.76

3.2

2

2.45

3.614

3

-1

0.414

SIDNEYCROSBY

1.16

1.31

0.53

3

5

2.47

3.524

4

1

0.524

EVGENIMALKIN

0.78

1.66

0.63

3.07

4

2.44

3.465

5

-1

0.395

ALEXANDEROVECHKIN

1.57

0.81

0.48

2.86

12

2.38

3.44

6

6

0.58

DANIELSEDIN

1.19

1.19

0.59

2.97

7

2.38

3.423

7

0

0.453

MARTINHAVLAT

1.15

1.2

0.55

2.89

11

2.35

3.369

8

3

0.479

RICKNASH

1.39

0.96

0.32

2.67

19

2.35

3.34

9

10

0.67

DERICKBRASSARD

1.29

0.92

1.1

3.3

1

2.21

3.335

10

-9

0.035

JAMIELANGENBRUNNER

1.11

1.23

0.35

2.7

18

2.34

3.303

11

7

0.603

MARIANHOSSA

1.69

0.56

0.5

2.75

15

2.25

3.287

12

3

0.537

ILYAKOVALCHUK

1.48

0.82

0.31

2.61

24

2.3

3.282

13

11

0.672

MARCSAVARD

0.86

1.39

0.75

2.99

6

2.25

3.253

14

-8

0.263

ZACHPARISE

1.47

0.73

0.73

2.93

9

2.2

3.252

15

-6

0.322

PAVELDATSYUK

0.99

1.15

0.77

2.91

10

2.14

3.127

16

-6

0.217

ALEXEIPONIKAROVSKY

1.05

1.11

0.58

2.74

16

2.16

3.114

17

-1

0.374

JEFFCARTER

1.4

0.72

0.52

2.64

21

2.12

3.087

18

3

0.447

TIMCONNOLLY

1.12

1.02

0.51

2.64

20

2.14

3.079

19

1

0.439

DANIELBRIERE

1.23

0.88

0.53

2.63

22

2.11

3.057

20

2

0.427

COREYPERRY

1.15

0.99

0.36

2.5

31

2.14

3.045

21

10

0.545

DAVIDKREJCI

0.9

1.15

0.9

2.95

8

2.05

3.03

22

-14

0.08

JAROMEIGINLA

1.07

1.02

0.37

2.46

39

2.09

2.973

23

16

0.513

DAVIDBOOTH

1.12

0.94

0.5

2.56

28

2.06

2.971

24

4

0.411

 

Rick Nash, Phil Kessel , Jerome Iginla, and again Ilya Kovalchuk seem to benefit the most from this analysis, with David Krejci and Derik Brassard coming up well overvalued. 

