## December 22, 2006

### Player Value Part III

It’s been a little less than a week since I released part II of my player evaluations. In this release I’m not using the term “rank”. This is a statistics that measure how well these players have played so far, whether that makes them the best player or lucky is a matter of opinion as it always is with statistics. If there were no opinion then we could just evaluate players based on salary (perfect correlation of performance to pay). There are still small tweaks I can make to the algorithm improve, however this is about as good as it will get. Remember also, that this evaluates player’s performance at even strength which accounts for 65% of all goals and 72% of ice time.

The most significant change was to regress to the mean, this means that I look at each player’s score and ask the question: “is it more likely this player is average than actually this good”. So a player with seven goals against per hour in one game might be extremely bad, but it’s more likely that they were unlucky and are actually only “semi-bad”. Using an estimated percent error as a function of ice time, I rescale each players Z score (how many standard deviations they are from average), if the amount of time is less than some amount (where percentage error >100%) I just assume the player is average until I have better data. This means that good players who’ve missed a good chunk of the season I can’t really rate. For example, Gaborik has a negative score, which will improve if he gets more ice time.

Since the regression doesn’t care about individual scores, but the scores of all possible cross products I had to rescale every pair using the above logic. So if a pair doesn’t play much together, but got a ton of goals in the time I just assume it was all luck and give them an average number of goals. So this regression primarily looks at significant pairings and ignores the insignificant pairings. This also prevents the regression from blowing up in both directions and makes the results in a much smaller band.

A good/poor score can be the result of coaching usage, player confidence, ability, luck etc. This is not a definitive number telling you how good a player is at even strength, but rather attempts to explain how they have done, whether that’s an anomaly or not is a matter of opinion. So with the technical discussion over a short list, the rest is available at my site.

Canucks
 N F Lastname V 1 H SEDIN 0.36 2 D SEDIN 0.33 3 M NASLUND 0.21 4 M OHLUND 0.12 5 K BIEKSA -0.03 6 J GREEN -0.10 7 S SALO -0.11 8 M CHOUINARD -0.14 9 B MORRISON -0.14 10 T LINDEN -0.15 11 A BURROWS -0.15 12 J BULIS -0.23 13 R KESLER -0.28 14 T PYATT -0.29 15 M COOKE -0.37 16 L KRAJICEK -0.51 17 W MITCHELL -0.66

Wild
 N F Lastname V 1 B ROLSTON 0.09 2 K CARNEY 0.01 3 S VEILLEUX 0.00 4 M SKOULA 0.00 5 M PARRISH -0.04 6 T WHITE -0.10 7 K FOSTER -0.18 8 B BURNS -0.20 9 P BOUCHARD -0.21 10 P DUPUIS -0.25 11 B RADIVOJEVIC -0.25 12 K JOHNSSON -0.43 13 M KOIVU -0.43 14 P DEMITRA -0.50 15 N SCHULTZ -0.51 16 P NUMMELIN -0.65

Edmonton
 N F Lastname V 1 R TORRES 0.67 2 J STOLL 0.40 3 D TJARNQVIST 0.35 4 F PISANI 0.35 5 M BERGERON 0.26 6 J SMITH 0.23 7 M GREENE 0.15 8 P SYKORA 0.07 9 A HEMSKY 0.06 10 R SMYTH 0.05 11 S STAIOS -0.01 12 B WINCHESTER -0.05 13 P THORESEN -0.08 14 S HORCOFF -0.10 15 L SMID -0.12 16 M REASONER -0.12 17 J LUPUL -0.15 18 T PETERSEN -0.43

 N F Lastname V 1 K KLEE 0.61 2 J SAKIC 0.47 3 T ARNASON 0.38 4 M SVATOS 0.33 5 A BRUNETTE 0.30 6 W WOLSKI 0.18 7 J LILES 0.14 8 B MCLEAN 0.12 9 P STASTNY 0.09 10 M HEJDUK 0.06 11 O VAANANEN 0.06 12 B CLARK -0.02 13 B RICHARDSON -0.15 14 I LAPERRIERE -0.15 15 A LAAKSONEN -0.15 16 P BRISEBOIS -0.17 17 M RYCROFT -0.19 18 K SKRASTINS -0.34

