Every now and again someone asks me how I calculate HARO, HARD and HART ratings that you can find on stats.hockeyanalysis.com and it is at that point I realize that I don’t have an up to date description of how they are calculated so today I endeavor to write one.

First, let me define HARO, HARD and HART.

HARO – Hockey Analysis Rating Offense
HARD – Hockey Analysis Rating Defense
HART – Hockey Analysis Rating Total

So my goal when creating then was to create an offensive defensive and overall total rating for each and every player. Now, here is a step by step guide as to how they are calculated.

Calculate WOWY’s and AYNAY’s

The first step is to calculate WOWY’s (With Or Without You) and AYNAY’s (Against You or Not Against You). You can find goal and corsi WOWY’s and AYNAY’s on stats.hockeyanalysis.com for every player for 5v5, 5v5 ZS adjusted and 5v5 close zone start adjusted situations but I calculate them for every situation you see on stats.hockeyanalysis.com and for shots and fenwick as well but they don’t get posted because it amounts to a massive amounts of data.

(Distraction: 800 players playing against 800 other players means 640,000 data points for each TOI, GF20, GA20, SF20, SA20, FF20, FA20, CF20, CA20 when players are playing against each other and separate of each other per season and situation, or about 17.28 million data points for AYNAY’s for a single season per situation. Now consider when I do my 5 year ratings there are more like 1600 players generating more than 60 million datapoints.)

Calculate TMGF20, TMGA20, OppGF20, OppGA20

What we need the WOWY’s for is to calculate TMGF20 (a TOI with weighted average GF20 of the players teammates when his team mates are not playing with him), TMGA20 (a TOI with weighted average GA20 of the players teammates when his team mates are not playing with him), OppGF20 (a TOI against weighted average GF20 of the players opponents when his opponents are not playing against him) and OppGA20 (a TOI against weighted average GA20 of the players opponents when his opponents are not playing against him).

So, let’s take a look at Alexander Steen’s 5v5 WOWY’s for 2011-12 to look at how TMGF20 is calculated. The columns we are interested in are the Teammate when apart TOI and GF20 columns which I will call TWA_TOI and TWA_GF20. TMGF20 is simply a TWA_TOI (teammate while apart time on ice) weighted average of TWA_GF20. This gives us a good indication of how Steen’s teammates perform offensively when they are not playing with Steen.

TMGA20 is calculated the same way but using TWA_GA20 instead of TWA_GF20. OppGF20 is calculated in a similar manner except using OWA_GF20 (Opponent while apart GF20) and OWA_TOI while OppGA20 uses OWA_GA20.

The reason why I use while not playing with/against data is because I don’t want to have the talent level of the player we are evaluating influencing his own QoT and QoC metrics (which is essentially what TMGF20, TMGA20, OppGF20, OppGA20 are).

Calculate first iteration of HARO and HARD

The first iteration of HARO and HARD are simple. I first calculate an estimated GF20 and an estimated GA20 based on the players teammates and opposition.

ExpGF20 = (TMGF20 + OppGA20)/2
ExpGA20 = (TMGA20 + OppGF20)/2

Then I calculate HARO and HARD as a percentage improvement:

HARO(1st iteration) = 100*(GF20-ExpGF20) / ExpGF20
HARD(1st iteration) = 100*(ExpGA20 – GA20) / ExpGA20

So, a HARO of 20 would mean that when the player is on the goal rate of his team is 20% higher than one would expect based on how his teammates and opponents performed during time when the player is not on the ice with/against them. Similarly, a HARD of 20 would mean the goals against rate of his team is 20% better (lower) than expected.

(Note: The OppGA20 that gets used is from the complimentary situation. For 5v5 this means the opposition situation is also 5v5 but when calculating a rating for 5v5 leading the opposition situation is 5v5 trailing so OppGF20 would be OppGF20 calculated from 5v5 trailing data).

