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# Introducing P+CORP: Points + Corsi Over Replacement Player

P+CORP = (P/60 +
Avg NHL Replacement Level P/60)
+ (Corsi Rel + Avg NHL Replacement Level Corsi Rel) / [coeffiecient] + (Corsi On +
Avg NHL Replacement Level Corsi Rel) / [coeffiecient]

P+CORP (I leave the pronunciation to your discretion) wasn't something I went looking for, but was really the consequence of defining NHL replacement level talent. It's a holistic stat forged under KISS principles that bloomed before me as an inevitable consequence of my previous post. Following that post I began to lament the fact that we currently didn't have an OBP+SLG like baseball. The concept to me was so perfect. OBP represents a player' s ability to setup his team to score, as getting on base perserves an out and puts a runner in position to score. SLG represents a player's ability to produce, that is, to generate runs if teammates are in scoring position. At that moment it occurred to me (and I honestly feel pretty stupid for not putting this together sooner) that we have 2 stats with a similar scope.

A player's Corsi tells us about possession. If a skater has great possession numbers, by inductive reasoning we can also say that he's putting his team in the position to generate scoring chances, and in all liklihood, limiting the opposition's scoring chances. P/60 represents a player's ability to produce. Although a little confounded by PDO, it still is a good measure of a player's ability to convert on those opportunities. I think many of us had unconsciously connected these 2 stats when evaluating players, but now I present them under one heading, while fine-tuning the coefficients to give us the best results. At it's heart it's a simple stat that serves as a good substitute or comparison piece to the current gold standard of player evaluation, GVT. The beauty is in it's ease of calculation, which requires looking up only 3 (or 4 for Defensemen) stats from the main Behind The Net page. My underlying assumption is that ice time increases with line status, ie. top lines are given the most ice time, but everything else falls out from detailed data collection. I didn't fine tune these numbers so the best players are at the top of the list, this is evidenced-based hockey analysis.

P+CORP for Forwards

Forward P+CORP = P/60 + (Corsi Rel + 7) / 20 + (Corsi On + 7) / 20

P+CORP is really built for forwards. It's an amalgam of offensive production and possession. The objective for most forwards is to score, and we directly measure that. With the addition of Corsi we measure that forwards ability to push play in the right direction, while adding reliability along the way. I used both Cosi Rel and Corsi On in attempt to utilize both their strengths and neutralize both their weaknesses. Corsi Rel tends to over-state players that play on weak teams, while Corsi On over-states players on good teams. By using both, the cream that rises to the top are players that are either good players on average teams, or average players on good teams. The elite being those with a strong Corsi on and Corsi Rel, that is, good players on good teams.

What I love the most about this stat is how accessible it is. I still consider GVT to be currently the best tool to evaluate player contribution, but I think this creates a widely available substitute that correlates very well with GVT. In addition, it is well integrated with replacement level. A score of 0 will always be our baseline replacement level talent. As P+CORP increases (and theoretically decreases) talent level increases as compared to (ie. over) replacement level.

We'll start our analysis with some simple year-over-year correlations in comparison to GVT. (I know, not the most rigourous, but sufficient because I don't have game-by-game GVT). What we're basically doing is comparing the previous year's results to the following year, and trying to see if the previous year predicts the following year accurately. My dataset (N=1077) included 2007-2012 (5 years) skaters who have over 450 total TOI, all (save GVT) are 5v5 numbers.

### Forward Year To Year Correlations

TOI/60 P/60 Corsi Relative Corsi On P+CORP GVT
r(Self) 0.77 0.5 0.62 0.56 0.65 0.65
r(toi/60) 0.77 0.56 0.43 0.32 0.55 0.63
r(P/60) 0.47 0.5 0.4 0.34 0.51 0.51
r(Corsi Rel) 0.41 0.4 0.62 0.43 0.58 0.37
r(Corsi On) 0.3 0.35 0.45 0.56 0.54 0.35
r(GVT) 0.55 0.55 0.41 0.36 0.54 0.65

The two most important numbers come from the r(self) and r(GVT) rows. These represent each stat (in the columns) ability to predict next year's (row) results. TOI/60 is the most repeatable (highest r(self)) which is understandble, as coaches are likely to play their top players no matter what kind of season they are having. Both GVT and P+CORP are equally repeatable, a good indicator of their respective reliability. We can see from the r(GVT) row that P+CORP does a reasonable job tracking along with GVT. At this level I would say the difference between TOI/60 and P+CORP is negligble, and both predict future GVT with equal ability.