Top 25 waP/60 players in 2009-2010

NAME

G/60

A1/60

A2/60

P/60

P/60 rank

Adj P/60

wP/60

wP/60 Rank

wP/60 Rank Chg

wP/60 - P/60

ALEXOVECHKIN

1.87

1.3

0.52

3.7

3

3.17

4.527

1

2

0.827

DANIELSEDIN

1.37

1.76

0.91

4.04

1

3.13

4.512

2

-1

0.472

SIDNEYCROSBY

1.68

1.14

0.59

3.41

4

2.82

4.06

3

1

0.65

HENRIKSEDIN

1.09

1.53

1.34

3.96

2

2.62

3.912

4

-2

-0.05

ALEXANDERSEMIN

1.74

0.93

0.52

3.19

5

2.67

3.852

5

0

0.662

ILYAKOVALCHUK

1.46

1.05

0.4

2.91

7

2.51

3.579

6

1

0.669

MARIANGABORIK

1.35

1.15

0.4

2.9

8

2.5

3.554

7

1

0.654

JOFFREYLUPUL

2.07

0.41

0

2.48

31

2.48

3.512

8

23

1.032

CHRISSTEWART

1.36

0.91

0.57

2.84

10

2.27

3.293

9

1

0.453

NICKLASBACKSTROM

1.03

1.17

0.83

3.03

6

2.2

3.226

10

-4

0.196

ERICFEHR

1.48

0.74

0.49

2.71

15

2.22

3.221

11

4

0.511

MIKEKNUBLE

1.48

0.77

0.32

2.57

25

2.25

3.219

12

13

0.649

PATRIKELIAS

1.15

1.07

0.54

2.75

14

2.22

3.195

13

1

0.445

SCOTTIEUPSHALL

1.54

0.58

0.58

2.7

16

2.12

3.118

14

2

0.418

FRAZERMCLAREN

0.44

1.77

0.44

2.65

18

2.21

3.076

15

3

0.426

WOJTEKWOLSKI

1.05

1.05

0.68

2.78

11

2.1

3.059

16

-5

0.279

ALEXBURROWS

1.34

0.75

0.59

2.68

17

2.09

3.057

17

0

0.377

PATRICKMARLEAU

1.31

0.75

0.55

2.61

20

2.06

3.005

18

2

0.395

JOEPAVELSKI

1.4

0.67

0.27

2.33

41

2.07

2.96

19

22

0.63

DUSTINPENNER

1.26

0.77

0.38

2.4

36

2.03

2.918

20

16

0.518

BRADRICHARDS

0.57

1.49

0.51

2.57

26

2.06

2.91

21

5

0.34

ZACHPARISE

1.3

0.67

0.62

2.59

21

1.97

2.902

22

-1

0.312

STEVENSTAMKOS

1.23

0.75

0.59

2.56

27

1.98

2.9

23

4

0.34

PATRICKKANE

1.02

0.97

0.58

2.58

23

1.99

2.886

24

-1

0.306

 

Some more movement now with lots more jumping around.  Joffrey Lupul, and Joe Pavelski come in the most undervalued.  Not much in the way of overvalued players this year.

Top 25 waP/60 players in 2010-2011

NAME

G/60

A1/60

A2/60

P/60

P/60 rank

Adj P/60

wP/60

wP/60 Rank

wP/60 Rank Chg

wP/60 - P/60

SIDNEYCROSBY

1.94

1.36

0.68

3.98

1

3.3

4.746

1

0

0.766

DANIELSEDIN

1.24

1.24

0.7

3.17

2

2.48

3.588

2

0

0.418

STEVENSTAMKOS

1.39

1.01

0.43

2.82

8

2.4

3.433

3

5

0.613

ALESHEMSKY

1.11

1.3

0.46

2.88

5

2.41

3.422

4

1

0.542

PAVELDATSYUK

1.09

1.17

0.62

2.89

3

2.26

3.261

5

-2

0.371

RICKNASH

1.42

0.79

0.62

2.84

7

2.21

3.232

6

1

0.392

DAVIDKREJCI

0.71

1.54

0.65

2.89

4

2.25

3.211

7

-3

0.321

DEREKROY

1.01

1.27

0.25

2.53

22

2.28

3.187

8

14

0.657

DANIELCLEARY

1.36

0.86

0.29

2.5

24

2.22

3.158

9

15

0.658

MILANLUCIC

1.46

0.64

0.64

2.75

11

2.1

3.097

10

1

0.347

DANIELBRIERE

1.42

0.71

0.49

2.62

14

2.13

3.095

11

3

0.475

CLAUDEGIROUX

0.79

1.36

0.62

2.77

10

2.15

3.081

12

-2

0.311

JONATHANTOEWS

1.06

1.11

0.37

2.54

20

2.17

3.077

13

7

0.537

MATTCALVERT

1.44

0.64

0.48

2.56

19

2.08

3.029

14

5

0.469

ALEXOVECHKIN

1

1.1

0.5

2.59

16

2.1

3.01

15

1

0.42

MARTINST.LOUIS

1.28

0.77

0.61

2.66

13

2.05

3.003

16

-3

0.343

ALEXANDERSEMIN

1.36

0.72

0.29

2.37

37

2.08

2.973

17

20

0.603

MICHAELGRABNER

1.44

0.62

0.34

2.4

35

2.06

2.968

18

17

0.568

HENRIKSEDIN

0.51

1.54

0.82

2.87

6

2.05

2.966

19

-13

0.096

ANZEKOPITAR

0.89

1.16

0.63

2.68

12

2.05

2.963

20

-8

0.283

JEFFCARTER

1.48

0.51

0.62

2.61

15

1.99

2.949

21

-6

0.339

TOMASFLEISCHMANN

0.81

1.31

0.2

2.32

45

2.12

2.941

22

23

0.621

MARTINHAVLAT

1.01

1.06

0.37

2.45

30

2.07

2.939

23

7

0.489

BOBBYRYAN

1.21

0.82

0.48

2.51

23

2.03

2.936

24

-1

0.426

 

Again we see some similar results from previous years.  Big movers this year include Semin, Roy, and Grabner.  Interestly Henrik Sedin seems to be very overvalued. 

Conclusions

Although there is not a massive amount of movement, I still feel waP is a better metric when looking at points.   In subsequent studies using a larger data set including intra-year correlations might very well tease out some of this information even more, and get a better weighted formula for points.  For now I think this is a good observation from a long overdue adjustment.  

If this FanPost is written by someone other than one of the blog's editors, the opinions expressed in it do not necessarily reflect those of this blog or SB Nation.

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