Now for a second iteration

The first iteration used GF20 and GA20 stats which is a good start but after the first iteration we have teammate and opponent corrected evaluations of every player which means we have better data about the quality of teammates and opponents the player has. This is where things get a little more complicated because I need to calculate a QoT and QoC metric based on the first iteration HARO and HARD values and then I need to convert that into a GF20 and GA20 equivalent number so I can compare the players GF20 and GA20 to.

To do this I calculate a TMHARO rating which is a TWA_TOI weighted average of first iteration HARO. TMHARD and OppHARO and OppHARD are calculated in a similar manner. TMHARD, OppHARO and OppHARD are similarly calculated. Now I need to convert these to GF20 and GA20 based stats so I do that by multiplying by league average GF20 (LAGF20) and league average GA20 (LAGA20) and from here I can calculated expected GF20 and expected GA20.

ExpGF20(2nd iteration) = (TMHARO*LAGF20 + OppHARD*LAGA20)/2
ExpGA20(2nd iteration) = (TMHARD*LAGA20 + OppHARD*LAGF20)/2

From there we can get a second iteration of HARO and HARD.

HARO(2nd iteration) = 100*(GF20-ExpGF20) / ExpGF20
HARD(2nd iteration) = 100*(ExpGA20 – GA20) / ExpGA20

Now we iterate again and again…

Now we repeat the above step over and over again using the previous iterations HARO and HARD values at every step.

Now calculate HART

Once we have done enough iterations we can calculate HART from the final iterations HARO and HARD values.

HART = (HARO + HARD) /2

Now do the same for Shot, Fenwick and Corsi data

The above is for goal ratings but I have Shot, Fenwick and Corsi ratings as well and these can be calculated in the exact same way except using SF20, SA20, FF20, FA20, CF20 and CA20.

Goalies are a little unique in that they only really play the defensive side of the game. For this reason I do not include goalies in calculating TMGF20 and OppGF20. For shot, fenwick and corsi I do not include the goalies on the defensive side of things either as I assume a goalie will not influence shots against (though this may not be entirely true as some goalies may be better at controlling rebounds and thus secondary shots but I’ll assume this is a minimal effect if it does exist). The result of this is goalies do have a HARD rating but no HARO, or shot/fenwick/corsi based HARD or HARO rating.

I hope this helps explain how my hockey analysis ratings are calculated but if you have any followup questions feel free to ask them in the comments.

With the Los Angeles Kings on the verge of winning the Stanley Cup and teams already making moves towards next seasons (i.e. Vokoun to Pittsburgh) it is time to take a closer look at class of unrestricted free agents.  Today I’ll take a look at the free agent forwards.

As I have mentioned previously, I feel the best and most reliable player ratings are my 5v5 zone start adjusted HARO+ offensive rating, HARD+ defensive rating and the combined HART+ rating (yes, I am biased but as far as single all inclusive ratings go, I feel these are the best) using the past 3 seasons of data.  So, with that in mind, here are how the 2012 unrestricted free agent forwards stack up.

I have a ton of information on my stats website stats.hockeyanalysis.com but one of the things I have always wanted to do is to make it more visual and I’d like to announce the first step in that process.  Thanks to google and their cool google chart api I have now added bubble charts when you do a stats search that returns no more than 30 players (more than 30 players makes the bubble charts too cluttered).  For example, if you did a search of all Maple Leaf Skaters with 500 minutes of 5v5 zone start adjusted ice time this past season you will see a nice bubble chart at the bottom plotting each players defensive rating (i.e. HARD+) along the horizontal axis and their offensive rating along the vertical axis (i.e. HARO+).  Or you can see the same thing using corsi ratings (i.e. CorHARD+ vs CorHARO+) if you are one of those people who prefer corsi based ratings.  Or, if you prefer, you can even look at multi-year goal ratings such as 3 year 5v5 zone start adjusted goal ratings for the Toronto Maple Leafs (though still not perfect, I believe 3 year goal ratings are the best indicator of a players value).