Flames
 N F Lastname V 1 J IGINLA 0.70 2 R WARRENER 0.53 3 D LANGKOW 0.52 4 D PHANEUF 0.49 5 A TANGUAY 0.41 6 R HAMRLIK 0.36 7 M LOMBARDI 0.32 8 R REGEHR 0.23 9 K HUSELIUS -0.12 10 M NILSON -0.12 11 B RITCHIE -0.23 12 J LUNDMARK -0.23 13 D MCCARTY -0.25 14 C KOBASEW -0.29 15 A FERENCE -0.31 16 J FRIESEN -0.37 17 T AMONTE -0.47 18 A ZYUZIN -0.65

I’ve also been doing the same thing to my PP and SH data as a result the columns on my website are significantly different. A NETV score, which represents goal differential provided by a given player, using even strength, power play and penalty kill data. You can estimate winning percentage by (2.86+NETV)2/((2.86+NETV)2 + 2.862), which might be more intuitive to readers. PP+, PP-, SH+, SH- are functions of goals for and shots against and do not represent typical plus minus numbers, they attempt to credit the player who is responsible for the goal rather than all players equally.

NETV =
+ V
+ (PP+ - PP- - PPavg)*PPhours/(0.15*Games)
+ (SH+ - SH- + SHavg)*SHhours/(0.15* Games)

I’m not quite satisfied with the constant used in the algorithm at this point to say these results are very good, but they are useful. All the NETV scores are on my website.

I want to do some more interesting analysis in the next week, so I’ll avoid dealing with my player rating system for a while, so I’ll keep these results for now. Not sure what topic I’ll cover next. It’s been a while since some of my more detailed better articles came out.

## December 18, 2006

### Player Ranking attempt II

I’ve been working on one primary scheme to determine who responsible for the performance. I have chosen a regression on the performance of all team’s players cross products to determine who is responsible for the goals for and against. My last attempt was criticized and for good reason as I choose to use expected goals, which are a poor measure of actual goals to predict offensive ability. A player like Iginla who hasn’t taken many good shots, but has scored a bunch of goals (or had goals scored while on the ice) was completely underrated by my old system and this was noted to me. So I choose instead to use goals (I will continue to use expected goals against as their variability almost perfectly matches expected random variation, with a few exceptions). By using goals, I have chosen to increase my variability three times in order to have more accurate information, this means it’s a lot easier for a player to get randomly into the top groups, so these numbers measure “possible talent” as apposed to actual talent and similarly on the low end.

Last time I only used the team to determine skill level, this time I included strength of opposition. I calculated the same regression as the previous article for offense and defense. Then I multiplied the ice time of every opponent by the score of the opponent and divided by the total number of seconds of match ups to get an average score of the opposition for the given player. (So if you spend all of your 1000 seconds against only Iginla I’ll give you an opposition offensive score of 4.3 [Iginla’s score]), basically I consider the opposition score the expected number of goals against, now if a player is better than average they should be able to lower the number (have fewer goals against than average). So I calculate the players score for goals for and against and subtract opposition’s defensive score from their goals for per hour and opposition offensive score from defensive, then I just subtract their “plus” (offensive score) from their “minus” (defensive score):
(Even strength G/hr – Even strength opposition GA/hr)
- (Even strength GA/hr – Even strength opposition G/hr)
= VAL
This means if you score a lot of goals against an opposition that allows a lot of goals your score won’t improve, but if you have very few goals against a very tough opposition your score won’t be hurt either. Now differences in strength of opposition are not that different, but they are different, so the players performance scores are much more important than their opposition’s score, however opposition scores help remove the team effects so these scores should be comparable across teams and they are not effected by line mates significantly so a player being moved from one team to another should get the same score (plus/minus coaching effects) theoretically speaking of course. These scores are not a definitive measure of talent. Now using a scoring rate I multiply by the amount of time a player is being played to calculate their value to the team. A player who gets 20 minutes of even strength time is arguably twice as valuable as an identical player getting only 10 minutes. Due to the ice time multiplier defensemen appear on top more frequently than forwards.

