I'm going to do some elaborate statistical analysis to decide who I think deserves the Norris as well as, regardless of the answer to that question, whether Green is such a defensive liability. Prepare for a long post.
I suspect that he isn't. The perception seems to be based on a couple mistakes in the playoffs last year that unfortunately were at important moments, combined with the fact that his record breaking offensive performance makes it easy to assume he's bad defensively for those who want to be appear to have nuanced opinions. Incidentally, I believe the value of offense in hockey is underestimated in general and haven't noticed him to be particularly bad defensively, especially considering how much time Washington appears to have possession and the fact that you can't be scored on when you have possession (unless you're Dan Boyle or Bryan McCabe, that is).
Additionally, his offensive contributions deserve consideration here regardless. The Norris trophy is awarded for the "defense player who demonstrates throughout the season the greatest all-round ability in the position." It's not based entirely on defensive play. But I also believe Keith and Doughty are great defenseman and am writing this before looking at the statistics, so I'll wait until the end to decide my opinion of the deserving winner. I'm doing all this math as I go along and none of my earlier comments are biased based on what I was able to prove later, and no stats I looked at will be withheld based on what conclusion they led to.
All three playing for teams I often watch in addition to Doughty being in the Sharks division, I've seen a lot of play by the nominees. None of them appear to me to contribute more or less to their scoring points than most defenseman or seem to particularly benefit statistically from their team in non-obvious ways (i.e. Green's plus/minus being inflated by Washington's scoring), so I trust a statistical analysis will lead to a convincing conclusion if the right stats are used. All three teams seem to succeed at playing a puck possession game, although the Kings can do this only when Doughty is on the ice. Doughty's agile stick handling and the way it lets him control the puck in, or through, traffic, compared to Keith and Green getting more time on useless ice and taking more passes from teammates makes me think, based on observation, that Doughty is the best defensively, but I don't necessarily think he deserves the trophy, as Green and Keith contribute more offensively and the stats may suggest Doughty's puck movement strength is more flash than substance.
First, let's look at their defensive ability by comparing the time on ice each player had to the goals scored against their team while they were on the ice. Obviously it's harder to prevent goals on the penalty kill, so I'll count that separately for each player. I'm entering the time on ice as the numerator, so a higher number is better, as it means they spent more time on ice on average between every goal scored against. I also ranked the three in each stat. Seeing as these numbers aren't tracked by any organization as far as I can tell and I did the math myself, unfortunately I don't know the league rank.
Drew Doughty
Even strength time on ice (minutes): 1519
Even strength team goals against: 50
ESTOI/GA: 30.38 (1st)
Penalty kill time on ice: 165
Penalty kill team goals against: 20
PKTOI/GA: 8.25 (3rd)
Mike Green
Even strength time on ice: 1369
Even strength team goals against: 62
ESTOI/GA: 22.08 (2nd)
Penalty kill time on ice: 161
Penalty kill team goals against: 18
PKTOI/GA: 8.9 (2nd)
Duncan Keith
Even strength time on ice: 1705
Even strength team goals against: 81
ESTOI/GA: 21.05 (3rd)
Penalty kill time on ice: 244
Penalty kill team goals against: 21
PKTOI/GA: 11.61 (1st)
By the rankings they're all tied, with Green in the middle of each stat and Keith and Doughty each first in one stat and last in the other. Adding up both stats to get a combined score, however, makes Doughty the clear leader, with his even strength score the only number way ahead of the pack in any stat. Doughty's combined score is 38.63. Keith's is 32.66 and Green is not far behind with 30.98.
Adding up the scores gives too much weight to the score that scales higher, though. (For instance, if you got 90/90 on one test and 0/10 on another, that adds up to 90/100. Meanwhile, if you got 10/10 on one test and 0/90 on another, that adds up to 10/100. But in both cases you were perfect on one and got zero on the other and it should actually average out to 50/100 if the tests are equally important.) To get a score that scales equally between even strength and penalty kill time, I'm going to divide each player's number in each stat by that of the person who has the highest of the three, giving a score out of 1 for each stat. This gives us...
Doughty ES: 1
Doughty PK: .71
Total: 1.71
Green ES: 0.73
Green PK: 0.76
Total: 1.49
Keith ES: .69
Keith PK: 1
Total: 1.69
Not surprisingly, adding weight to the PK gave Keith a boost, but he still doesn't pass Doughty. The ranking is the same as with the nonscaled scores but instead of a distant lead by Doughty, Keith trails Doughty closely with Green now a distant third. Barring the influence of team success (which I'll talk about later), statistically Doughty is the clear winner defensively.
However, I think that it's nonideal to give ES and PK exactly equal weighting. I'm going to change the weighting yet again, based on the proportion of goals against the three teams that were on the PK or ES. The order necessarily won't change, but we'll see how it changes the spacing and how far Green will be from Keith. The three teams allowed a total of 445 even strength goals this year and a total of 166 goals on the penalty kill, meaning that 72.8% of the weighting will be for even strength and 27.2% for the penalty kill. Taking that percentage of each of the above scores, adding the two scores together for a new score out of one, and then multiplying by ten for a score out of ten gives us this.
Doughty: 9.2
Green: 7.4
Keith: 7.7
This new score, which I consider an ideal weighting, makes Doughty the clear defensive winner again and puts Keith only marginally ahead of Green. (Note: a 10 would be someone with Doughty's even strength numbers and Keith's PK numbers).
The last two issues to consider are the influence of each player's team members on each record and each player's offensive offensive contributions.
