Reviving Quality of Competition (TOI% QoC)

[TomasHertlsRooster]

As some of you may know, TOI% QoC was a very popular metric that judged a player's quality of competition based on the opponent's ice time. To my knowledge, this metric was most recently available on corsica.hockey, which is unfortunately now defunct.

Some quality of competition metrics have become available in recent years, such as PuckIQ's Woodmoney and Micah McCurdy's competition/teammate visualizations. But while I find these useful, I've really just wanted to see TOI% QoC ever since Corsica became defunct, and I know I'm not the only one.

So I decided to calculate TOI% QoC myself. And I wanted to share this with everybody else in order to get a better idea of how different players are used league-wide. The results for 5-on-5 TOI% QoC over the past three seasons are published on my Tableau:

Tableau Public

You can filter by TOI, team, player, and position. For example, if you've heard that Shea Theodore is sheltered and you want to know whether or not this is true, you can filter by Vegas' defensemen who played at least 100 minutes and see for yourself:

If you're unfamiliar with TOI% QoC, here is the formula:

Spoiler

{[(TOI Vs. Opponent 1) * (Opponent 1's TOI%)] + [(TOI Vs. Opponent 2) * (Opponent 2's TOI%)] + ... + [(TOI Vs. Opponent n) * (Opponent n's TOI%)]} / [(TOI Vs. Opponent 1) + (TOI Vs. Opponent 2) + ... + (TOI Vs. Opponent n)]

With an opponent's TOI% being the percentage of their team's minutes that they played in games they dressed in.

Click to read more...

 

[Butch 19]

As some of you may know, TOI% QoC was a very popular metric that judged a player's quality of competition based on the opponent's ice time. To my knowledge, this metric was most recently available on corsica.hockey, which is unfortunately now defunct.

Nerd!

 

[canuckking1]

JTR>THR

 

[TomasHertlsRooster]

Nerd!

Isn't QoC the ultimate stat for non-nerds?

 

[JaegerDice]

QoC has always been a useful contextual stat when comparing players' on-ice impact. Same with zone starts.

 

[Sidney the Kidney]

Isn't QoT (linemates) better than QoC? Playing with two all-star linemates against slightly better competition is still probably more beneficial for a player than playing with two scrubs against slightly worse competition, no?

 

[TomasHertlsRooster]

Isn't QoT (linemates) better than QoC? Playing with two all-star linemates against slightly better competition is still probably more beneficial for a player than playing with two scrubs against slightly worse competition, no?

Absolutely. Quality of teammates is about 3 times as important as quality of competition, in part because the variance is much higher than it is for quality of competition.

But quality of competition is the one that seems to get brought up more frequently in arguments, and I think it’s very interesting to look at how different coaches deploy their players.

Part of the reason that I wanted this information (and that I wanted to make it available) is that this information being available can help DISPEL a lot of the false narratives that come from people who over-emphasize quality of competition. For example, I’ve heard multiple people essentially say that Anthony Cirelli’s results “don’t count” because he is sheltered and he plays for a stacked Tampa team. But he actually plays the highest quality of competition of any Tampa center, and it’s a lot easier to say that than it is to say “actually, quality of competition isn’t that big of a deal...”

Having the stats available also drives home the point that the variance in quality of competition from player to player is a lot lower than people make it out to be.

 

[brentashton]

When i need a slide rule to compute and understand a hockey forum, i know that I am undereducated. Nothing but respect to those of you that can follow this, but I’m out...i will now go back over to the “is Don Cherry Still Relevant” thread...

 

[Raccoon Jesus]

Well presented and easy to use, too!

 

[Filthy Dangles]

I do wonder how much 'noise' is involved those numbers. You already mentioned the value of it isn't much, I wonder if you could make it more valuable by distilling it. I 'feel' like players will just sort of accumulate time against top players here and there even if they aren't 'really playing against them' if that makes sense, I think that's part of the problem with the stat and why it's not deemed very valuable statistically.