Another way to parse the data (N= 281) is looking only at players that ended the season on different teams. BTN doesnt provide season splits, so it's possible and likely that some players appear on other teams due to trade deadline acquisition, and really played a majority of their time on the same team. This could disrupt the results, but we'll take that as we analyze the data.

### Forwards Year To Year Different Team Correlations

TOI/60 P/60 Corsi Rel Corsi On P+CORP GVT
r(Self) 0.682 0.423 0.570 0.386 0.572 0.481
r(P/60) 0.361 0.423 0.305 0.191 0.386 0.376
r(GVT) 0.456 0.484 0.342 0.240 0.447 0.481
r(toi/ 60) 0.683 0.524 0.371 0.287 0.498 0.589

What grabbed me immediately was how repeatable Corsi Rel was year to year when skating for a different team. I hadn't seen this before, and it really shows the importance of that stat. P+CORP uses this to it's advantage and vaults over GVT in this set of data.

Lastly we'll look at % variance explained by a stat intra year. This tells us which stats give us the most information about our GVT and P+CORP results, and really unearths my biggest criticism of GVT (and PC, for that matter).

### % of Variance Explained

On-Ice Sh% On-Ice Sv% PDO P/60 Corsi Rel Corsi On P+CORP gvt
PDO 0.514 0.304 1.000 0.292 0.009 0.001 0.089 0.218
TOI/60 0.160 0.039 0.040 0.237 0.123 0.074 0.207 0.442
P/60 0.681 0.051 0.292 1.000 0.249 0.187 0.654 0.681
Corsi Rel 0.083 0.045 0.009 0.249 1.000 0.528 0.747 0.235
Corsi On 0.024 0.021 0.001 0.187 0.528 1.000 0.697 0.200
GVT 0.434 0.017 0.218 0.681 0.235 0.200 0.529 1.000

The columns represent the % of variance explained by the stat in the row

As you can see, nearly 2/3 of GVT can be accounted for by TOI/60 and PDO. . This is my biggest problem with accounting all successes and failures of a team to specific players. Ultimately the randomness (non-repeatable) elements are assigned as well. P+CORP is a rate stat, so it doesn't consider contribution over the entire year. Small samples may be a little out of whack with reality, and would require adjusting (regressing) to the mean. There is utility in the accounting approach of GVT and PC. With P+CORP we now have a reliable rate stat for comparison.

Here is the obligatory table of top players that really doesn't tell you anything you don't already know. I usually prefer to filter through stats like zone% and Corsi Rel QOC, but here I adjusted P+CORP for both.

Forward Zone and Competition Adjusted P+CORP = P/60 + (Corsi Rel + 7) / 20 + (Corsi On + 7) / 20 + (Corsi Rel QOC + 1)/5 + (49 - Ozone%)/12

