Tuesday, December 14, 2010

Is Alex Edler the best defenseman in Canada?

What makes a good defenseman? Not allowing goals against? Ice-time? Plus/minus? I think it has a little more to do with how good shooters are when they're out against you.

I'm at my parents' place, so my copy of Moneyball isn't handy, but I recall baseball historian and statistician Bill James being quoted in it as saying that he didn't want statistics to manipulate his thought. James wanted to watch a game, compile data from the game and see what gave the winning team its success.

To determine the qualities that make a good goal scorer great, you have to take the reverse to determine what makes a defenseman good. The data that I've compiled based on 15 games isn't enough to draw up totally what makes a hockey team good, but I've noticed a couple of trends:

#1 - Goals against the flow of play account for about 25% of goals, and tend to influence the outcome of a close game. Flow of play is determined by crude graphs I make to represent the game. A goal against that occurs when it happens after a team has been outplayed in possession in the minute leading up to a goal. It works to mirror "points of turnovers" in football. These goals are great because they have zero predictable value.

#2 - Shooting efficiency and percentage matter. Shot percentage based on goals to shots on goal is very crude and comes with a lot of noise since a lot of goals are total flukes. A lot of players miss shots and have them blocked, so my shooting percentage is based on shots on goal in relation to total shots attempted at net. What I've noticed is that teams who are shutout get less than 50% of their shots on net, while teams that get 4 or more goals tend to get 60%. Efficiency is a little different. It adds together three percentages: goals / shots taken, goals / shots on goal and shots on goal / shots taken. The absolute formula for this is:

( SOG + [ G x 2 ] ) / ( [ SOG x 3 ] + 2 x [ BkS + MsS ] )

Since goals tend to influence the outcome of games, every game that has been won in regulation of the games I've tracked has been won by the team with a higher shooting efficiency. 10 of the 11 games decided in regulation that I've tracked were won by the team with the higher shooting percentage.

Point #2 is easier to track and more statistically relevant. A goal against the flow of play can come because of a bad change or a bad pinch by a teammate, or a soft goal allowed by a goaltender. So, this is how I'm going to track defensive statistics, by compiling which defensemen had the lowest shooting percentage and shooting efficiency against in 5 on 5 situations.

I'm a Vancouver Canucks fan and have watched more of their games than those of any other team, so I did my best to work this out with Vancouver defensemen and see if observational evidence matches with numerical evidence. Data for goals, saves, misses and blocks were taken from the fine folks at Behind The Net. This is what I have for the seven regular Canuck defensemen:

(Rank - Name - Shooting efficiency against - Shot percentage against)

#1 - Edler - .2216 - 49.60%
#2 - Ehrhoff - .2227 - 49.21%
#3 - Rome - .2392 - 52.87%
#4 - Alberts - .2405 - 50.30%
#5 - Hamhuis - .2599 - 54.25
#6 - Ballard - .2608 - 57.19%
#7 - Bieksa - .2628 - 54.16%

Observationally, that's not far off the mark. I spend a lot of time with friends from Northern BC at school, so I can't get away with saying that Dan Hamhuis (from Smithers) is having a bad season, but his start with the Canucks has been less than impressive. I've found he's often on the ice for scoring chances against and has made some poor decisions in his own end. Not that I don't think he can turn it around.

It's quite obvious that Edler and Ehrhoff are the top two defensemen on the Canucks, have been all season, will be for the rest of the season and (hopefully) well into the playoffs. Both are young, fast, move the puck well, stick check effectively and pinch responsibly. Kevin Bieksa is not surprisingly at the bottom of the list. I like him and he contributes well enough offensively for the team, but he makes some wild decisions in his own end.

In general, I think that this list pigeonholes the defensemen in a way consistent with observational reality, so I'm going to trust it.

So, I took four defensemen from each Canadian team so interesting enough as to see their statistics. To account for better or worse goaltending, I added in a control of the team's EV SV% to the EV SV% of the goalie when the player was on the ice.

The exact formula worked like this:

( 1 - Shooting efficiency ) * ( [ IndEV SV% ] / TEV SV% )

This compiles a player's DEF rating. Zone starts, while they are extremely valuable bits of information, are not factored into the rating because I wanted to keep it somewhat simple and consistent with observational evidence. An absolute DEF rating of over .80 is considered great, while one under .75 is not very good.

(Rank - Name - DEF rating)

#1 - Edler - .8025
#2 - Ehrhoff - .7963
#3 - Kaberle - .7950
#4 - Carkner - .7899
#5 - Schenn - .7879

Consistent imagery with the top five, these players all have a high save percentage. I think save percentage, while a big part of PDO and useful to tell when a player's +/- is based on goaltender or teammate performance, is still in the immediate control of a player who's on the ice. The other thing with Carkner is that in this group, he's the player who has had the fewest total attempts at net per 60 minutes of play.

PK Subban was #6, and while he's been on the hot-seat recently and was a -3 against Toronto on Saturday, he's still a pretty reliable defenseman and still hasn't been on the ice for a shorthanded goal against.