In the charts, forwards and defensemen are differentiated by different colors and the size of the bubble is indicative of the amount of time the player was on the ice for (the largest bubbles for the players with the most ice time and the smallest bubbles for the players with the least).  As always with my ratings, any value over 1.00 is above average and any rating below 1.00 is below average and these ratings take into account quality of teammates and quality of opposition and the players on-ice statistics.  This means players with bubbles to the right side of the chart are stronger defensive players and players with bubbles towards the top of the chart are stronger offensive players.  The best players are good at both and thus have their bubbles in the upper right quadrant.   Players with bubbles in the lower right quadrant are the worst performing players.  The nice thing about these charts is it gives a very easy to read visual representation of every player on a team.

I am hoping that this is just a start of things to come with more charting enhancements (and others as well) to be implemented in the future.  As always, if you have any suggestions submit a comment below or drop me a message.

So word has come out over the last day that Rick Nash is, at least on some level, available in a trade from the Blue Jackets.  So, the question is, who is Rick Nash and would you want him on your team?

Nash has been a Blue Jacket from the day he was drafted first overall in 2002.  He has played 648 regular season games and has scored 277 goals and 527 points.  Since the lockout he is 10th in goals (only Ovechkin, Kovalchuk, Heatley, Iginla, Staal, Lecavalier, Marleau, Vanek and Hossa) and 25 in points.  He has a pair of 40+ goals seasons and has been a 30+ goal scorer six times.  He has just 4 NHL playoff games under his belt when he scored 1 goal and a pair of assists.  He was a member of the 2010 Canadian Olympic team scoring a pair of goals and 3 assists in 7 games on route to the gold medal.  That is the raw facts that we all know about Nash.  But what about advanced statistics.

Here are my HockeyAnalysis ratings for Rick Nash over the past 4 seasons plus this season as well as his 2007-11 four year average.

 2007-08 2008-09 2009-10 2010-11 2011-12 2007-11 (4yr) HARO+ 0.991 1.070 1.257 1.502 1.079 1.200 HARO+ rank 142/235 118/241 59/245 8/260 116/229 60/217 HARD+ 0.827 0.992 0.802 0.882 0.732 0.895 HARD+ rank 164/235 96/241 196/245 162/260 197/229 162/217 HART+ 0.909 1.031 1.030 1.192 0.905 1.047 HART+ rank 172/235 115/241 123/245 36/260 169/229 95/217

HARO+ is an offensive rating, HARD+ is a defensive rating and HART+ is his total/overall rating which is simply an average of his HARO+ and HARD+ ratings.  These ratings are for 5v5 close zone adjusted situations and the rank includes any players who played 400 ore more minutes in single seasons, 300 minutes for 2011-12 partial season (through this past Saturday’s games) and 1500 minutes for the 4 year average.  These ratings take into account quality of teammates and quality of competition.

Overall in 5v5 close situations Rick Nash looks to be a solid offensive player, but not elite overall and defensively he is relatively weak.

To put Nash’s 4 year numbers in perspective, the most closely ranked players in terms of HARO+ are Cammalleri, Weiss, Hemsky, Jussi Jokinen, Vanek, Boyes, Bertuzzi, Grabovski, Alfredsson and Parise.

How about Nash’s 5v4 power play numbers.

 5v4 HARO+ 2007-08 1.010 2008-09 0.853 2009-10 1.203 2010-11 0.902 2011-12 0.951 2007-11 (4yr) 0.967 2007-11 rank (500 min.) 154/184 2007-11 rank (750 min.) 92/99

Generally speaking, his PP numbers are quite poor relative to other top PP forwards.

An interesting comparable is Joffrey Lupul.  It is an interesting comparable because it is quite likely that the Leafs will have an interest in Rick Nash and also because Lupul is an interesting case because he has really had a break through season this year.  Or so it seems anyway.

