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.