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# Quality of Competition

 08-18-2012, 11:15 AM #1 BigFatCat999 I love GoOoOlD     Join Date: Apr 2007 Location: Campbell, NY Country: Posts: 11,584 vCash: 500 Modified Corsi Numbers? I have had one problem with corsi. Yes, it records shots allowed but what about blocks? Is there a modified corsi number which adjusts with number of blocks? For example: Shots allowed per game - blocked shots per game = modified number.
 08-18-2012, 11:35 AM #2 barneyg Registered User   Join Date: Apr 2007 Posts: 2,383 vCash: 500 That number is called Fenwick.
08-18-2012, 11:37 AM
#3
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 Originally Posted by barneyg That number is called Fenwick.
Thank you

 08-22-2012, 09:31 PM #4 Pietraneglo222     Join Date: Jul 2009 Location: Gatineau Country: Posts: 3,271 vCash: 500 Quality of Competition Consider player A and player B (fictional) Player A CorsiRelQoC = -1 CorsiRel = 12 +/- Rel = 1.2 Player B CorsiRelQoC = 1 CorsiRel = 3 +/- Rel = 0.4 Say they had comparable team mates, wouldn't player A be Mathematically superior since the quality of competition is only like 2-3% different while the other stats seems to vary strongly? The QoC difference I illustrated is pretty much worse case scenario too. Just wanna talk about my impression that Quality of Teammates is almost always a more important consideration. (whether Corsi QoT or +/- QoT) That players that play a lot tend to play against a variety of players over a season and it averages out almost perfectly no matter what a coach tries to do. Last edited by Fugu: 09-14-2012 at 12:46 PM. Reason: enough
08-23-2012, 02:09 AM
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sjaustin77
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Quote:
 Originally Posted by Immanuel Consider player A and player B (fictional) Player A CorsiRelQoC = -1 CorsiRel = 12 +/- Rel = 1.2 Player B CorsiRelQoC = 1 CorsiRel = 3 +/- Rel = 0.4 Say they had comparable team mates, wouldn't player A be Mathematically superior since the quality of competition is only like 2-3% different while the other stats seems to vary strongly? The QoC difference I illustrated is pretty much worse case scenario too. Just wanna talk about my impression that Quality of Teammates is almost always a more important consideration. (whether Corsi QoT or +/- QoT) That players that play a lot tend to play against a variety of players over a season and it averages out almost perfectly no matter what a coach tries to do.
I don't know which one is more important but I wouldn't assume QOT is always more important than QOC. Depending on how a player is used QOT could be closer than QOC. On your team you play with a lot of the same teammates even if it is in different quantities. With QOC you could always be matched up with an easier line which will give a big difference.

I think in general both might be overstated but hardly irrelevant and the percentage difference will be much greater than 2-3% even among top defensemen. While they are all NHL players and some 1st liners will play with or against some 4th liners that might even things out some; there are huge differences even in the way "top pairing" defenders are used. Most top defenders if used to shutdown the oppositions top lines will have a fairly similar QOC. Some aren't used that way though. Some are used as an offensive #1 defenseman and some are used as shutdown #1 defenseman, while others are used more evenly.

Let's use Chara and Yandle as examples. Both considered 1st pairing or number one Dmen.
The median 1st line forward scored 62 points last year.
The median 2nd line forward scored 41 points.

Generally Chara is always on the ice against 1st line forwards. Yandle is generally on the ice against 2nd line forwards. For the most part that will be their average QOC. That 21 point difference is huge. Chara would be playing QOC that is 51% better than Yandle's by points scored. My biggest problem is with the systems. I don't think anyone knows how to measure the difference between players now. What does QOC of .093 vs .046 vs -.023 mean? How much better is each player than the other one?

I am working on my own system basically based on Pts/60 instead of +/- or Shots. I use all positive numbers so that you can more directly compare all players across the league. I have done more work on QOT than QOC so far because I can't find the data I need in an easy to use form yet for each players opponents.

