Stats Nerds: Working out the values of defensemen

[Lehtonen32]

Unfortunately I\'m only a part-time stats nerd, so while I think I\'ve figured some of this out, I need some help finishing it off.

My aim is to find a way to work out how valuable a defensemen is in comparison to forwards (and to a lesser extent, forwards in comparison to goalies and dmen in comparison to goalies) in any given year in a league that I\'m in. Yes, why would you guys care, but hopefully this can easily be used in other points leagues so you too can accurately compare values of players at different positions. As far as I can tell this would be impossible in H2H or roto leagues, but because point leagues have set values for each statistic I\'m sure you can do it in point leagues.

Unless the scoring system is heavily in their favour, the average defensemen is always going to score less than the average forward or the average goaltender. But this shouldn\'t reduce their value; every respectable league has a compulsory number of defensemen spots, and if your team has a stack of above average defensemen you can definitely gain a large advantage over the competition (especially because so many people make the mistake of neglecting this \'lesser\' position).

This league in particular is a 30 team league with full size rosters (12 f, 6 d, 1g). The scoring system is identical for dmen & fwds, except that goals are worth double for dmen. I have attached (edit: attachment won\'t work) a screenshot of the full scoring system if you\'re interested. This year, up to this point, all the forwards combined have averaged about 19 points per game (I\'m going to just use PPG from now on, so don\'t get it confused with powerplay goals or actual NHL points per game), while the defensemen have averaged just under 15 PPG. Goalies are 44.6 PPG, but I won\'t worry about them too much at this point.

So, fwds vs dmen. I thought at first the way to work out the value that a player brings to your team is to compare his PPG against the average for his position. So, if Phaneuf scores 34.31 PPG, his \'value\' (let\'s call this number \'V\') was 19.54 PPG (Phaneuf\'s PPG - Avg Dmen PPG = Phaneuf\'s V). I then compared this to a forward with a similar V (ie. Joe Thornton\'s PPG - Avg Fwd PPG = Thornton\'s V). Would it then be fair to say that Phaneuf was as valuable to his team as Joe Thornton was to his, because their V numbers were almost identical?

I was happily thinking this was fairly solid until just the other day, when there was a discussion on who the MVP of this fantasy league was (playoffs have just started). I thought it had to be Brodeur for sure; he scored 4887 points, while the next best goalie was 3788 (Luongo, who is having an incredible season himself). By comparison, the top forward was Heatley (more games than Crosby, and the scoring system favours the goal scorers) who had 3409 points (Crosby had 3392).

However, using the V number above, Crosby is clearly in the lead. His V is 33, Heatley\'s is about 30, Brodeur\'s is just under 30 and Souray (the top D) is at 25.6.

That just doesn\'t seem right to me - Brodeur scored 1100 points more than anyone else, how could he not be the most valuable player to have? Is it that the V system isn\'t as solid as I thought (likely), or is it just that it doesn\'t work well with goalies (also likely; the less games played probably screws with it a bit)?

So, questions:
Does this all make sense?
Is it right to say Phaneuf was as valuable in this league as Thornton this season?
Should I be taking into account the fact that there are 12 forwards and only 6 D somehow?
Is the combined forward average/combined defensemen average the number(s) I should be using?
What am I missing?

Post edited by: Lehtonen32, at: 2007/03/14 18:18

[Steffen]

I definitely think you\'re on the right track. I\'ve also done a fair bit of statistical analysis in an effort to rank players for my deep keeper roto pool, and I also compare individual skaters\' projected performance to the league average for their position.

However, rather than rely on directly calculated projections for each player, instead I convert those to z-scores to account for the fact that projections are rarely that accurate. Z-scores indicate roughly how much above (or below) the average a given skater\'s projected performance might be, and the calculation is:

(Skater\'s projected stat - Avg projected stat for that position) / Standard Deviation for projected stat for that position

So, for example, Phaneuf got the following z-scores by my method coming into this season:
3 G/GP, 1 A/GP, 0 PIM/GP. (I intentionally round them to whole numbers to force me to use my own judgement to break ties.)