If you could find a way to look at higher leverage minutes against top players where you only look at those minutes where the player is really being deployed against those players, and weigh higher leverage minutes (such as ones that occur on Dzone starts, late game situations, score adjustments) and even a way to account for if a team is getting shellacked the coach might ride his horse(s) and they are going to bear the brunt of that.

I don't know, maybe it all evens out team/league wide? Or maybe not considering some teams deploy players differently.

 

[TomasHertlsRooster]

I do wonder how much 'noise' is involved those numbers. You already mentioned the value of it isn't much, I wonder if you could make it more valuable by distilling it. I 'feel' like players will just sort of accumulate time against top players here and there even if they aren't 'really playing against them' if that makes sense, I think that's part of the problem with the stat and why it's not deemed very valuable statistically.

If you could find a way to look at higher leverage minutes against top players where you only look at those minutes where the player is really being deployed against those players, and weigh higher leverage minutes (such as ones that occur on Dzone starts, late game situations, score adjustments) and even a way to account for if a team is getting shellacked the coach might ride his horse(s) and they are going to bear the brunt of that.

I don't know, maybe it all evens out team/league wide? Or maybe not considering some teams deploy players differently.

Yeah, as mentioned here, my goal wasn't necessarily to create a new metric that I found useful, but rather to revive an old metric that hadn't been available for at least a year and then make it available to the public since I know I'm not the only one who wants to see this information.

Your suggestion sounds dangerously close to RAPM though. Which, in all seriousness, is what I believe is the best way to account for quality of competition. What exactly do you have in mind by a team getting shellacked?

 

[majormajor]

I would like some help interpreting the stat.

For example what is one percentage point difference in QoC? Can it be more simply expressed as an average TOI of opponents?

Also are you familiar with the work to establish the value of QoC? How much does it change results all else equal?

 

[TomasHertlsRooster]

I would like some help interpreting the stat.

For example what is one percentage point difference in QoC? Can it be more simply expressed as an average TOI of opponents?

Also are you familiar with the work to establish the value of QoC? How much does it change results all else equal?

It can be interpreted as an average TOI% of opponents that is weighted by the number of minutes against each opponent, yes. For example if hockey were a one-on-one sport and you played 100 minutes against opponent A who has 30% TOI and 200 minutes against opponent B who has 40% TOI, your TOI% QoC would be 36.67%. The key difference between the two being that TOI% only includes games that a player plays in.

I've read a decent amount of the work on QoC. To me, it has very little value when all else is equal. Various efforts to quantify its impact through multi-linear regression have established this. But, there is the caveat that QoC is correlated with other factors that correlate closely with positive results like QoT and skill (coaches tend to trust their best players more against top competition) and that even ridge regressions can struggle to parse out its "true" impact.

I personally take note of it when player's results come in especially difficult or easy minutes but I'm more confident in models such as RAPM that account for QoC than I am in subjectively over-emphasizing it if that makes sense.

 

[Machinehead]

If I'm reading this right, Adam Fox isn't *that* sheltered and Zibanejad is doing his thing in very hard usage.

I appreciate the good news, Mr. Bacon.

 

[TomasHertlsRooster]

If I'm reading this right, Adam Fox isn't *that* sheltered and Zibanejad is doing his thing in very hard usage.

I appreciate the good news, Mr. Bacon.

Yeah, that sounds about right.

 

[Michael Farkas]

Nice work. Surprised slightly by the lack of variance. There's probably a few ways you could go to "drum up" variance to paint a clearer picture.

"Simplest" (he says, not knowing how any of this is coded) would be home/road splits to accommodate for last change quickly.
"Better" would be probably be closer to: home deployment after a non-icing stoppage in +/- 2 goal margin scenarios.

That may well be impossible...but I suspect (as a former line matcher myself) that would increase your output range, if you're into that kind of action...