What does VAL measure?
The units for VAL are goals per game, where goals is the expected goal differential for that individual, which doesn’t necessarily measure true value as a lower goal differential is acceptable for a player with a fewer events so defensive players will be undervalued. If all the players were identical and goal tending is average this should be the plus minus for that player every game, so 82*VAL = plus minus in an ideal system (all players on team identical with average goal tending). So a score of 0.33 would work out so +27, considering the best player last season as +35 this is probably a sort of limit value of this statistic (scores about 0.5 probably don’t mean much other than random error). Of course these scores are for individuals not lines so one player could easily do much better than his line (Selanne). For these metrics (even strength stats) I like to use Malik as he is a consistent plus player and former Canuck (+96 in over last 4 seasons). Malik scores an excellent 0.48 in my system for +40. I'm posting the results for the Northwest division on this site as it's what I'm familiar with, however the complete list can be found on my statistics website. I have also adapted my SH and PP scores on the site, I'm not 100% satisfied with the results yet for the however feel free to comment on them as well.
Vancouver
 I L VAL 1 D SEDIN 0.28 2 H SEDIN 0.26 3 A EDLER 0.25 4 M NASLUND 0.23 5 K BIEKSA 0.17 6 M OHLUND 0.14 7 J GREEN -0.01 8 B MORRISON -0.02 9 T LINDEN -0.05 10 A BURROWS -0.06 11 R FITZPATRICK -0.08 12 R KESLER -0.09 13 S SALO -0.09 14 J BULIS -0.11 15 M CHOUINARD -0.16 16 T PYATT -0.19 17 L KRAJICEK -0.20 18 M COOKE -0.31 19 W MITCHELL -0.42

Minnesota
 N I L VAL 1 K CARNEY 0.18 2 M GABORIK 0.14 3 S VEILLEUX 0.09 4 W WALZ 0.05 5 M PARRISH 0.04 6 B BURNS 0.00 7 B ROLSTON -0.01 8 M SKOULA -0.03 9 K JOHNSSON -0.09 10 T WHITE -0.12 11 B RADIVOJEVIC -0.12 12 P BOUCHARD -0.12 13 M KOIVU -0.24 14 W SMITH -0.29 15 P DUPUIS -0.31 16 N SCHULTZ -0.34 17 K FOSTER -0.42 18 P DEMITRA -0.45 19 P NUMMELIN -0.65

Edmonton
 N I L VAL 1 R TORRES 0.74 2 J STOLL 0.39 3 M BERGERON 0.37 4 F PISANI 0.34 5 D TJARNQVIST 0.23 6 P SYKORA 0.23 7 M GREENE 0.14 8 B WINCHESTER 0.11 9 A HEMSKY 0.11 10 P THORESEN 0.08 11 J LUPUL 0.06 12 J SMITH 0.04 13 S STAIOS 0.03 14 M REASONER 0.02 15 R SMYTH 0.01 16 L SMID -0.06 17 S HORCOFF -0.15 18 M POULIOT -0.18 19 T PETERSEN -0.28 20 J JACQUES -0.37 21 J HEJDA -0.61

 N I L VAL 1 K KLEE 0.62 2 J SAKIC 0.34 3 M SVATOS 0.32 4 T ARNASON 0.30 5 O VAANANEN 0.29 6 J LILES 0.28 7 W WOLSKI 0.19 8 A BRUNETTE 0.19 9 M HEJDUK 0.19 10 B CLARK 0.12 11 B MCLEAN 0.12 12 P BRISEBOIS 0.03 13 B RICHARDSON -0.03 14 P STASTNY -0.03 15 M RYCROFT -0.03 16 A LAAKSONEN -0.05 17 I LAPERRIERE -0.09 18 K SKRASTINS -0.21

Calgary
 N I L VAL 1 R WARRENER 0.64 2 M LOMBARDI 0.38 3 A TANGUAY 0.37 4 D PHANEUF 0.36 5 J IGINLA 0.36 6 D LANGKOW 0.28 7 R REGEHR 0.27 8 R HAMRLIK 0.16 9 M GIORDANO 0.14 10 K HUSELIUS 0.13 11 M NILSON 0.02 12 A FERENCE -0.07 13 C KOBASEW -0.12 14 J LUNDMARK -0.12 15 B RITCHIE -0.13 16 D MCCARTY -0.18 17 T AMONTE -0.25 18 J FRIESEN -0.26 19 A ZYUZIN -0.70

Remember these stats are for even strength and not power play and other places, some great players perform amazing on the power play, but are less than impressive at even strength. I would argue these stats emphasize offense over defense, so it likely undervalues defense.

## December 15, 2006

### Face-offs

A few weeks ago Vic Ferrari and I had a lively debate on face-offs, due to school I have been unable to respond to the post correctly and felt I should complete the discussion. Before starting I would like to thank Vic Ferrari for pointing me to some excellent resources and much of this article is based on the great face-off article found at that site.