Note that these are NOT projections of goals-per-game etc. Because z-scores indicate roughly where on a normal (or bell) curve a player\'s stats might be, Phaneuf\'s z-score of 3 in goals-per-game indicated he\'d be better than about 99.5% of all defensemen in that stat, better than about 83% of defensemen in assists-per-game, and about average in PIMs-per-game.

With this method, z-scores typically range between -3 and +3. (Although higher z-scores are sometimes generated, these should be considered outliers that necessitate further analysis.)

Thornton, by the way, got z-scores of +1 (G/GP), +3 (A/GP) and 0 (PIMs/GP).

Hope this helps.

[lanky522]

I\'m writing a new stat column for dobberhockey.com each month (with the first one coming in a couple days). I\'ll work on doing this in my spare time.

I already have a pretty good system that I use in my fantasy league. I\'ll tweak it and post it in the near future.

[Lehtonen32]

Steffen - sounds interesting (albeit close to being over my head!); I would love to hear more about your work, if you have the time.

Lanky - Looking forward to seeing your system too. What sort of subjects will the column be focusing on?

[lanky522]

That\'s actually quite intuitive. I like putting their projections on a bell curve, since it offers a visual (even if it\'s just a mental picture) of where they fall amoung players in their postion.

P.S. Thornton should have had a -3 in penalty minutes. He\'s been a little sissy this year. He may even get the lady Byng trophy this year.

[Steffen]

Yeah, Thornton\'s PIMs aren\'t the only thing I got wrong. I did these back in September, and several have been off here and there...

I calculated my own projections for stats per game for each player, then averaged them out with other published and trusted projections, and then bell-curved those averages (yielding the aforementioned rounded z-scores). (My first personal computer in 1982 came with 512K of RAM -- I had to upgrade to the then-max of 640K within the first month of ownership.)

I had enough patience to input career stats (in all leagues) for all players invited to camp last fall, using www.hockeydb.com as my stats source. Therefore I only had G, A and PIMs, by year, by league, by player. I then tried to develop unique regression formulae for all permutations and combinations of career paths, using just those inputs.

In retrospect, this approach needed a wider variety of input data. If I had access to Stats Inc\'s database, maybe I could fulfill my dream of being hockey\'s Bill James some day. Until then, I\'m not quitting my day job.

A sample of outlier results (many of these will never get the ice-time) and some regulars:
Player G A PIM
Thomas Pock +4 +5 +1
Jack Johnson +2 +2 +4
Ryan Caldwell +3 +4 +1
Aaron Rome +3 +3 +2
Ross Lupashuck +2 +2 +4
Gregg Johnson +2 +2 +3
Keith Yandle +2 +2 +3
Andreas Holmqvist +2 +2 +3
Eric Werner +2 +2 +3
Joni Pitkanen +2 +2 +1
Bryan McCabe +2 +2 +1
Mathieu Schneider +3 +2 0
Zdeno Chara +2 +1 +2
Sergei Gonchar +2 +2 +1
Marek Zidlicky +2 +2 +1
Rob Blake +2 +2 +1
Cam Barker +2 +1 +2
Boris Valabik +1 +1 +3
Ray DiLauro +1 +2 +2
Nicklas Lidstrom +2 +3 -1
Dion Phaneuf +3 +1 0
Tomas Kaberle +2 +3 -1
Ed Jovanovski +1 +2 +1
Ric Jackman +1 +1 +2
James Wisniewski +2 +2 0
Mario Scalzo +1 +1 +2
Kris Letang +1 +1 +2
Janne Niskala +2 +2 0
Jeff Dwyer +1 +1 +2
Andrej Sekera +1 +1 +2
Trevor Hendrikx +1 +1 +2
Ed Hill +1 +1 +2
Mel Angelstad +2 -1 +3
Sergei Zubov +1 +3 -1
Shane O\'Brien 0 0 +3
Wade Brookbank 0 -1 +4
Dale Purinton 0 0 +3
Martin Grenier 0 -1 +4
Rocky Thompson -1 -2 +6
Mike Egener -1 0 +3
...