NAME TOI (>2000) GP P/60 Corsi Rel Corsi On Corsi Rel QOC OZ% P+CORP Rank Adj P+CORP Adj rank
PAVELDATSYUK 5364 369 2.58 12.03 20.09 0.80 52.38 4.89 3 4.97 1
SIDNEYCROSBY 4042 274 3.48 9.76 7.09 0.32 53.60 5.02 2 4.90 2
HENRIKZETTERBERG 6264 390 2.78 10.40 12.69 1.07 51.80 4.63 5 4.81 3
PATRICEBERGERON 4025 308 2.22 10.12 12.07 0.78 45.42 4.03 19 4.68 4
JUSTINWILLIAMS 5690 388 2.38 8.62 17.33 0.45 52.00 4.38 6 4.42 5
RYANKESLER 5442 403 1.83 10.34 9.33 0.91 44.96 3.51 50 4.23 6
PATRIKELIAS 4889 371 2.28 11.63 11.51 0.84 54.04 4.14 14 4.09 7
BRADMARCHAND 2164 173 2.14 9.13 11.61 0.47 50.50 3.87 24 4.04 8
JOETHORNTON 6048 405 2.42 7.49 11.02 0.46 52.70 4.05 17 4.03 9
DANIELSEDIN 5367 381 2.86 17.77 14.23 0.00 65.22 5.16 1 4.01 10
RYANGETZLAF 5891 373 2.16 15.26 7.14 0.19 51.76 3.98 20 3.98 11
NICKLASBACKSTROM 3870 285 2.12 15.33 15.69 0.03 56.14 4.37 7 3.98 12
ZACHPARISE 4967 339 2.37 11.32 10.74 0.44 55.12 4.17 12 3.95 13
HENRIKSEDIN 5906 410 2.86 14.24 11.81 0.02 62.48 4.87 4 3.95 14
ALEXOVECHKIN 4776 362 2.16 13.23 14.80 0.01 55.26 4.26 10 3.95 15
MARCSAVARD 3072 222 2.34 2.86 4.63 0.36 46.25 3.42 64 3.92 16
MARTINERAT 4920 356 2.14 6.53 3.51 1.00 46.90 3.34 75 3.91 17
CHRISKUNITZ 5149 361 2.32 10.10 14.95 0.29 56.52 4.27 9 3.90 18
TYLERKENNEDY 3887 326 1.98 9.11 9.53 0.49 49.26 3.61 40 3.89 19
ALEXANDERSEMIN 4545 340 2.58 7.48 11.05 0.24 55.94 4.20 11 3.87 20
ANDREWLADD 5180 390 2.08 7.69 10.22 0.81 51.16 3.68 37 3.86 21
DAVIDBACKES 5365 397 1.99 6.67 6.44 0.74 47.00 3.34 73 3.86 22
COREYPERRY 6105 392 2.21 13.59 5.29 0.18 51.98 3.86 26 3.84 23
JOEPAVELSKI 5098 385 1.88 6.80 10.73 0.93 49.38 3.46 56 3.81 24
NIKOLAIZHERDEV 2931 220 2.04 12.63 13.08 0.34 54.83 4.03 18 3.81 25

I was caught in a "damned if you do, damned if you don't" scenario when adjusting for ozone% and Corsi Rel QOC. The Sedins are at the top of the unadjusted results, but by adjusting players like Kesler end up in the top 10, despite barely cracking top 50 unadjusted. Like I mentioned before, I usually prefer filtering, but presented it this way for brevity.

