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) interyear, 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 splithalf 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 interyear data from the 20062007 season through this year (20102011) with a minimum of 20 games played. This totaled 2040 playerseasons 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 
Pvalue 
Lower 95% 
Upper 95% 
Lower 95.0% 
Upper 95.0% 
Intercept 
0.462361512 
0.024887892 
18.57776918 
2.72626E71 
0.413553124 
0.511169899 
0.413553124 
0.511169899 
G/60 
0.866300528 
0.03124301 
27.72781923 
7.8447E144 
0.80502893 
0.927572127 
0.80502893 
0.927572127 
A1/60 
0.819312773 
0.041444731 
19.76880413 
1.03059E79 
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 
Pvalue 
Lower 95% 
Upper 95% 
Lower 95.0% 
Upper 95.0% 
Intercept 
0.477112683 
0.020184502 
23.63757518 
2.2774E109 
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 
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 
Pvalue 
Lower 95% 
Upper 95% 
Lower 95.0% 
Upper 95.0% 
Intercept 
0.514341646 
0.019667806 
26.15144984 
3.0988E130 
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 
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 
Pvalue 
Lower 95% 
Upper 95% 
Lower 95.0% 
Upper 95.0% 
Intercept 
0.355996698 
0.023118934 
15.3984912 
1.0701E50 
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 
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 (interyear 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 misinformation. 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.

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 20072008
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 
JEANPIERREDUMONT 
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 overvalued 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 20082009
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 20092010
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 20102011
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 intrayear 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.
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