The above graph shows the effects of the different face-offs on goals against (O = offense zone, D = defensive zone), you should notice a lag for offensive zone face-offs in terms of goals against as one has to skate the length of the ice before scoring. One should notice that the primary effects occur in the first 15 seconds, the results after that aren’t clearly dominant like the first 15 seconds with a net effect (difference between offensive and defensive face-offs) of around 400 goals (incorrectly estimated it to be 200 in the above comments as my scripts were poor). There is a slight increase in scoring after the initial 15 seconds as well, which could be the result of better teams having get more offensive draws or it could also be a slight effect of possible zone control 15 seconds after a face-off. 400 goals over the course of 26,000 face-offs works out to 0.016 goals per defensive face-off so the cost associated with the defensive face-off is: 0.016 goals against (this should be a good metric to quantify the cost of icing). The majority of the effect is caused by losing the draw in the defensive zone, so if you don’t win the draw the effect isn’t really there (at least not as much).

In terms of individual players, this effect will be minimal due to the simple fact that some players see a very small difference in offensive zone vs. defensive zone resulting in a mean of 0 and standard deviation of around 50, so 95% of the players are within around ±100. This results in a standard deviation for the cost to a center man of around 0.016*50 = 0.8, in fact only 8% of players saw their pluses improve by more than 1 as result of taking more offensive face-offs and 10% saw their minus hurt by less than -1. Lecavalier has the largest difference of 207 resulting in an estimated benefit to Lecavalier of around +3.3 and left Andreychuk to pick up some extra defensive zone face-offs (160 defensive vs. 46 offensive). So in terms of individuals this is not a huge issue. One team saw an extra 360 defensive zone face-offs (Minnesota) and that cost them probably about 5 goals against or basically 1 win. If you’re looking at a more global view: a player who sees 200 defensive draws should see a 5.3% chance of a goal against vs. 3.4% chance of a goal for in the 45 seconds or less after the draw or -11 (sd = 3) and +7 (sd = 2.5), where three of the minuses I would consider are as a result of the defensive zone face-off the rest depend on the responsibility (skill) of the player in question. Of course that player will also have a few offensive draws to make up for those defensive draws so it balances out in the end.

## December 8, 2006

### Personnel, Coach or GM?

There’s been a lot of discussion of the lack of scoring by the Canucks this season. Averaging 2.07 goals per game, just isn’t good enough in the new NHL. The Canucks defense have managed to pull off 13 wins a number of which were luck early season come backs, that the Canucks have been unable to repeat in the last few weeks. If you calculate the Pythagorean prediction with the Canucks goals for and against you get an estimated 40% record or 75 points over the course of season. The real question is: Who on earth is responsible for the Canucks lack of scoring? To answer this question we need to look at scoring per situation: Well the Canucks are ranked 2nd last in power play scoring, 3rd last in even strength scoring and they’re the only team without a shorthanded goal. Interestingly the Canucks have the largest difference of 22 in the NHL in expected goals (80) and goals of (58). If you were considering the possibly of “luck” then this result is 2.46 standard deviations away from expected or the 0.7% of possible “pathetic-ness”. Since about one third of the season is over then we can say that there will be 1 team every two years who sees this sort of random variation in one of the three thirds of the season (games: 0-27,28-55,56-82). Watching the Canucks I know that this probably isn’t the case, rather the team is having some major scoring problems that go far beyond luck.

GM: Nonis

Let’s first look at the GM. He signed and traded a number of players away [Bracket goals are approximate historical averages]. Including the loss of Jovanovski (15 goals), Bertuzzi (30 goals) and the gain of Bulis (15 goals), Choinard (10 goals) and Pyatt (10 goals). Nonis has also signed three new backups, four if you include Auld, in less than two years: Sabourin, Ouellet, Noronen, none have stellar or even average NHL histories. I would be more than happy to argue Nonis’ ability to determine talent is certainly lacking. The forwards he chooses to keep aren’t exactly great scorers either: Kesler (10 goals), Cooke (15 goals), Morrison (20 goals). If you add up the expected goals (based on historical averages) of our forwards and defense it works out to something like [arrows represent how they’re doing this year compared to their average]:

Naslund: 40
D. Sedin: 20
Morrison: 20
H. Sedin: 15
Salo: 15
Cooke: 15
Bulis: 15
Choinard: 10
Pyatt: 10
Green: 10
Kesler: 10
Ohlund: 10
Bieksa: 5
Linden: 5
Burrows: 5
Krajicek: 3
Fitzpatrick: 3
Mitchell: 2

Total: 213 goals or 2.6 goals per game, if the Canucks had gotten 2.6 goals per game they’d have 73 goals so far this season, which is perfectly reasonable. They’ve lost around 15 goals (3 wins) as a result of whatever is causing these players to not score.