Here are my QOC ratings for a few players weighted by ice time vs each player:

Chara - 3.195
Boychuk - 2.904
Karlsson - 2.688
Weber - 2.973
Pietrangelo - 2.744

So Chara played:
7% harder competition than Weber
10% over Boychuk
16% over Pietrangelo
19% over Karlsson.

That matches what my eyes tell me when I watch those players play. I'm interested to do more players like Gorges, Girardi, McDonagh but it could be a while unless I find an easier way to do it. I think those three will closely match or beat Chara on QOC.

08-23-2012, 10:50 AM
#6
seventieslord
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 Originally Posted by sjaustin77 I don't know which one is more important but I wouldn't assume QOT is always more important than QOC. Depending on how a player is used QOT could be closer than QOC. On your team you play with a lot of the same teammates even if it is in different quantities. With QOC you could always be matched up with an easier line which will give a big difference. I think in general both might be overstated but hardly irrelevant and the percentage difference will be much greater than 2-3% even among top defensemen. While they are all NHL players and some 1st liners will play with or against some 4th liners that might even things out some; there are huge differences even in the way "top pairing" defenders are used. Most top defenders if used to shutdown the oppositions top lines will have a fairly similar QOC. Some aren't used that way though. Some are used as an offensive #1 defenseman and some are used as shutdown #1 defenseman, while others are used more evenly. Let's use Chara and Yandle as examples. Both considered 1st pairing or number one Dmen. The median 1st line forward scored 62 points last year. The median 2nd line forward scored 41 points. Generally Chara is always on the ice against 1st line forwards. Yandle is generally on the ice against 2nd line forwards. For the most part that will be their average QOC. That 21 point difference is huge. Chara would be playing QOC that is 51% better than Yandle's by points scored. My biggest problem is with the systems. I don't think anyone knows how to measure the difference between players now. What does QOC of .093 vs .046 vs -.023 mean? How much better is each player than the other one? I am working on my own system basically based on Pts/60 instead of +/- or Shots. I use all positive numbers so that you can more directly compare all players across the league. I have done more work on QOT than QOC so far because I can't find the data I need in an easy to use form yet for each players opponents. Here are my QOC ratings for a few players weighted by ice time vs each player: Chara - 3.195 Boychuk - 2.904 Karlsson - 2.688 Weber - 2.973 Pietrangelo - 2.744 So Chara played: 7% harder competition than Weber 10% over Boychuk 16% over Pietrangelo 19% over Karlsson. That matches what my eyes tell me when I watch those players play. I'm interested to do more players like Gorges, Girardi, McDonagh but it could be a while unless I find an easier way to do it. I think those three will closely match or beat Chara on QOC.
Hopefully you are referring only to even strength.

 08-23-2012, 11:36 AM #7 Talks to Goalposts Registered User   Join Date: Apr 2011 Location: Edmonton Country: Posts: 5,096 vCash: 500 The thing is that relCorsi QoC is really only a proxy stat used to identify whose matching against whom. There are all sorts of second order effects that IMO outweigh just the expected corsi of your opposition. Defensemen tend to get the most hierarchical QoC usage and I think what can be observed to happen to a defenders stats when they go from 3rd pair to 1st pair usage exceeds the difference in the relCorsi of their opponents. The thing is that good players tend to play other good players, so there is a strong trend pushing ability to control of the game towards the middle. We can overstate the impact of QoC though, in most cases its the gap between playing mostly 2nd and 1st liners and playing mostly 2nd and 3rd liners. Coaches like choosing matchups but they have far from perfect control of them.
08-23-2012, 05:36 PM
#8
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 Originally Posted by seventieslord Hopefully you are referring only to even strength.
Can you expand on that? Are you saying that I shouldn't try to come up with a QOC for anything other than Even Strength, or that I shouldn't use anything but even strength to determine the Quality of that player?

If the latter, why? Wouldn't taking a look at a player's overall game - Pts/60 at both ES and PP give a more accurate measure of that player's quality?