 Nash Lupul 2007-11 5v5close HARO+ 1.200 1.385 2007-11 5v5 HARO+ 1.080 1.118 2007-11 5v4 HARO+ 0.967 1.246

It’s interesting that Joffrey Lupul ranked better than Nash in each of the three categories.  Due to injury Lupul didn’t put up 1500 minutes of 5v5 close ice time (he had 1374:44), but of all 251 players to play 1350 minutes of 5v5 close ice time Lupul ranked 10th.  When looking at these numbers it is actually not a surprise to see Lupul tied for 5th in points and 17th in goals.  He is finally being given an opportunity to play big time first line minutes with offensive zone starts and #1 PP unit ice time and as a result, he is producing.

So, getting back to Nash, let’s take a look at how he has done with his various linemates over the previous four seasons.  Here are the scoring rates (goals for per 20 minutes) for all the forwards who have played at least 250 minites of 5v5 close zone adjusted minutes during the 2007-11 four year time period.

 Linemate TOI Together Nash /wo Linemate Linemate /wo Nash Huselius 969:45 0.969 0.938 0.907 Vermette 607:35 0.757 1.016 0.782 Umberger 448:34 0.803 0.985 0.845 Brassard 441:22 1.359 0.860 0.930 Voracek 426:33 1.313 0.873 1.020 Malhotra 425:06 0.894 0.963 0.790

Nash played best when he was paired up with Voracek and Brassard and only Voracek, Brassard and Huselius made Nash a better offensive player when playing with him.  Vermette, Umberger and Malhotra were drags on his offensive numbers.  When playing apart, Voracek’s numbers are better than Nash’s.  Same for Brassard’s (who is doing it again this year, 0.782 GF20 vs Nash’s 0.613 when apart).  As an aside, the numbers suggest that Voracek is a very good offensive player  and it was probably a big mistake to trade him.  It also suggest that the Flyers aren’t getting full value from him by playing him primarily with Maxime Talbot.  If someone acquired Voracek and put him in the right situations, he could be the next Joffrey Lupul.

So, to summarize, yes Nash is a good offensive player who may put up better numbers playing with better offensive players but he is probably not an elite offensive forward.  Also, he isn’t a great defensive forward so offense really is what you get him for.  If I were Columbus I would be willing to trade him if I can get a quality NHL ready player capable of playing in their top 6 forwards, a top tier prospect and a first round pick.  If I were other teams, I would be very wary of over paying because he is not an elite player but he is paid like one (\$7.8M cap hit for 6 more seasons).

I wrote an article a few weeks ago about the offensive and defensive contribution (i.e. their HARO+ or HARD+ rating multiplied by ice time) of each position (C, LW, RW, D and G) but I have come to realize that my methodology is incorrect and thus the conclusions are incorrect (at least when looking at league-wide results).  The reason is, in my rating system contribution is evenly distributed among the 5 players on the ice so if I sum up all contributions of all players playing at a particular position I should see each position be given an equal share, and for the most part that is what I saw.  The exception being centers being given more influence and wingers less, this is because players that are listed as being centers often play the wing where as wingers are less often on the ice playing as centers.

The proper method for identifying the contribution a position has on offense and defense is not to sum up their contribution but to look at the variation observed in the players ratings for that position.  Recall that with my ratings a 1.00 is a neutral rating or an indication that the player has no positive or negative effect for that aspect of the game (offense or defense) compared to the expected level of performance when quality of competition and quality of teammates are considered.  Anything less than 1.0 implies a negative impact and anything above 1.0 implies a positive impact.  So, if a position can significantly influence offensive production then we should see a larger variance among centers HARO+ ratings.  The good players at that position will have ratings well above 1.00 and the weaker players well below 1.00.  For positions that do not have a significant impact we should see players at that position have ratings much closer to 1.00 and less variation between the best and worst players.   So, here is what we find.

 HARO+ HARO+ HARD+ HARD+ HART+ HART+ Position Average StdDev Average StdDev Average StdDev C 0.918 0.171 0.994 0.116 0.956 0.091 RW 0.927 0.162 1.001 0.096 0.965 0.084 LW 0.939 0.167 0.993 0.099 0.966 0.086 D 0.894 0.095 0.990 0.101 0.942 0.068 G 0.984 0.080 0.992 0.040

The above uses four year ratings (2007-11) and only forwards and defensemen with at least 2000 minutes of 5v5 even strength ice time and goalies with 3000 minutes were considered.  The resulting group included 122 centers, 85 LW, 103 RW, 194 defensemen and 53 goalies.