I'm not going to do any complex math in regards to the influence of the player's teammates because a cursory glance unambiguously leads to the same two conclusions that the previous stats do, that Doughty is far and above better defensively than the other two players while Green is not as far behind Keith as people think. Doughty is second on his team in plus minus and first among defenseman, while Green is third on his team and Keith is fourth. Green and Keith are both first in their team in time on ice and team goals against, neither obviously by more than the other, while Doughty is first on his team in time on ice but fourth in team goals against. Green and Doughty have no big name defenseman on their team other than themselves, while Keith has Seabrook and Campbell. Chicago as a whole was sixth in the league in (fewest) goals against per game, while LA was 8th and Washington was 16th. The only stat regarding team context that makes Keith look better is is Huet and Niemi's save percentages, which were slightly lower this year than Varlamov, Theodore and Quick's. Even giving weight to that (and none of the issues that made it appear that the Blackhawks were easier to play with) gives us the same conclusion.
To weight this completely in Keith's favor, I'm going to go by the highest save percentage of a 20+ game goalie on the Capitals or Kings, Theodore's .911, and the lowest on Chicago, Huet's .895. That's a difference of 1.7%, using Huet's save percentage as the base of the percentage (it being the lowest number, this will make the percentage higher than if the difference were a percentage of Theodore's save percentage or the absolute difference, which is a percentage of 1 or 100.) Adding 1.7% to Keith's score brings it to 7.8. However, the calculator showed 7.83, and when I calculated 7.7 the number after 7 was barely rounded down (.4 or something), so let's give Keith a score of 7.9. With Doughty's 9.2 and Green's 7.4, the situation is basically the same.
Doughty is clearly the best at preventing goals and Green is probably the worst, but the difference between Doughty and Keith is much larger than the difference between Keith and Green no matter how you look at it, unless you give a disproportionate amount of weighting to the PK. But there's no argument that the Penalty Kill should have equal weighting as even strength. Less time is spent and less goals are scored on the PK, so the defender's contribution is primarily during even strength play, and the above scores gave Penalty Killing a score proportionate to its relevance. With these scores, Doughty is 1.8 points ahead of Green and Keith is (using the generious 7.9) 0.5 ahead, meaning that the defensive superiority of Doughty over Green is more than three and a half times as much as that of Keith over Green.
Offense, on the other hand, puts them in the opposite order. Green was (goals, assists, points) 19 57 and 76, Keith was 14 55 and 69, and Doughty was 16 43 and 59. I can't think of an objective way to measure the value of goals versus assists (which in my opinion really depends on which goal and which assist, with assists being worth less on average but many assists still being worth more than many goals) and I can't think of a way to measure the value of offense versus defense for a defenseman that wouldn't be way too time consuming for me right now. However, I think most reasonable people would agree that a defenseman's primary job is defense, not offense, but offense still matters a bit, and that an assist is usually worth less than a goal but is still a significant stat. So I'm going to make an assist worth two thirds as much as a goal and a defenseman's offensive contributions worth half as much as his defense to make my final score for each player. You might have noticed that Green's points lead over Keith is less than Keith's over Doughty, but giving goals more weight should give Green a roughly equal lead as Keith has over Doughty.
First, I'm going to give each player an offensive number based on each assist being worth .67 points. This gives Green 57.19, Keith 50.85, and Doughty 44.81. Dividing each number by the highest score gives us a score out of 1, which we can multiply by ten for a score out of ten. This gives Green an offensive score of 10, Keith a score of 8.9, and Doughty 7.8. Dividing this score by two (to give it half as much weighting), and adding it to the defensive score (giving Keith his 7.9) for a score out of 15, then taking 2/3 of that to get us back to a score out of 10 gives us our final score out of ten. (For this score, someone with Doughty's even strength goal prevention, Keith's penalty kill goal prevention, and Green's offensive record would be 10).
Doughty: 8.7
Keith: 8.2
Green: 8.3
Even after adding offense to the equation, Doughty is the clear winner, although this does pull him closer to the pack. Green finally outright pulls ahead of Keith, even though offense is only weighted half as much as defense. Green's scoring lead over Keith was just too much for Keith to overtake considering Keith's small defensive superiority. This confirms my suspicion that the complaints about Green are based on fallacies, cliches, and folk wisdom, and that an objective analysis would show him to be a valuable defenseman. It also leads me to a conclusion I didn't have coming into this, that Doughty clearly most deserves the Norris by a wide margin. Considering he's only a sophomore, not to mention 20, his future is a force that should be feared in the NHL... especially because he's in my team's division.
My prediction for the winner, unfortunately, is different. I expect Keith to win the award because of the biases of most hockey writers, who are the ones that vote for the trophy. The list of past winners suggests to me that they don't look at more nuanced statistical analysis like I used, but rather just go to NHL.com and rank by points, then by plus minus, and see who's high on both. (Plus minus isn't a very good stat for measuring defensive ability, because half of it is offense while you're on the ice (which is usually provided by the forwards anyway, so it doesn't even measure that player's offensive ability), and it's massively influenced by team success.) Many seem to share the presumption that Green is a defensive liability and the popular view of him I described near the start of the post, and valuing defense first is a popular cliche, so he probably won't win despite leading both in plus minus and points. Keith is second in both stats and Doughty is last in both, making Keith the likely winner after Green is taken out of consideration.
Even if they have the perceptiveness to see Doughty is better defensively, Keith being second in both makes him the moderate, balanced choice, which is often popular with the naive because it feels safe, no matter what the margins involved are. Lastly, while all three teams improved in the standings from last year, Chicago's defense as a whole was the best this year and they finished well ahead of LA, and team success is given a lot of weight. I consider Green the second most likely, so I will be pleasantly surprised if Doughty wins the award.
But there's no doubt the kid deserves it the most.
It gives me chills too.
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