 08-23-2012, 06:03 PM #9 Pietraneglo222     Join Date: Jul 2009 Location: Gatineau Country: Posts: 3,271 vCash: 500 Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed pretium ante ipsum, et ornare mi. Morbi imperdiet blandit sem non fermentum. Proin sem nulla, condimentum et vulputate a, ullamcorper non velit. Vivamus tristique, tellus et iaculis fermentum, nibh libero dignissim erat, sit amet suscipit mauris turpis sit amet magna. Quisque vitae arcu risus, ac tristique turpis. Vivamus scelerisque faucibus cursus. In cursus aliquam pretium. Phasellus sit amet dolor a nunc cursus malesuada ac et tellus. Proin at dolor placerat nunc ultricies consequat tempus id dui. In hac habitasse platea dictumst. Nam tortor ligula, pharetra sed sodales id, adipiscing nec purus. Donec nisi erat, aliquet ut feugiat ut, rutrum non urna. Praesent convallis risus non erat dignissim eget feugiat eros tincidunt. Aliquam sed suscipit magna. Sed ac leo erat. Nullam malesuada convallis arcu eu sollicitudin. Sed sit amet eleifend tellus. Aenean vitae orci est, placerat adipiscing arcu. Nulla sit amet accumsan risus. Nam id turpis velit. Quisque sit amet lorem vel ante vulputate suscipit. Donec tellus tellus, lobortis ac rhoncus at, ullamcorper eget magna. Quisque placerat, tellus id congue rhoncus, mauris magna commodo quam, id fermentum nunc urna et erat. Aenean ornare ipsum ac quam condimentum quis semper est aliquet. Proin viverra suscipit feugiat. Pellentesque gravida bibendum nisl in scelerisque. Nunc laoreet porta justo eu pulvinar. Proin facilisis tortor sed nisi tempor lobortis. Duis eget lacinia odio. Vivamus dictum elit eget felis tempor ultricies. Vestibulum convallis ligula sodales sapien rutrum auctor. Nullam lacus sapien, laoreet et dapibus sit amet, sollicitudin id justo. Donec pulvinar erat ut ligula ullamcorper nec congue leo tempus. Donec at augue dolor. Donec eget pulvinar lectus. Cras eu sem a ipsum mattis hendrerit ut vitae lorem. Phasellus posuere convallis sem, sit amet porttitor dui rhoncus nec. In pretium fringilla risus, non viverra lectus bibendum ac. Nullam porttitor tortor eu odio semper ornare et eu ligula. Aliquam dictum malesuada ipsum, et vehicula justo blandit id. Curabitur et massa in tortor varius dapibus. Maecenas ultricies lorem eget risus rhoncus dapibus. Suspendisse ac ligula vitae purus pellentesque porta. Morbi consectetur quam et lectus venenatis varius. Nulla tristique velit ac nibh ullamcorper lobortis. Nunc erat sapien, placerat quis sodales sed, tempus non ante. Praesent egestas quam vitae est mollis eget tincidunt tellus porta. Quisque a rhoncus nunc. Phasellus eu velit non magna aliquam euismod eget vitae lectus. Donec accumsan, libero sed varius dignissim, purus ipsum lobortis dui, at mollis augue urna vitae nibh. Suspendisse id felis et magna adipiscing fringilla ac a ipsum. Fusce neque tellus, porta quis ultrices ac, suscipit sed lectus. Donec et quam erat. Integer sed fermentum sapien. Etiam consectetur auctor nunc, iaculis sollicitudin nibh euismod a. Sed venenatis, mi vel consectetur pulvinar, lacus elit mollis elit, ut consectetur urna massa a risus. Nullam imperdiet, tortor sit amet elementum tincidunt, mauris odio porta neque, ac viverra libero mi et quam. Integer vitae aliquam magna. Phasellus ut justo id purus hendrerit convallis vel eu orci. Morbi dui velit, imperdiet ac ornare vel, sollicitudin vel lorem. Last edited by Pietraneglo222: 09-14-2012 at 10:44 AM.
08-23-2012, 06:47 PM
#10
Iain Fyffe
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 Originally Posted by sjaustin77 If the latter, why? Wouldn't taking a look at a player's overall game - Pts/60 at both ES and PP give a more accurate measure of that player's quality?
I'm assuming he's referring to the fact that pretty much anybody can put up points on the PP. Points at ES are much harder to come by, and require more skill.