On offense, the three forward positions have significantly higher standard deviations (0.162-0.171) than defensemen (0.095) which intuitively makes sense.  It means that forwards have a greater ability to influence offensive production than defensemen which is no surprise.  Defensively the greatest variation in HARD+ occurs for centers with defensemen and wingers more or less the same a step below centers and goalies another step back again.  It is possible centers rank ahead of wingers and defensemen in part because they are the ones who take face offs and thus are a major factor in the team gaining control of the puck.

The other thing that you’ll notice is that for HARO+ the average rating is well below 1.00 for both the forwards and the defense.  This probably indicates that the big minute players are the offensive players which makes the average rating (which is ice-time neutral) well below the ice time weighted average (which in theory should be very close to 1.00).  Lets take a look at how the players rate according to total ice time.

Centers

 Ice time HARO+ HARD+ HART+ >4000 min. 1.042 0.968 1.005 3000-3999 0.906 0.988 0.947 2000-2999 0.864 1.015 0.940 1000-1999 0.784 1.025 0.905

Left Wing

 Ice time HARO+ HARD+ HART+ >4000 min. 1.089 0.939 1.014 3000-3999 0.987 0.990 0.989 2000-2999 0.824 1.015 0.920 1000-1999 0.760 1.036 0.899

Right Wing

 Ice time HARO+ HARD+ HART+ >4000 min. 1.071 0.963 1.018 3000-3999 0.953 1.003 0.979 2000-2999 0.871 1.008 0.940 1000-1999 0.775 1.047 0.911

For the three forward positions it is clear that the top offensive players get the most playing time while players who get less playing time are slightly better defensive players.  This isn’t really a big surprise as the majority of a team’s offense comes from their top line(s).  The question is, how much does coaching/playing style influence the results.  By that I mean, would first line forwards be better defensively if they were on the third line and asked to play a defensive role as opposed to being on the first line and being asked to and expected to produce offense?  I suspect for most players the answer would be yes.  I suspect the reverse (third/fourth line guys having better offensive ratings if given first line roles) is also true, but probably to a lesser extent.

Defense

 Ice time HARO+ HARD+ HART+ >5000 min. 0.923 0.988 0.955 4000-4999 0.919 0.997 0.958 3000-3999 0.871 0.998 0.934 2000-2999 0.874 0.974 0.923 1000-1999 0.864 1.025 0.944

For defensemen the best offensive defensemen still get the most ice time, though the variation is much less than seen with the forwards.  Defensive ability seems to have very little variation across ice times until you get to the lower minute players who appear to be more defensive specialists.

Goalie

 Ice time HARD+ >10000 min. 1.040 >8000 min. 1.028 >6000 min. 1.012 >4000 min. 0.992 >2000 min. 0.984

As one would expect, the best goalies are given the most time in goal.  There were 9 goalies with greater than 10,000 minutes of 5v5 ice time and all had ratings over 1.00 except Tomas Vokoun whose rating was 0.978.  According to my rating system, Vokoun is a pretty ordinary goalie which means he is likely one of the more over rated goalies in the NHL because some (or most) consider him elite.  It’ll be interesting to see where he ends up this summer as a UFA and how that team performs next year.  Could Vokoun be another goalie failure in Philadelphia?  Could happen.

The best and most consistent line for the Maple Leafs this past season was the Grabovski-Kulemin-MacArthur line.  This trio of forwards are all just entering their primes at ages 27, 24 and 26 respectively and they were the second, third and fourth leading point producers on the Leafs.  I thought it might be interesting to take a look at how these three guys careers have progressed up to now.  Here are each players basic stats over the past 4 seasons (3 for Kulemin) along with their 5v5 even strength HARO+, HARD+ and HART+ statistics (my HockeyAnalysis.com offense, defence and total ratings).