If you just went by reverse shooting efficiency, the top five would be as follows:

#1 - Phaneuf - .2188
#2 - Edler - .2216
#3 - Schenn - .2220
#4 - Ehrhoff - .2227
#5 - Beauchemin - .2239

There are an awful lot of Leafs up here, and this has to do with the Leafs being a pretty above average team 5 on 5 when you're looking at possession statistics alone. They have problems putting the puck in the net, which explains their record. They are also brutal on special teams with a PK + PP rate of 91.4%. (League average is 100)

And, if you go by reverse shooting percentage, the top five would be so:

#1 - Phaneuf - 44.62%
#2 - Beauchemin - 46.07%
#3 - Schenn - 47.92%
#4 - Ehrhoff - 49.21%
#5 - Edler - 49.60%

Again, the Leafs problems this year have been offensive, or due to the play of their non-Swedish goaltender.

Going by DEF rating, which is better since Phaneuf and Schenn DO give up a lot of attempts at net, the average defenders (the four closest to the average .75 mark) would be:

Sarich - .7497
Foster - .7493
Alberts - - .7492
Giardano - .7473

That's not so wild. Marc Giardano's goalies do worse when he's on the ice as opposed to not, and his benefit has been felt by the Flames at the other end of the ice. I supposed many Vancouver fans, though appreciative of Andrew Alberts' play would classify him as slightly below average.

The worst DEF players in the group are:

Phillips - .7302
Peckham - .7232
Hamhuis - .7215
Bieksa - .7125
Gilbert - .6986

Make any sense? Edmonton's goalies have had a pretty solid .923 EV SV% this year, but are still allowing quite a few goals, which is probably felt by the number of shots they allow. They've outshot the opposition just 4 times in 27 games this year.


This is a very simple metric with probably too little data to draw a logical conclusion, and definitely, whether to make a decision on which player to sign.

If you are a fan of one of the other teams, this is how these numbers would rank your defensemen on pure defensive performance. Does it make sense? Chime in through the comments. If my data is way off your own observational evidence, then I may go back to the drawing board, but it's very accurate for Vancouver performance.














  1. Good stuff. I don't know enough of the players to offer comment on the rankings, so I'll focus on the formulas instead.

    Short version: I think this can be simplified quite a bit, and expressed in a clearer way.


    The efficiency rating is a good idea, but the algebra is a little screwy, and I think the result is overly complicated. Adding together A/B and C/D, for example, is not the same as taking (A+C)/(B+D), which I think you've done here. And if you want to combine goals per shot on goal, goals per shot taken, and shots on goal per shot taken, you could multiply them, but that would reduce it to goals squared per shots taken squared, which might as well just be goals per shots taken.

    Is there some reason why goals per shots taken wouldn't capture what you're looking for here?


    If we make that change, then we can modify the DEF rating. We now have goals per shot taken, and we want to control somewhat for goaltending. Here I would actually multiply by the difference in the two save percentages (not the ratio), so it would look like this:

    (Goals per shots taken) * (IndEV SV% - TEV SV%)

    But if we're doing this then we might as well just ignore the first term (which doesn't add anything at this point) and go with "1 minus shots per shots taken while on the ice" (on-ice non-goal percentage, I guess? Can't call it save percentage.) minus the off-ice version of the same.

    If I'm reading my Behind The Net tables correctly, that would look like this for Edler:

    On-ice: 1 - 1.56 / (1.56 + 25.5 + 12.8 + 14.7) = .971
    Off-ice: 1 - 2.85 / (2.85 + 24.5 + 9.3 + 14.4) = .944
    Difference = +.027

    That means Edler has been worth +.027 goals per shot, or 0.8 per game (treating 30 shots as a "game"). Some more math tells me that makes him worth about a tenth of a win over the course of a season. Seems low, but you'd have to do this for all defensemen (and forwards for that matter) to see what the leaders' numbers look like. It could be a garbage stat for all I know.

    Anyway, hope that helps. I had to use that math degree of mine somewhere...

  2. Thanks Rob. I guess I don't want to dwell on 'goals per shot taken' because that doesn't reward players who force opponents to miss more than players who are playing in front of better goaltending.

    I've simplified my rating to account for 'goals per attempt' and 'shots per attempt' which is just:

    Goals and Shots / Attempts all divided by two. This means a goal is worth a 1 rating and each shot is worth a .5 rating.

  3. Cam

    Interesting, and to some extent the eye matches what you are seeing. Couple of things. First, having spent the last two days at Bell Centre watching the Habsburg, PK is a horror show in his own end. I have no idea if this is the norm for him, as my experience with him is the last two games, but if it is, then no metric should ever show him as above average. He's endlessly talented and entertaining, but wow! Second, and more importantly, wouldn't you want to correct for competition as well? If Hamhuis is playing against top line guys all the time, one would presume he would see more shot attempts then if he played against Jim Sandlak./