Also, PP points are largely driven by opportunity, where some players get mounds of PP time and other next to none, while all decent players get within a certain range of ES minutes.

08-23-2012, 07:37 PM
#11
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 Originally Posted by Immanuel In the wild, CorsiRel varies from +22 (daniel sedin) to -32 (manny malhotra). Meanwhile CorsiRel QoC only varies from about +2 to -2 in extreme cases. This tells me that players face a largely uniform level of competition. When you scale players out of 40 (+20 to -20) you only have a variation of 4 which is about 10% in the worst case and on average closer to 2 or 3%. On the other hand CorsiRel QoT varies a lot more. +7 to -7 let's say. Which is 250% more important a difference than in QoC. This also makes sense intuitively. If you're a 1st line center you're gonna play with your team's best players on a very reliable basis. Meanwhile the coach has to make active and difficult decisions to match the player against better or worse competition. At the same time the other team's coach is also matching lines so it's almost a balanced force in that sense. (Mostly noise though. Looking at the stats it seems Coaches are completely incapable of controlling who matches up against who.) This also ties into my opinion that there is great opportunity for a team that recognizes that the popular opinion (that you shouldn't give prime opportunities to players that play on lower lines) is actually wrong. The fear that a player will fold "facing tougher competition" isn't rational because the higher he climbs in the line hierarchy, the easier his time will be because the quality of his team mates will increase dramatically while the competition he faces will remain relatively stable. There seems to exist a LOT of overrated top liners and a lot of excellent third liners that could populate a very competitive team for cheap. (I used a max of -20 regarding CorsiRelQoC because only a handful of players have a CorsiRelQoC lower than -20. It plays against my argument anyway right?) I also looked at your p/60 QoC post sjaustin77. My problem is that it isn't a measure of a player's overall ability. While Corsi and +/- are probably better suited to. At least intuitively.

To the bolded, at this point it is more for myself - I doubt that I will ever have the time or resources to develop and present it the way that I would like but I will explain it a little bit. I actually use an adjusted figure so purely offensive players will move down and defensive players will move up so it has a component of defense. Maybe not as much defense as other systems but those also leave out a lot of context on how and why players get those numbers.

Until or if I ever get my systems into the public I guess no one would ever give them any weight (and at this point no one really knows about them); but from the work I have done so far I think my numbers have a more accurate order, make more sense, are easier to calculate the differences and can be explained by going through each player individually though that would take forever. As a small example, +/-QOT has Krejci, Horton, Lucic near the bottom of the league on par with Thornton, Paille, Campbell. About the only difference between them and Bergeron, Seguin, Marchand is each other and those 3 rank near the top of the league. They played similar amounts with all 6 Bruins D and the other forwards. There are many similar inconsistencies in both +/- and Corsi that just don't make sense.

I also think that while Corsi may be better at predicting future results I think production is a better measure of what actually happened so I think production is a better place to start. I think when people talk about QOC they are largely talking about offense. Top defenseman aren't put out there to stop third liners who are good at defense. Look at any best player lists and they are dominated by offense first players. Even defensemen lists are mostly dominated by high offense defenseman.

Another problem I have is with relative numbers. As far as I know they are relative to teammates. All that tells me is how good a player was relative to a teammate not to the player I want to compare him against. Take the top player on a team of all stars they all look the same basically with relative numbers of 0. If you took the same top player on a team of 4th liners wouldn't he now look like the much better player even though he is the exact same person?

How are you figuring out the difference between players? To me whether it is +2 to -2 or +7 to -7, that looks like a huge difference, much more than 2, 3 or even 10%. How do you measure either of the systems? Here is +/-QOC for Backes - .117, Callahan - .062, Pacioretty - .000, Yandle - neg .057, and Emmerton - neg .169. How do you calculate how much better Backes' competition is over Callahan, Pacioretty, Yandle and Emmerton? It has to be greater than 10%.

In general there won't be a huge difference in top defenseman who are playing the same role but when used differently I think it is much greater. Coaches are actually pretty good at matching up their top D vs the top forwards. At home they get last change so they can basically always do it. When they are away a player like Chara is always ready to change quick to go on or off as the guy he is shadowing does.

