2013 Bruins Defensemen: A Numerical Breakdown

Introduction / Preview / Whatever you want to call this (Abstract? But not really)

With free agency opening a week ago, there's been a lot of talk about cap hits and contract negotiations. With every signing that's made by a level-headed GM (so not Nonis or Holmgren), some will argue that the deal is too high, while others will argue that it's too low. Of course, that's something only time will tell. But how can you actually tell if a player is being paid appropriately? Specifically, for this last season (2012-13), did the Bruins pay each defenseman too much or too little?


I could spend all day talking about methodology, but I'll try to keep this short. Essentially, as an engineer (in training), my life is about modeling the world with numbers. So why not apply that to hockey? I know some of you are big proponents of that, but the thing is, no model is perfect. But we do what we can.

You may remember the ideal gas law from high school chemistry (or whenever): PV = nRT. Using this is like using basic stats, like goals and whatnot. It kinda works, but it's not great (Mindblown? It's the ideal gas law, and...most gases aren't ideal!).

So engineers and scientists have come up with all these other equations of state. This is like using advanced stats - Corsi, Fenwick, that kind of thing. It's a much better approximation of reality...but it's still not 100% perfect - it's still an approximation.

Regardless, numbers are awesome. They can tell you a lot, if you use them right. But it's important to keep in mind not only what exactly they mean (not just the final number, but how we got there), but that they're not 100% perfect all the time.

So I did use statistics as I went through this. You could probably look at Corsis only and pull out something meaningful, but what kind of fun is that? So, I used the methodology that Pension Plan Puppets developed when calculating the deserving Norris winner. It's not a model I'm completely content with - I personally think PPG might be overweighted, since I'm a big fan of defensive defensemen - but it's pretty good for our purposes here. And I'm lazy, so borrowing it is easier. But be warned, it's not exactly a proven formula, and it favors a specific type of defenseman. Using something like ES TOI to judge performance might seem like a terrible idea (and really, it might be), but we'll see how it turns out in the end.

Regular Season

For every defenseman that played at least one game for the Bruins this year, I looked up the appropriate statistics from the regular season (primarily off, but some off and espn). And then I ran the calculations using my best friend, Microsoft Excel, and bam. It spat out a performance score for each d-man.

Player "Performance Score"
Zdeno Chara 83.55
Dennis Seidenberg 79.35
Andrew Ference 69.20
Johnny Boychuk 67.60
Dougie Hamilton 66.00
Aaron Johnson 57.45
Adam McQuaid 56.80
Wade Redden 56.80
Torey Krug 51.45
Matt Bartkowski 50.80

I took those scores and plotted them against the respective cap hits for each player (found off capgeek).


So...what does this mean? Well, first, it would be nice to have a trendline to compare everything to. Initially, I thought it might be linear, but I realized that logarithmic would probably work a lot better. Cap hits are skewed right (very few players are paid a lot, many players are paid a little), but skill/performance should theoretically be approximately bell-shaped. So logarithmic it was, and indeed it looks alright. An R-squared value of 0.7175 isn't amazing, but given that I'm working with actual human beings and not the largest sets of data here, it's pretty good. (Honestly though, using a logarithmic fit is still a pretty big assumption - could be totally wrong.)

Now that the line's there as a reference, we can start trying to reach some conclusions. Players over the line are being underpaid, while players below the line are being overpaid. In other words, players over the line exceeded expectations, while players under the line underperformed (relative to how much they're being paid, but I'd argue that's a good indicator of their expectations).

So as you can see, Chara, Seidenberg, Ference, Dougie, and Aaron Johnson are above the line. Chara and Seids should be no surprise. Ference didn't have an extraordinarily big cap hit, so that's reasonable. Dougie should be no surprise either, and he also doesn't have a very big cap hit. Johnson, well, good for him.

On the other hand...we have Boychuk, McQuaid, and Krug under the line (Redden and Bart are basically on it). Boychuk's contract was a bit baffling, so there's his explanation. I'm not going to make excuses for Quaider. Krug? Well, this is the Torey Krug of 1 regular season game this season. Tiny, tiny sample size. Plus, the stats used in this equation don't really work in his favor - his TOI are low (he plays more on the PP than the PK), and he gets killed by zone shift since he starts in the o-zone so much.