 Season Games Goals Assists Points +/- HARO+ HARD+ HART+ 2007-08 24 3 6 9 -4 1.185 0.641 0.913 2008-09 78 20 28 48 -8 0.959 0.891 0.925 2009-10 59 10 25 35 3 1.209 0.904 1.057 2010-11 81 29 29 58 14 1.343 1.064 1.204 2008-11 (3 yr) 218 59 82 141 9 1.137 0.972 1.055

In limited ice time he showed some decent offensive capabilities in his rookie 2007-08 season and progressed nicely in 2008-09 statistically but his ratings suffered some.  Many people considered his injury shortened 2009-10 season to be a bit of a disappointment but his HARO+ rating indicates that he really helped his team offensively when he was on the ice and in 2010-11 he took his offensive game to another level again.  Of the 221 players who have played at least 1500 minutes of 5v5 even strength ice time over the past 2 seasons, Grabovski ranks 18th in HARO+ and 24th in HART+ which is outstanding.

 Season Games Goals Assists Points +/- HARO+ HARD+ HART+ 2008-09 73 15 16 31 -8 1.092 0.757 0.925 2009-10 78 16 20 36 0 1.050 1.034 1.042 2010-11 82 30 27 57 7 1.264 1.024 1.144 2008-11 (3 yr) 233 61 63 124 -1 1.109 0.952 1.030

Kulemin had a more than respectable 15 goal rookie season and he showed that his good shot will work in the NHL but last season was a bit of a breakout year for him even though he didn’t dramatically improve his offensive numbers.  It was a breakout season because he really learned how to assert himself physically.  He isn’t a big physically imposing player, but he is strong on his skates and has learned that he can hold his own against opposing forwards.  This has really helped his defensive game and then this year he took his offensive game to another level.  Kulemin ranks 57 in HARO+ and 40th in HART+ among forwards over the past 2 seasons.

 Season Games Goals Assists Points +/- HARO+ HARD+ HART+ 2007-08 37 8 7 15 3 1.219 0.922 1.070 2008-09 71 17 14 31 -4 0.941 0.902 0.922 2009-10 81 16 19 35 -16 0.983 0.792 0.887 2010-11 82 21 41 62 -3 1.206 0.971 1.089 2008-11 (3 yr) 234 54 74 128 -23 1.025 0.904 0.964

Of the three players, MacArthur has clearly been the lease consistent so far in his career, offensively anyway.  He showed some good things in limited action in his rookie year but his offensive production stagnated for a couple seasons before taking a jump forward his season.  Defensively he has been mostly mediocre for his whole career so far.  Overall we can be less certain about what MacArthur will bring to the Leafs in the future.  At best I think he is a decent second line center who can provide some secondary offense.

Of the three players, I think MacArthur is the least valuable and the Leafs will have to make a decision on where he fits in going forward.  He probably has more pure playmaking skills than either Grabovski or Kulemin which makes him a good fit for that line.  Overall thought he is easily replaceable and a decision will have to be made as to whether to whether to keep him around and at what salary.  An alternative would be to work a youngster such as Kadri onto that line either at wing or at center (moving Grabovski, who struggles at the face off dot, to wing) and use MacArthur as trade bait to fill a hole elsewhere.

Before I get into the main subject of this post let me first point out that I have updated stats.hockeyanalysis.com to include all 1, 2, 3 and 4 year player ratings that can be calculated using the last 4 years of NHL data.  For more information on my player ratings read this.