Most defenseman aren't used as much like this and that is why in general there may be only a couple % difference but there should be a huge gap between them and the middle or lower tier defenseman. There will and should be a huge difference between Chara and Yandle (both top defensmen but used differently) or Chara and MA Bergeron (not a top tier defenseman and definitely not used to shut down top lines). I don't see how it can only be a small difference.

08-23-2012, 07:47 PM
#12
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 Originally Posted by Iain Fyffe I'm assuming he's referring to the fact that pretty much anybody can put up points on the PP. Points at ES are much harder to come by, and require more skill. Also, PP points are largely driven by opportunity, where some players get mounds of PP time and other next to none, while all decent players get within a certain range of ES minutes.
Somewhat true though I don't give them the same weight because they are a much smaller % of a players ice time and overall goals scored. Most of the play and points come from Even Strength but that doesn't mean that you should ignore the powerplay numbers right?

Yes, and that is why I use the rate stats instead of raw numbers.

I shouldn't have opened this can of worms since I don't have the time or all the data I need to explain everything and bring it into the public to be scrutinized. Maybe someday.

 08-23-2012, 08:20 PM #13 Pietraneglo222     Join Date: Jul 2009 Location: Gatineau Country: Posts: 3,271 vCash: 500 Delete me Last edited by Pietraneglo222: 09-14-2012 at 10:31 AM.
08-23-2012, 09:51 PM
#14
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 Originally Posted by Immanuel Well as far as the Bruins go, that's only because Behindthenet's +/- QoT uses relative +/- not raw +/-. Lucic's most common linemates were krejci and Horton. Both of whom had much lower +/- than the rest of the team so it seems to make sense that Lucic's +/- QoT is very low. I'd like a raw +/- QoT I think. For why I said 10% difference in CorsiRelQoC and numbers like that ... I just calculated that mathematically. -2 to 2 is a difference of 4 units and the scale is 40 wide (-20 to +20). 4 is 10% of 40. That was the worst-case scenario and the biggest difference possible. For most people their CorsiRelQoC hovers around zero.
Like I said I don't like relative so that explains a lot of it. Basically every player on all the worst teams is ranked better than Krejci, Looch and Horton. I don't think it works to accurately compare players on other teams vs each other. The rest of Lucic's top ten teammates match almost exactly with Bergeron and in very close % to Bergeron's ice time as well.

I still don't get the difference. I get the 4 units difference between 2 and -2. Why do you scale it? What are you using to make it 20 to -20? Why not 10 and -10 or whatever? I guess I don't see how you can put a cap on the difference in QOT or QOC or why it should be at 10%. Why don't you just use 4 so that a player with a 2 vs a 1 rating will have a 25% difference (1 divided by 4 units)?

It doesn't make sense that there is only a 10% difference at worst. In theory it should be unlimited. I would say that Crosby is more than twice as good as the worst player in the league. So if someone went exclusively vs Crosby and someone else vs the worst player in the league. He should have twice the QOC value. Now that isn't reality as you do play against some of the same players (and Crosby is probably 10 times better) but there is no reason to put a cap at 10%.

The average player used in the same way should have similar numbers but there are a lot of players way above and below average and top players spend the majority of time against the top and bottom vs the bottom.

Even the same pair D - Chara and Boychuk have top players that Chara played against exclusively and/or played against a lot higher percentage of his minutes. Chara played against Jagr, Thornton, Pavelski, Carter, Gerbe, Marleau, Hartnell, & Malone that Boychuk didn't play at all. Kovalchuk, Parise, Lupul, Kessel, Spezza, Neal, Malkin, Michalek are some of many examples that Chara played a lot more minutes against. When you weight by ice time Chara should come out more than a couple percent ahead of his own D pair.