Rank Single Season P+CORP SEASON P+CORP Single Season S.J P+CORP SEASON P+CORP
1 ALEXOVECHKIN 2009-2010 Season 6.03 JOETHORNTON 2011-2012 Season 5.04
2 HENRIKZETTERBERG 2007-2008 Season 5.85 JOEPAVELSKI 2010-2011 Season 4.80
3 SIDNEYCROSBY 2010-2011 Season 5.70 RYANECLOWE 2010-2011 Season 4.75
4 PATRICEBERGERON 2011-2012 Season 5.62 PATRICKMARLEAU 2009-2010 Season 4.40
5 HENRIKSEDIN 2009-2010 Season 5.47 JOEPAVELSKI 2011-2012 Season 4.35
6 DANIELSEDIN 2009-2010 Season 5.41 KYLEWELLWOOD 2010-2011 Season 4.26
7 PAVELDATSYUK 2007-2008 Season 5.38 PATRICKMARLEAU 2008-2009 Season 4.18
8 PAVELDATSYUK 2008-2009 Season 5.37 JOETHORNTON 2007-2008 Season 4.15
9 ANDREWLADD 2008-2009 Season 5.37 LOGANCOUTURE 2010-2011 Season 4.15
10 ZACHPARISE 2008-2009 Season 5.33 JOETHORNTON 2009-2010 Season 4.12
11 JUSTINWILLIAMS 2007-2008 Season 5.33 JOEPAVELSKI 2009-2010 Season 4.10
12 MARIANHOSSA 2008-2009 Season 5.26 TORREYMITCHELL 2010-2011 Season 4.04
13 BRADMARCHAND 2011-2012 Season 5.22 JOEPAVELSKI 2008-2009 Season 3.71
14 PATRICEBERGERON 2010-2011 Season 5.18 JOETHORNTON 2008-2009 Season 3.71
15 ALEXANDERSTEEN 2011-2012 Season 5.16 MANNYMALHOTRA 2009-2010 Season 3.64
16 PAVELDATSYUK 2010-2011 Season 5.09 RYANECLOWE 2009-2010 Season 3.63
17 TYLERSEGUIN 2011-2012 Season 5.09 MILANMICHALEK 2008-2009 Season 3.58
18 SIDNEYCROSBY 2007-2008 Season 5.09 LOGANCOUTURE 2011-2012 Season 3.55
19 JOETHORNTON 2011-2012 Season 5.04 PATRICKMARLEAU 2010-2011 Season 3.49
20 ALEXBURROWS 2008-2009 Season 5.02 PATRICKMARLEAU 2011-2012 Season 3.49
21 SIDNEYCROSBY 2009-2010 Season 4.96 DANYHEATLEY 2009-2010 Season 3.34
22 JUSTINWILLIAMS 2010-2011 Season 4.92 DEVINSETOGUCHI 2008-2009 Season 3.33
23 JOHANFRANZEN 2008-2009 Season 4.90 JOETHORNTON 2010-2011 Season 3.05
24 DANIELSEDIN 2008-2009 Season 4.89 RYANECLOWE 2008-2009 Season 3.04
25 CLAUDEGIROUX 2010-2011 Season 4.85 MILANMICHALEK 2007-2008 Season 2.84

No surprises for me when it comes to either column. That 2010-2011 season for the Sharks saw a lot of production from a lot of players. The fact that JT's 2011-2012 campaign outshines every other year tells you something about the role he was given last year. Wellwood's number is really interesting. He only played in 35 games, a small sample, and posted a fantastic 4.26. A year later playing top 6 minutes with the Jets and Wellwood's P+CORP? A 4.27, how's that for reliable? Both those years are well above his career average, but maybe he has finally found a good role.

P+CORP for Defensemen

Defensemen P+CORP = P/60 + (Corsi Rel + 2) / 10 + (Corsi On + 2) / 10 + (Corsi Rel Qoc + 0.5) / 2

The difference between forwards and defensemen is so substantial that nearly every stat is effected by the difference in roles, and P+CORP is no exception. A defensemen's responsibility is is to prevent the opposition from producing goals. The unfortunate thing is we don't have anything such as negative Points/60, because we can't as easily assign the value a goal against to a specific player. However, defensemen still contribute a fair amount of offense, just not nearly as much as forwards. Subsequently, we have to add another stat to P+CORP for defensemen, Corsi Rel QOC, which is our best understanding of the level of competition a defensemen faces. Normally I advocate for filtering contextual stats, rather than adjusting for them outright, but the level of competition a defensemen faces is so important to their role that it's incorporation is inescapable.

### Defensemen Year to Year Correlations

TOI/60 P/60 Corsi Relative Corsi On Corsi Rel QoC P+CORP GVT Corsi Rel QOC adj P+CORP
r(self) 0.641 0.317 0.480 0.514 0.527 0.551 0.586 0.541
r(p) 0.155 0.317 0.352 0.286 -0.055 0.380 0.385 0.392
r(toi) 0.641 0.238 0.199 0.184 0.404 0.299 0.447 0.311
r(GVT) 0.363 0.367 0.398 0.392 0.177 0.501 0.586 0.510
r(pdo) 0.008 -0.022 0.013 0.061 0.026 0.039 0.039 0.035

### General Information

Name Mean Standard Deviation
Forward P+CORP 2.43 1.19