Aaron Voros +3 0 +5
Sidney Crosby +2 +3 +2
Jaromir Jagr +3 +3 0
Garrett Burnett 0 -1 +7
Alexander Ovechkin +3 +2 0
Scott Gomez +3 +2 0
Keith Tkachuk +2 +1 +2
Sean Avery 0 0 +5
Eric Lindros +2 +1 +2
Joe Thornton +1 +3 0
Ilya Kovalchuk +3 +1 0
Peter Forsberg +1 +3 0
Doug Doull -1 -1 +6
Brannt Myhres -1 -1 +6
Jason Spezza +1 +3 -1
Chris Neil 0 -1 +4
Kip Brennan -1 -1 +5
Dan Baum 0 0 +3
Darryl Bootland -1 -1 +5
Kurtis McLean -1 +5 -1
...

So, I hope I haven\'t blown my credibility (or your patience) by now.
I used these this year to quickly evaluate call-ups and beat my competitors to my pool\'s waiver wire. I\'ll win my deep keeper and perhaps the TMRX this year, but all in all, my time would have been better spent doing paying work.

The formulae need a broader range of input data and some tweaking, but I\'ve found these pretty useful for a first attempt...

[lanky522]

wow... that\'s rediculous. I can\'t imagine the amount of man hours invested in that so far.

You do your statistical analysis for the same reason I do. I want to be as informed as I can to give me that extra edge during fantasy hockey. I don\'t honestly understand how people can play fantasy hockey and not do a rediculous amount of research.

[SirIrish]

This is great stuff guys. I love seeing that the obligatory stats class in university actually has some practical use.

Lehtonen…when you say average for the position, how do you acquire the average? Do you take the average from all available players (in that position) minus obvious outliers? Or is the average acquired from all players that have already been selected (i.e. – free agents on the wavier wire not included)?

The only issue I can see with this system in relation to goalie is that goalies, on average, get more points per game in your league then players, thus reducing their value. In other words, the difference between Brodeur and the worst goalie used in your calculations are much closer then say, Heatley and the worst player used in your calculation. Actually, having said that, I’m not sure that is a issue, as this system says that having Heatley and the worst goalie is better then having Brodeur and the worst player…. ok I can buy that.

What I don’t understand is how Crosby could get a higher V then Heatley if you were using the same average PPG. That just doesn’t make sense at all. 3 (heatly) – 1 (avg) = 2 , but 2.5 (Crosby) – 1 = 4?…

Cool system though guys, thanks for sharing.

[lanky522]

Ok. In my Head-to-Head keeper league, the breakdown of our stats is as follows:

All Skaters:
Penalty Min 0.15 points
+/- 0.65 points

Forwards:
Goals 0.625 points
Assists 0.5 points
PPG 1 point
PPA 0.75 points
SHG 2 points
SHA 1.5 points
GWG 1.25 points
HT 2.5 points
Face-off Wins 0.02 points

Defenders:
Goals 1 point
Assists 0.725 points
PPG 1.5 points
PPA 1 point
SHG 3 points
SHA 2 points
GWG 1.875 points
HT 4 points
Face-off Wins 0.325 points

Goalies:
Wins 1.25 points
Losses -1.325 points
Saves 0.11 points
GA -0.55 points
Shutouts 4 points

======================================

This is a sampling of our current rankings (Top 10 Forwards, Defenders, Goalies):

Crosby, Sidney C PIT 132.1
Heatley, Dany RW OTT 131.9
Selanne, Teemu RW ANA 126.2
Lecavalier, Vincent C TB 126.2
Hossa, Marian RW ATL 121.4
Thornton, Joe C SJ 112.6
Zetterberg, Henrik C DET 110.5
Briere, Daniel C BUF 108.4
Brind\'Amour, Rod C CAR 108.3
St. Louis, Martin RW TB 108.2

As you can see we make up for the fact that centers often don\'t score as many goals, by counting face-off wins.