08-24-2012, 01:25 AM
#15
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Quote:
 Originally Posted by Immanuel Consider player A and player B (fictional) Player A CorsiRelQoC = -1 CorsiRel = 12 +/- Rel = 1.2 Player B CorsiRelQoC = 1 CorsiRel = 3 +/- Rel = 0.4 Say they had comparable team mates, wouldn't player A be Mathematically superior since the quality of competition is only like 2-3% different while the other stats seems to vary strongly? The QoC difference I illustrated is pretty much worse case scenario too. Just wanna talk about my impression that Quality of Teammates is almost always a more important consideration. (whether Corsi QoT or +/- QoT) That players that play a lot tend to play against a variety of players over a season and it averages out almost perfectly no matter what a coach tries to do.
By focusing exclusively on Corsi and Corsi QoC, you are missing a big part of QoC. Better forwards tend to have better shooting percentages, and players that play against these top forwards will take a larger hit to their plus-minus than to their Corsi.

Also consider that QoC is a first-order rating only. It hasn't gone through multiple iterations, which would expand the observed range of QoC.

For these reasons, I suspect your measurement of the range of QoC is low by at least a factor of 2.

That said, you may be correct that quality of teammates is more important. I think playing with a star player can certainly boost a player's stats more than the tough matchups that come with that role will sink his stats.

 08-24-2012, 01:41 AM #16 TheDevilMadeMe Registered User     Join Date: Aug 2006 Location: Brooklyn Country: Posts: 45,932 vCash: 500 There is a serious logical fallacy going on in the original post. Statement 1: Quality of Teammates is more important than Quality of Competition Statement 2: Quality of Competition isn't important Those are two seperate statements and the truth of 1 does not prove the truth of 2. I'm making a judgement as to the truth of statement 1.
 08-24-2012, 03:16 AM #17 Pietraneglo222     Join Date: Jul 2009 Location: Gatineau Country: Posts: 3,271 vCash: 500 Delete me Last edited by Pietraneglo222: 09-14-2012 at 10:33 AM.
08-24-2012, 10:18 AM
#18
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http://hockeyanalysis.com/2012/01/25...tionteammates/

Quote:
 If you have a great offensive player, the theory is your opponents will want to match up their great defensive players against him. But, at the same time you are trying to match up your great offensive player against their weakest defensive players. When at home, you get the line matching advantage, while on the road your opponent does. When all is said and done everything more or less evens out.

08-27-2012, 10:22 AM
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 Originally Posted by Terrence http://hockeyanalysis.com/2012/01/25...tionteammates/
I also believe (but can't statistically prove heh) that it is easier to match defensive players against who you want than offensive players, because offensive players tend to need to get into a rhythm to be most effective, while defense relies less on instinct and more on learned technique.

All that said, quality of competiton definitely varied much more pre-lockout, when teams could ice the puck if they didn't like a certain matchup.

Also, coaches are more likely to use on the fly changes to maintain matchups in the playoffs

Most importantly, can someone please explain why absolute QualComp values are meaningful? I always looked at them as more relative to each other.

Last edited by TheDevilMadeMe: 08-27-2012 at 11:23 AM. Reason: Misread the paper

08-27-2012, 10:24 AM
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 Originally Posted by Immanuel Well the proof of statement 2 is this: -CorsiRelQoC has a variation of 2-3% on average and at most 10%, therefore not very important. I did not state explicitly as a proof like that but it's in there.
As overpass points out, this ignores the ability of star players to increase shooting percentage

08-27-2012, 12:03 PM
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 Originally Posted by TheDevilMadeMe As overpass points out, this ignores the ability of star players to increase shooting percentage
+/- QoC mirrors my findings on RelCorsiQoC.

08-27-2012, 01:10 PM
#22
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Quote:
 Originally Posted by Immanuel You mean if I look at QoC over 2 seasons or more there will be a larger QoC range? Wouldn't they huddle around the middle at about the same rate though? If that's not what you mean you can say I'm stupid or explain or whatever.
By first order I mean the rating is only calculated once.

A second order rating would calculate QoC, adjust the rating of all players by the first order QoC, and then calculate QoC a second time using the adjusted ratings. A third order rating would add another iteration, and so on.

If good players tend to play against good players and bad players against bad players, first order QoC values will be smaller than 2nd order, 3rd order, or fully iterated QoC values.