I wanted to help Krug out a little, so this inspired me to see if the data from the playoffs would look any different. I repeated the same process and generated a similar graph. Except now, the R-squared value is 0.5058, so I don't want to read into this one too much. Besides, it's the Stanley Cup Playoffs - weird things happen.

Player "Performance Score"
Zdeno Chara 94.05
Dennis Seidenberg 65.75
Andrew Ference 61.55
Johnny Boychuk 70.15
Dougie Hamilton 67.40
Adam McQuaid 50.35
Wade Redden 52.75
Torey Krug 57.85
Matt Bartkowski 65.20


Krug still falls below the line unfortunately, but my attention was drawn to three other dots - Seidenberg, Ference, and Bartkowski. More on this later.


Now that we have data from the regular season and data from the playoffs, why not combine them? The regular season was 48 games and the B's played 22 in the playoffs, so approximately half of 48. I took two weighted averages:

overall score = (2 * regular season + playoffs) / 3

overall score = (regular season games played * regular season + playoffs games played * playoffs) / total games played

The second one should only really make a difference for guys like Krug, who played more games in the playoffs than in the regular season.

Player "Performance Score" "Performance Score (GP Weighted)"
Zdeno Chara 87.05 86.85
Dennis Seidenberg 74.82 75.53
Andrew Ference 66.65 67.47
Johnny Boychuk 68.45 68.45
Dougie Hamilton 66.47 66.20
Adam McQuaid 54.65 54.17
Wade Redden 55.45 56.20
Torey Krug 53.58 57.45
Matt Bartkowski 55.60 56.40



These gave me the highest R-squared values yet (0.7576 and .78). But for the most part, the data looks the same. Chara is otherworldly, Seidenberg and Dougie are solid, Ference has dropped slightly, Boychuk is alright though hindered by his cap hit, McQuaid's low, and Krug...I guess there's no helping him out here, unless I go back and reweigh the scoring to favor points over ice time. There is very little argument that Krug is being overpaid/underperforming, because he pretty clearly wasn't - a good example of not reading too much into data, especially that generated by an unprofessional who has no inkling of how these things work. Meanwhile, Bartkowski's made the jump to over the line due to his playoff performance, while Redden's still pretty much on there.

As an aside - earlier, I alluded to Bart, Ference, and Seidenberg shifting a lot when comparing the playoffs to the regular season. Since I had all the performance scores calculated and ready, this was an easy way to see who elevated their game in the postseason. So, yeah, Seidenberg was definitely injured or something.


And lastly, I used the trendline from the weighted data (figure 4) to calculate what each player 'should' be being paid.

Player Actual Cap Hit Adjusted Cap Hit Difference
Zdeno Chara $6,916,667 $9,576,536 -$2,659,869
Dennis Seidenberg $3,250,000 $4,259,587 -$1,009,587
Andrew Ference $2,250,000 $2,394,406 -$144,406
Johnny Boychuk $3,366,677 $2,567,816 $798,861
Dougie Hamilton $1,494,167 $2,186,058 -$691,891
Adam McQuaid $1,566,667 $924,671 $641,996
Wade Redden $1,000,000 $1,069,356 -$69,356
Torey Krug $1,704,167 $1,169,015 $535,152
Matt Bartkowski $660,000 $1,084,424 $-424,424

For the most part, the Bruins' defensemen are actually far outplaying what you might expect from someone with their cap hits. The three glaring exceptions are Boychuk, McQuaid, and Krug, as noted. Boychuk and McQuaid shouldn't be big surprises, and for now I'm just going to call Krug an outlier.


I didn't go into this expecting to find anything mindblowing, and I didn't. Krug was the only real surprise, but a specialized PMD who's played 16 games is probably going to be an outlier no matter what. Other than that, the Bruins aren't really wasting valuable cap space on useless d-men (hello, Philadelphia!), but they are somewhat overpaying Boychuk (and McQuaid), confirming what we already thought.

(It's important to note that there's a difference between underperforming and being overpaid. One falls on the player, the other falls on management. But I'm not one to judge what happened with Boychuk and McQuaid here - if there's anything to judge at all)

It'd certainly be interesting to see how this model holds up over a larger set of data - either through previous years or around the league. Even more interesting (in my opinion) would be to assess the forwards the same way - but then I'd have to develop my own formula for that. We'll see.

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