I generate offense, defense and overall ratings for each and every player in the NHL and I wanted to get an idea of how much each position contributes to the performance of the team.  To accomplish this I multiplied each players offensive and defensive ratings (HARO+, HARD+) by their ice time (5v5 ratings and ice time used) and summed them up by position and then compared the positions total to the overall total.  I did this using the ratings calculated for the past 4 seasons combined as well as for each of the past 4 individual seasons.  This is the result I came up with :

Offense:

 Season(s) Center RW LW D D 2007-11 24.64% 18.04% 17.14% 20.09% 20.09% 2007-08 26.91% 16.22% 16.47% 20.20% 20.20% 2008-09 25.23% 18.01% 16.66% 20.05% 20.05% 2009-10 23.93% 18.47% 17.49% 20.06% 20.06% 2010-11 25.13% 18.02% 16.76% 20.04% 20.04%

Defense:

 Season(s) Center RW LW D D G 2007-11 20.67% 15.08% 14.27% 16.72% 16.72% 16.55% 2007-08 22.46% 13.83% 13.81% 16.75% 16.75% 16.39% 2008-09 21.06% 15.49% 13.76% 16.67% 16.67% 16.35% 2009-10 19.98% 15.46% 14.79% 16.73% 16.73% 16.30% 2010-11 21.35% 15.08% 14.21% 16.51% 16.51% 16.35%

Average of Offense + Defense:

 Season(s) Center RW LW D D G 2007-11 22.65% 16.56% 15.71% 18.40% 18.40% 8.28% 2007-08 24.69% 15.03% 15.14% 18.48% 18.48% 8.19% 2008-09 23.14% 16.75% 15.21% 18.36% 18.36% 8.17% 2009-10 21.95% 16.96% 16.14% 18.39% 18.39% 8.15% 2010-11 23.24% 16.55% 15.48% 18.27% 18.27% 8.17%

Note:  I split the defense contribution over 2 positions.

Now, the first thing I noticed with these numbers is how surprisingly consistent they are from season to season, especially for defense and goaltending.  Up front players frequently shift from center to wing and from left wing to right wing so that may account for some of the (still relatively small) seasonal fluctuations.  Maybe I shouldn’t be surprised at this consistency but it does give me some confidence in my rating system that it is consistent across seasons as well as with multiple season ratings.

The second thing that caught my attention was the importance of defensive contribution to the offense.  Approximately 40% of offensive production can be attributed to the two defensemen on the ice and the defensemen are more important than the wingers. Part of this is simply that defensemen get more ice time than forwards since there are only 3 defense pairs versus 4 forward lines.  The other part is probably that they play an integral part of collecting rebounds and transitioning the team from defense to offense so they may have greater influence in the percentage of time played in the offensive zone.

Of the three forward positions, the center position is clearly the most important but we probably figured that.  Face offs might be a contributing factor but also we might just find that the most talented players end up playing center.  Right wings are slightly more important than left wings but the difference is not substantial.

Next I wondered what this data would mean to what teams should allocate for salaries.  For a 60 million payroll the average salary for position should work out to the following:

 Pos Salary (Million\$) Center 13.6 RW 9.9 LW 9.4 D 11.0 D 11.0 G 5.0

Of course elite players skew the team payroll structure a fair bit.  As a LW earning over \$9.5M Alexander Ovechkin is eating up the entire Capitals allotment for LWs and Crosby, Malkin and Staal are way over budget for the Penguins but you have to work around the talent you have.  A couple months ago Behind the Net Hockey Blog had a post outlining the salary allocated to players by position (split between forwards, defense, and goaltending).  Forwards were allocated 59.1% of a teams payroll, defense 32.2% and goaltending 8.7% over the past 4 seasons which compares to 54.9%, 36.8% and 8.3% for my ratings.  That would mean that forwards are overpaid (relative to their contribution) by about 4.1%, defense under paid by 4.6% and goalies over paid by about 0.4%.