08-28-2012, 02:43 AM
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 Originally Posted by overpass By first order I mean the rating is only calculated once. A second order rating would calculate QoC, adjust the rating of all players by the first order QoC, and then calculate QoC a second time using the adjusted ratings. A third order rating would add another iteration, and so on. If good players tend to play against good players and bad players against bad players, first order QoC values will be smaller than 2nd order, 3rd order, or fully iterated QoC values.
Can you explain "second order," "third order" ratings for those of us who haven't taken a class in stats in over a decade?

08-28-2012, 09:23 AM
#24
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 Originally Posted by TheDevilMadeMe Can you explain "second order," "third order" ratings for those of us who haven't taken a class in stats in over a decade?
First order QoC: The rating of the average opponent.

Second order QoC: Adjust every player's rating to include the first order QoC. Recalculate QoC.

Third order QoC: Adjust every player's rating to include second order QoC. Recalculate QoC.

Rinse and repeat until the results stabilize.

Example: Consider a simple model of forwards only where:

1st line players play against other 1st lines 60% of the time, against 2nd lines 20% of the time, and against 3rd lines 20% of the time

2nd line players play against other 2nd lines 60% of the time, 1st lines 20% of the time, and 3rd lines 20% of the time.

3rd line players play against other 3rd lines 60% of the time, 1st lines 20% of the time, and 2nd lines 20% of the time.

4th lines only play each other, so we will ignore them from here because their QoC can't be compared to the others.

1st lines have a rating of 5.
2nd lines have a rating of 0.
3rd lines have a rating of -5.

First order QoC
1st lines: 0.6*5 + 0.2*0 + 0.2*(-5) = 2
2nd lines: 0.2*5 + 0.6*0 + 0.2*(-5) = 0
3rd lines: 0.2*5 + 0.2*0 + 0.6*(-5) = -2

New ratings
1st lines: 5 + 2 = 7
2nd lines: 0 + 0 = 0
3rd lines: -5 - 2 = -7

Second order QoC
1st lines: 2.8
2nd lines: 0
3rd lines: -2.8

New ratings
1st lines: 7.8
2nd lines: 0
3rd lines: -7.8

Third order QoC
1st lines: 3.12
2nd lines: 0
3rd lines: -3.12

QoC for 1st lines
Fourth order: 3.25
Fifth order: 3.30
Sixth order: 3.32
Seventh order: 3.33

In this model the first order QoC for first lines is 2.0. But after multiple iterations the "true" QoC for first lines is roughly 3.33.

(In this simple case we could find an algebraic solution for the "true" QoC. This could also be attempted for the NHL as a whole but would require a lot of computing power.)

08-28-2012, 08:14 PM
#25
seventieslord
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Quote:
 Originally Posted by sjaustin77 Somewhat true though I don't give them the same weight because they are a much smaller % of a players ice time and overall goals scored. Most of the play and points come from Even Strength but that doesn't mean that you should ignore the powerplay numbers right?
Yes, it does mean that.

If your goal is to demonstrate who is the best at recording points per unit of ice time, it is absolutely important to know what situations they played in. If you separate it into two situations, fine, but don't try to have a "catch all" stat that pretends that ES and PP time are the same thing.

(offensive GVT, for example, is a "catch all" stat that determines how many points a player "should" have, based on how much ES and PP icetime they received, not just a total number)

player A: 800 ES minutes, 300 PP minutes, 40 ESP, 30 PPP
player B: 800 ES minutes, 0 PP minutes, 50 ESP

who is the better producer? Player A has 3.81 points per 60 minutes, and player B has 3.75. Player A appears better, or, if we're not splitting hairs, they are about equal. And certainly, from a "hockey card stats" perspective, player A looks much better.

But if the only thing making player A the better "per minute" producer is his PP opportunities, what good are these 3.81 and 3.75 numbers? Why would we not want to get to the bottom of who was outperforming who? Those two numbers might shed light on who was better, or they might just shed light on who was playing on the PP and who wasn't.

Most players score at about double the rate on the PP. Player A did. Player B would also likely see a rate of production on the PP that was close to double his ES scoring rate. But because that wasn't how his coach used him, did that make him a lesser offensive player?

This isn't an absurd extreme example, either. This happens.

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