Daniel Sedin facing a top-flight defenseman, as always
By kcxd (Canucks!) [CC-BY-2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons

Our traditional quality of competition metrics aim to answer the question "how tough was this player's competition?"

To do that, they start by assigning each player some kind of score to assess how tough an opponent he is; then to calculate a player's quality of competition, you average his opponents' scores together. There are a variety of choice for what score you use -- one metric uses the team's shot differential with that player on the ice, another looks at how the team's shot differential changed when he stepped on the ice.

Each of those scores has certain weaknesses, and the stat community recognizes that none of them can be used as a single metric to rank players and declare someone to be the best in the league. Yet in essence, that's what the quality of competition metrics do.

A little over a year ago, a group of analysts was asked what stats they turn to first. Such leaders in the field as Gabe Desjardins, Jonathan Willis, and Tom Awad all said that if they only get one stat, they're going to look at ice time.

It makes sense -- a player's ice time is a direct reflection of the coach's opinion of the player, and at this relatively early stage in the evolution of analytics, the coach's opinion is more accurate than any one individual statistic.

So why not try to build a quality of competition metric using ice time as the measure of how good each opponent is? Let's try it.

The differences between using Corsi Rel and TOI

The most commonly used competition metric right now is Corsi Rel QoC, so we'll compare the results of our TOI Qualcomp to that measure.

For defensemen with 40 games played, the two metrics turn out to be almost identical; the correlation between the two was 0.953. There are a few differences between the lists -- Zdeno Chara moves up from 35th in Corsi Rel QoC to 3rd in TOI Qualcomp, and James Wisniewski moves down from 17th in Corsi Rel QoC to 56th in TOI Qualcomp. However, these are the rare examples; few players moved more than a handful of spots, and ranking within a team rarely changed.

So for defensemen, Corsi Rel QoC and TOI Qualcomp are more or less interchangeable, but the story is different with forwards. Here is a table showing the biggest risers and fallers when we switch metrics (all ranks are out of 368 forwards with at least 40 games played):

The players who are being boosted the most are the elite offensive players, and they are moving up at the expense of the defensive specialists.

In fact, the trend is more general than that -- top line players in general are moving up the list and third line players are moving down. The rankings boost might not be as large for players who were already high on the Corsi Rel QoC list, but the elite two-way players do move up in TOI Qualcomp: Pavel Datsyuk goes from 28th to 1st, Mikko Koivu goes from 124th to 5th, Claude Giroux goes from 82nd to 12th, Jonathan Toews goes from 48th to 20th, Patrice Bergeron goes from 146th to 51st, and so forth.

Basically, what we're finding is that a team's best line tends to face opponents who get a lot of ice time, even if those opponents don't tend to outshoot their opponents. At first I'd assumed that was because of the interconnectedness of usage and results -- maybe the Sedins' opponents don't carry the play because they're always starting in the defensive zone against players like the Sedins.

But there was something nagging at me: the flip side of the equation. It's not too hard to imagine the Sedins facing opponents who play a lot of defensive minutes without winning the shot battle, but are James Wyman and Andreas Nodl really facing a bunch of opponents who don't get much ice time despite handily outshooting their opponents? That doesn't sound right; the leaderboard in Corsi Rel isn't exactly a list of bench-warmers.

Usage patterns and multidimensional qualcomp

I think the answer is that whether a player sees the opponents' top forwards and whether he sees their top defensemen are two separate questions. Here's a look at the average TOI of opposing forwards and of opposing defensemen for an assortment of players, where we can see the disconnections:

It looks to me like we are separating out not just the quality of competition, but the type of opponents a player faced. The defensive specialists (Staal, Dwyer, Bolland, Sutter) faced top forwards but lesser defensemen. Conversely, the offensive stars (Lupul, Sedin, Ovechkin) saw top defensemen regardless of what kind of forwards they were used against. The top two-way players (Datsyuk, Thornton, Koivu, Perry, Kopitar) saw the best of both.

Now instead of just a single competition metric that answers the question "how good were his opponents", we have a two-dimensional competition metric that answers the more complex question "what kind of opponents did he face?"

For a team like St. Louis, there isn't much difference, since they generally matched their best line with the opposing best line:

The guys who faced tough competition are in the top right and the guys who faced weak competition are in the bottom left. However, for a team like Washington that employed a scoring line and a shutdown line, the picture is quite different:

Here, we find the scoring line in the top left (facing top D and weak F) and the shutdown line in the bottom right (facing top F and weak D). In addition to the strength of the competition, we can identify the type of competition faced, distinguishing between those who were used in a scoring role (Ovechkin) from those who were truly sheltered (Knuble) better than a single competition metric can.

Thus, by using ice time as an indicator of player strength, we can eliminate the complications that zone starts and competition have on the shot-based metrics. We then find indications that top line players may face stronger competition than is suggested by the existing competition metrics. Moreover, separating the opposing forwards and defensemen gives a more specific indication of how the coach structured his lines and what each player's role was.

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