For interest sake I decided to take a look at the Vancouver Canucks performance distribution since they have a fairly well balanced team and are a serious cup contender.  Here is what I found:

 2007-11 2010-11 Position Offense Defense Average Offense Defense Average Center 23.44% 19.96% 21.70% 21.04% 17.15% 19.10% RW 11.44% 9.88% 10.66% 9.97% 10.34% 10.15% LW 25.14% 21.88% 23.51% 31.12% 25.11% 28.11% D 19.99% 17.21% 18.60% 18.94% 15.92% 17.43% D 19.99% 17.21% 18.60% 18.94% 15.92% 17.43% G 0.00% 13.86% 6.93% 0.00% 15.55% 7.77%

(Note:  The above is calculated using the current roster using the ratings and ice time over the past season or four seasons regardless of whether that ice time was with the Canucks.  This is an evaluation of the team ending the 2010-11 season with the Canucks, not the Canucks team performance over past seasons.  Also four season ratings should give a better player evaluation than single season ratings due to the larger sample size so I would consider them closer to true value.)

The Canucks are definitely a team driven by a group of quality left wingers or at least players listed as playing LW such as D. Sedin, Burrows, Raymond, Torres but I suspect some get shifted to RW from time to time.  Also, as good as Luongo is the quality and depth of the team in front of him reduces his relative contribution to his team to below average levels.  In the future I’ll take a look at some other teams as it’ll be interesting to see how goalie contribution changes from good teams with subpar  goalies (Detroit maybe) to bad teams with good goalies (Florida – Vokoun!! Though my ratings don’t value him as highly as many others do).

I have been pretty quiet here recently not because of a lack of things I want to write about but because I needed to get my stats site up and running first so I can reference it in my writings.  Plus, getting my stats site up has been on my todo list for a real long time.  There will be a lot more stats to come including my with/against on ice pairing stats which I had up a season or two ago and many of you found interesting as well as team stats but for now let me explain what is there.

What you will find there now is my player rating system which produces the following ratings:

HARD – Hockey Analysis Rating – Defense

HARO – Hockey Analysis Rating – Offense

HART – Hockey Analysis Rating – Total

HARD+ – Hockey Analysis Rating – Defense

HARO+ – Hockey Analysis Rating – Offense

HART+ – Hockey Analysis Rating – Total

HARD is the defensive rating and is calculated by taking expected goals against while on the ice and dividing it by actual goals against while on the ice.  The expected goals against is calculated by taking the average of a players team mates goals against per 20 minutes (TMGA20) and averaging it with the players opposition goals for per 20 minutes (OppGF20).  Similarly HARO is calculated by taking a players actual goals for while on the ice and dividing it by the expected goals against while on the ice.  For both, a rating above 1.00 means that the player helped the team perform better than expected when he was on the ice where as a rating below 1.00 means the player hurt the teams performance when he was on the ice.  HART is just an average of HARD and HARO.

HARD+, HARO+ and HART+ are enhanced ratings which result from an iterative process that iteratively feeds HARD and HARO ratings into an algorithm to refine the ratings.  For the most part this iterative process produced a nice stable state but sometimes the algorithm goes haywire and things fail (i.e. for a particular season or seasons).  For this reason I am calling the + ratings experimental but if you don’t see anything wacky (i.e. large differences in every players ratings) they should be considered reliable and probably better ratings than the straight HARD, HARO and HART ratings.  Anything better than 1.00 should be considered better than the average player and anything less than 1.00 should be considered below average.

On Monday I outlined an all-encompassing player evaluation model that allows us to evaluate every forward, defenseman and goalie under the same methodology.  In short, the system compares how many goals are scored for and against while a player is on the ice and compares it to how many goals scored for/against one should expect based on the quality of his line mates and opposition.  That model, I believe, makes a reasonable attempt at evaluating a players performance, but it can be improved.

The first method of improvement is to utilize the additional information we have about the quality of a players line mates and opposition once we have run the model.  Initially I use the goals for and against performance of his line mates and opposition when the player being evaluated is not on the ice at the same time as his line mates and opposition.  But now that we have run the model we, at least theoretically, have a better understanding of the quality of his team mates and opposition.  I can then take the output of the first model run and use it as the input of the second model run to get new and better results.  I can then continue doing this iteratively and the good news is that after every iteration the difference between the player rating from that iteration and the previous iteration trends towards zero which is a very nice result.