# A competition metric based on ice time

Eric T.
August 16 2012 07:49AM

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

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):

 Player Corsi Rel QoC rank TOI Qualcomp rank Alex Ovechkin 302 130 Erik Cole 259 90 Daniel Sedin 195 27 Henrik Sedin 204 41 Evgeni Malkin 220 60 Max Pacioretty 247 96 Matt Duchene 288 141 Jason Spezza 217 76 Nicklas Backstrom 290 149 James Neal 197 66 Matt Hendricks 100 221 Michael Frolik 86 217 Tom Pyatt 63 199 Samuel Pahlsson 45 182 Manny Malhotra 155 294 Adam Hall 32 173 James Wyman 27 171 Andreas Nodl 38 187 Derek Dorsett 53 212 Dominic Moore 111 298

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:

 Player TOI Qualcomp rank F TOI Qualcomp rank D TOI Qualcomp rank Pavel Datsyuk 1 6 23 Martin Erat 2 1 46 Mike Fisher 3 4 50 Joe Thornton 4 10 22 Mikko Koivu 5 19 5 Sergei Kostitsyn 6 3 63 Joe Pavelski 7 9 29 Corey Perry 8 11 26 Anze Kopitar 9 18 11 Patrick Marleau 10 7 42 Olli Jokinen 13 2 78 Jordan Staal 40 8 118 Patrick Dwyer 115 22 228 Dave Bolland 119 16 262 Brandon Sutter 125 20 274 Joffrey Lupul 45 147 1 Claude Giroux 12 39 2 Rick Nash 15 41 3 Daniel Sedin 27 79 4 Alex Ovechkin 130 241 14

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.

## Recently by Eric T.

Eric T. writes for NHL Numbers and Broad Street Hockey. His work generally focuses on analytical investigations and covers all phases of the game. You can find him on Twitter as @BSH_EricT.
#1 JP Nikota
August 16 2012, 08:00AM

This is fantastic, Eric.

#2 Woodguy
August 16 2012, 08:31AM

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.

First of all, awesome stuff as usual. I really like where this is going.

In regards to the quote above, wouldn't a lot of the TOIQC rank be dictated by the opposing coach?

Let say SJS is playing VAN. Is SJS playing Thornton up front, Boyle on the blue against Sedins or Dom Moore & Boyle?

Whether or not the Sedin's see top TOIQC F is probably up to McLellan more than Vignault.

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.

I think the D rankings should be fairly static across the NHL. Coach will put out their "best" Dpairing against the top Offensive forwards. Like I indicated above, whether or not they see top TOIQC F is more or less a function of the opposing coaches preference.

Are you using 5v5 TOI or total TOI?

If I look at Horcoff in EDM, he plays against the best opposition forwards and has for years.

If we look at his 5v5 TOI he ranked 7th among Oiler forwards, but if you look at total TOI he ranked 1st.

Sorry if my post is a jumble, just writing what comes to mind.

#3 antro
August 16 2012, 08:44AM

This is really interesting stuff, and I really like the charts showing the different team strategies. The charts even seem like a possible way to represent a single game in one snapshot. I await the comments or blog replies of the seasoned analysts. However, I did wonder about any possible differences between home and away games. That is, if you compared the Washington-type teams when they can dictate match-ups versus when they can't. It might be a wash, ultimately.

#4 Woodguy
August 16 2012, 08:51AM

@antro

However, I did wonder about any possible differences between home and away games.

I was thinking that too.

Might be a big swing with some teams.

#7 dave
August 16 2012, 10:31AM

Just want to say this is great

#9 nhlcheapshot
August 16 2012, 10:51AM

Holy crap Eric, great stuff. Nice to have an alternative QComp stat.

#11 Tach
August 16 2012, 11:26AM

I am starting to think that this Eric T. is not a person, but a computer program designed by some nefarious NHL overlord to spit out interesting and useful statistical information to distract us from CBA foolishness. Yeoman's work. Well done.

Do you have charts like the St. Louis and Washington ones for all 30 teams? Any others with interesting results? Is their categories of strategies that can be picked out?

Also agree with many that the home/away differentials would be super interesting.

Thanks again.

#12 AronV
August 16 2012, 11:29AM

Excellent as usual Eric

#13 Ben Wendorf
August 16 2012, 11:49AM

As you mention in the piece, this is something that just seems so intuitive. I've known in the back of my mind that top-liners should generally be accredited for facing top competition, but it's nice to see it more clearly demonstrated here. Nifty stuff.

#14 Bob Spencer
August 16 2012, 12:28PM

Quick thought--interpretability. CorsiRelQoC is sort of elegant because it's easy to interpret a rating quickly... +1 tough, 0 neutral, -1 cupcake. In this article you have presented ranks, but I wonder how the raw scores, expressed in minutes(?), would be in terms of their interpretability. Keep up the great work!!

#15 Ian
August 16 2012, 04:39PM

Relatively new to advanced stats here, and want to say off the bat I think the stat and the findings here are very interesting and well done. Only thing that comes to mind is that the stat doesn't necessarily measure how well a player has performed, just how he was used in the game (or over the season). Obviously there probably isn't much of a difference (wouldnt keep getting put against top d pairing if weren't producing) but might it not undervalue the offensive production of a good third liner, compared to the Corsi rel?

#16 Bob
August 16 2012, 05:30PM

@Ian: neither CorsiRelQoC nor TOIQoC measure a player's output, just what kind of competition he faced. Both are meant to meant to provide context (i.e. this player posted this many points against soft competition, this other player had more points against tougher opponents.) They are all just puzzle pieces and the trick is knowing how to use them in combination with each other.

#17 Patrick D. (SnarkSD)
August 16 2012, 10:50PM

Eric, Phenomenal work as usual. A couple questions.

-What database did you use to pull this information? -Did you use any end points to assess TOI QOC vs Corsi Rel QOC? -Did you separate Corsi Rel QOC into F and D to see how those results compared with TOI QOC? -What do you think is the biggest weakness of TOI QOC?

#18 DLJr
August 17 2012, 06:30AM

@Patrick D. (SnarkSD)

I was wondering if Eric separated the Corsi Rel QOC in to F and D as well. I would be interested to see how it compares.

#19 daoust
August 17 2012, 07:46AM

This is really great stuff Eric.

#22 Kent Wilson
August 17 2012, 02:18PM

@Eric T.

I think only because we became focused on developing and proliferating shot metric analytics.

#23 Corey S.
August 17 2012, 03:29PM

Fantastic work, Eric.