Coach: Vigneault

Who couldn’t run a competitive defensive system with such a great goaltender as Luongo? The Canucks are only slightly better (2.4 g/hr) than average (2.6 g/hr) at even strength at preventing good shots against at even strength. And ranked 27th in terms of expected goals on the penalty kill, Luongo’s performance allows the Canucks to be ranked 6th in terms of actual goals against. So Luongo is making the Canucks porous defense look good. But that’s not the problem, the problem is scoring: here’s what the Vancouver Sun writer: Elliott Pap has to say about the Canucks offense: “Obviously there is a crisis of confidence and a dearth of proven marksmen but, please, don’t blame coach Alain Vigneault for stifling the offense with his system.” He explains further that: “You take 66 shots [directed at the net] and don’t score on any, blame the shooters.” Considering the above arrows for the forwards above I have to wonder how you can’t blame the coach when all the scorers aren’t scoring, Bieksa being the lone exception largely due to the fact that he’s seen twice as much power play time this season in 28 games this compared to all 39 games last season. Considering the expected vs. actual we know the Canucks are getting what appear statistically good chances, but haven’t seemed to go in. I certainly will say that there is a possibility that the shoot first ask questions later approach to scoring isn’t working out too well.

If you’re familiar with the Canucks you would know it’s uncommon to see the same two players skating together two games in a row, unless the Canucks win or they have the same last name. 28 games into the season, Vigneault still hasn’t figured out what line combinations maximize scoring. He choose to send down Coulombe, who was significantly leading the power play in terms of expected and actual goals, however his 7 goals against per hour at even strength was too much for Vigneault, although I would argue he had some tough luck due to the fact he has some of the best expected goals against statistics on the team. Either way, Vigneault isn’t letting players play together long enough to figure out if they’re effective together, so every game different players have to try to adapt to new combinations and score at the same time. As a result goal scoring is lower. Most combinations of players can play together defensively, which is what we are seeing, but scoring takes time and patience, which it appears Vigneault is lacking and it’s hurting the team in terms of confidence, this confidence can be heard in this quote by Ryan Kesler: “I must have had a bad practice or something, I don’t know…I was pretty excited to get the chance to play with [the Sedin twins], but I;m still playing with a couple of good guys on my line…who knows what’s going on.” There’s not much more to say, but many of the players are frustrated with how this line juggling has worked. Bulis, who was promised top line minutes, is getting opportunity to try out on the top line with the Sedins (they’ll play their 3rd shift of the season together tonight). Either way, every player’s scoring is lower with Vigneault. It would appear all those shots aren’t helping Vigneault, maybe he’s disrupting some sort of chemistry or it’s just extraordinary bad luck, but either way the Canucks can’t score with Vigneault.

Can we still blame the Players?

The argument provided from the Vancouver Sun was that if players aren’t scoring on a lot of shots then their confidence is gone and this is somehow their fault. Now if you ask me, if there’s a problem with one player you look at that one player, when there’s a problem with all the players, you look to the guy in charge. There’s still a few things to see in terms of individuals that are worth noting. Last season Naslund had 98 shots in the first 28 games and 15 goals, this season he has 93 and 12 goals, well within reasonable random variations. Interestingly the shots this year produced more expected goals. If you look at shots as a percent though, Naslund had 11.4% last year in the first 28 games and this season he’s getting 10.6%, certainly not statistically significant, but still worth noting. Daniel Sedin went from 5.6% to 8.5%, which is no surprise as his ice time also improved. Problem is, while Sedin’s shots increased his shooting percentage fell. In fact with the extra 19 shot he scored one fewer goal. Of course none of these results are statistically significant the sample sizes are way too small, but many are disturbing indicators. Of course scorers, need good passes and if the Canucks aren’t getting those it would certainly make their shooting worse, of course since the NHL only prints the passes that result in a goal and not those that result in a shot that is stopped it almost impossible to analyze whether some passers help the shooting percentage more than others.

Random

Still a god chuck of this variation could be randomness; we’ll see if the Canucks can eventually pick up their scoring, but 28 games in it appears the Canucks we’ll struggle to score goals all season.

*I wanted to post something this week, but due to exams I lack time so I wrote this quick article about the Canucks. I'll have a lot more time when my last exam is finished on the 13th, otherwise there'll be little new material here.