Lidstrom, Nicklas D DET 123.6
Souray, Sheldon D MON 121.6
Gonchar, Sergei D PIT 111.6
Pronger, Chris D ANA 107.4
Boucher, Philippe D DAL 101.9
Boyle, Dan D TB 101.5
Phaneuf, Dion D CGY 100.1
Schneider, Mathieu D DET 97.0
Niedermayer, Scott D ANA 97.0
McCabe, Bryan D TOR 89.1

As you can see, our top 10 defenders have a slightly lower average rating, but they are more on par than most leagues I think (especially when you consider that both wings and centers are taken into account in the top 10 \"forwards\" list).

Brodeur, Martin G NJ 189.0
Kiprusoff, Miikka G CGY 144.1
Luongo, Roberto G VAN 142.9
DiPietro, Rick G NYI 136.5
Lehtonen, Kari G ATL 124.3
Emery, Ray G OTT 123.4
Giguere, Jean-Sebastien G ANA 123.0
Fleury, Marc-Andre G PIT 118.5
Hasek, Dominik G DET 114.0
Thomas, Tim G BOS 109.5

As you can see our goalie rankings are fairly in line with the other 2 positions except for Brodeur. This is because of his rediculous 12 shutouts this year. This is not the sort of thing you could have predicted, and most of the time, goalies won\'t get more than 8-9 shutouts in a season. The goalie ranking is heavily based on the number of shots taken, a testament to why Thomas is in the top ten. He has 600 more saves than Hasek, but because of Hasek\'s 3 extra shutouts, and only 9 losses, he is ahead of Thomas.

======================================

Tell me what you all think.

I think these rankings are fairly close to what they should be. Considering that they are based solely off the stats of this season, I\'d say they\'re pretty good.

[Steffen]

SirIrish wrote:

This is great stuff guys. I love seeing that the obligatory stats class in university actually has some practical use. ...

hehe, I taught that class...

[Steffen]

Lanky, that is one extremely well-calibrated points system. I love the resulting rankings, not least because they offer a pretty good way to compare players of different positions.

Of course, the trickier part is projecting next year\'s stats in all of those categories.

Check out http://www.puckerings.com/research/analysis.html for a good essay on \"hockey metrics\".
Let\'s get Dobber to sponsor a conference some time where all thirteen of us (rounded to the nearest 13) can get together to discuss... lol.

[Lehtonen32]

SirIrish wrote:

This is great stuff guys. I love seeing that the obligatory stats class in university actually has some practical use.

Lehtonen…when you say average for the position, how do you acquire the average? Do you take the average from all available players (in that position) minus obvious outliers? Or is the average acquired from all players that have already been selected (i.e. – free agents on the wavier wire not included)?

The only issue I can see with this system in relation to goalie is that goalies, on average, get more points per game in your league then players, thus reducing their value. In other words, the difference between Brodeur and the worst goalie used in your calculations are much closer then say, Heatley and the worst player used in your calculation. Actually, having said that, I’m not sure that is a issue, as this system says that having Heatley and the worst goalie is better then having Brodeur and the worst player…. ok I can buy that.

What I don’t understand is how Crosby could get a higher V then Heatley if you were using the same average PPG. That just doesn’t make sense at all. 3 (heatly) – 1 (avg) = 2 , but 2.5 (Crosby) – 1 = 4?…

Cool system though guys, thanks for sharing.

We use officepools.com, which can spew out reports including the points recorded by every player who has played in the NHL this year. I then worked out the total points accumulated by forwards, the total games played by forwards, and then calculated the average (repeating the process for dmen and goalies of course).

Crosby is higher than Heatley because he has a higher points per game stat. He was just below Heatley on the total points list, but had played 4 less games and thus was higher on the points per game list.

[lanky522]

Thanks for the link. Yeah... predicting has been my trouble... I\'ve calibrated this system that works really well for scoring, but as far as predicting goes, all I can really use is what the system spit out the privious season.

Nice link btw too.

[diablos]

One of my philosphies though is to have a rock steady def core. As if you have a def core that out scores other teams def core that would/should compensate if u lack a middle of road star.

Always gotta get a star on the team then couple of highenders

will make for good off season reading

[diablos]

not sure why double posting

Post edited by: diablos, at: 2007/03/15 17:39