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Player Discussion: - Winnipeg Jets Defense | Page 91 | HFBoards - NHL Message Board and Forum for National Hockey League
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Player Discussion: Winnipeg Jets Defense

I wonder where this question is going.
In statistics, data gathering and cleanliness is the single most important thing, so it's not an out of line question to ask.
I'm sure the professional statistician has no understanding of confirmation bias.
And? Criminals often know what they are doing is a crime and it doesn't prevent them from doing it.

I like Garret - I miss him on these boards, but that doesn't mean his methodology is scientifically sound or peer reviewed (peer being an actual data scientist).

Who crowned him as the 'professional statistician'? Is it simply the product of him working and earning money in that role? If I called myself a doctor and started treating patients because I watched youtube videos, would that make me a doctor?

Hockey advanced stats are still in their infancy. There are a lot of people pushing a lot of 'their' metrics, some gimmicky and some not. There are tons of questions with these metrics:
  • How are they compiled?
  • How are they interpreted?
  • How are they weighted or used in calculations?
  • What is the background of the people doing this work?
  • Are they subjective or objective?
  • How likely is there to be bias?
I keep bringing this stuff up but those who use statistics as the bible or foundation of their understanding of hockey and players ignore the questions, it's almost like a cult.

I think what is happening in a lot of cases is that the NHL and teams use their own metrics and advanced stats to make determinations, and couple that with what they are seeing and hard outcomes. Those metrics are usually not what we see, and they aren't shared with the public.

That's why you see a lot of team and coaching moves that don't align with the advanced stats Garret, JFresh, whomever else are promoting.

I'm not saying that these stats are dereft of accuracy or value, but there are a TON of question marks, and when the stats don't match an experienced eye, it can call it in to question. Of course, eye test is very prone to bias as well.

In my profession, I see statistics compiled, bent, and manipulated to tell a story all the time. That's why you need a scientific method and peer review if you want accuracy.

I think if it was a pick that would have had to be announced as part of the trade. Future considerations I think is much softer than that and we will likely never know what it was.
I don't think that's true - at least not from what I've read (please someone correct me if I'm wrong). I don't think disclosure is necessary, though it would be written in the contract.
 
In statistics, data gathering and cleanliness is the single most important thing, so it's not an out of line question to ask.

And? Criminals often know what they are doing is a crime and it doesn't prevent them from doing it.

I like Garret - I miss him on these boards, but that doesn't mean his methodology is scientifically sound or peer reviewed (peer being an actual data scientist).

Who crowned him as the 'professional statistician'? Is it simply the product of him working and earning money in that role? If I called myself a doctor and started treating patients because I watched youtube videos, would that make me a doctor?

Hockey advanced stats are still in their infancy. There are a lot of people pushing a lot of 'their' metrics, some gimmicky and some not. There are tons of questions with these metrics:
  • How are they compiled?
  • How are they interpreted?
  • How are they weighted or used in calculations?
  • What is the background of the people doing this work?
  • Are they subjective or objective?
  • How likely is there to be bias?
I keep bringing this stuff up but those who use statistics as the bible or foundation of their understanding of hockey and players ignore the questions, it's almost like a cult.

I think what is happening in a lot of cases is that the NHL and teams use their own metrics and advanced stats to make determinations, and couple that with what they are seeing and hard outcomes. Those metrics are usually not what we see, and they aren't shared with the public.

That's why you see a lot of team and coaching moves that don't align with the advanced stats Garret, JFresh, whomever else are promoting.

I'm not saying that these stats are dereft of accuracy or value, but there are a TON of question marks, and when the stats don't match an experienced eye, it can call it in to question. Of course, eye test is very prone to bias as well.

In my profession, I see statistics compiled, bent, and manipulated to tell a story all the time. That's why you need a scientific method and peer review if you want accuracy.


I don't think that's true - at least not from what I've read (please someone correct me if I'm wrong). I don't think disclosure is necessary, though it would be written in the contract.
I just went through this talking about Lindgren. The stats said he was ok with Fox, worse without him. Which is fine, but dig deeper. How bad was the Trouba effect. It was bad. Fox was better without Lindgren, but the player replacing him was a better player. The last stat you see is Lindgren is really good with Schneider. This was very similar to arguments used against Pionk last year. That he was worse away from Dillon, but the results with Samberg were kind of glossed over. In the end the Jets chose to follow the analytics of that pairing, which was the Jets best d-pairing to start the year. I always ask questions about stats, even when Garret was on here he was crusading against Pionk, but he had some stats at his disposal that showed that Pionk was an effective puck mover, they weren't stats he provided in his original argument. Sometimes you have to dig deeper. Sometimes the stats work, where Garret's crusade against Mark Stuart probably helped the Jets turn a corner by buying him out. His anti-Stanley stance may still hold water. But the picture is so wide in the stats that I am sure that they are not as isolated as statisticians try to make them. In hockey every single player has an impact on the stats. Where you start from has an impact on the stats. What the score is has an impact on the stats.

I became real skeptical of stats when the government was locking people down based on stats, which if you did quick math meant that 0.01% of the population posed a legitimate public health risk, and the number of beds available was a direct result of government policy that closed two emergency care facilities.
 
In statistics, data gathering and cleanliness is the single most important thing, so it's not an out of line question to ask.

And? Criminals often know what they are doing is a crime and it doesn't prevent them from doing it.

I like Garret - I miss him on these boards, but that doesn't mean his methodology is scientifically sound or peer reviewed (peer being an actual data scientist).

Who crowned him as the 'professional statistician'? Is it simply the product of him working and earning money in that role? If I called myself a doctor and started treating patients because I watched youtube videos, would that make me a doctor?

Hockey advanced stats are still in their infancy. There are a lot of people pushing a lot of 'their' metrics, some gimmicky and some not. There are tons of questions with these metrics:
  • How are they compiled?
  • How are they interpreted?
  • How are they weighted or used in calculations?
  • What is the background of the people doing this work?
  • Are they subjective or objective?
  • How likely is there to be bias?
I keep bringing this stuff up but those who use statistics as the bible or foundation of their understanding of hockey and players ignore the questions, it's almost like a cult.

I think what is happening in a lot of cases is that the NHL and teams use their own metrics and advanced stats to make determinations, and couple that with what they are seeing and hard outcomes. Those metrics are usually not what we see, and they aren't shared with the public.

That's why you see a lot of team and coaching moves that don't align with the advanced stats Garret, JFresh, whomever else are promoting.

I'm not saying that these stats are dereft of accuracy or value, but there are a TON of question marks, and when the stats don't match an experienced eye, it can call it in to question. Of course, eye test is very prone to bias as well.

In my profession, I see statistics compiled, bent, and manipulated to tell a story all the time. That's why you need a scientific method and peer review if you want accuracy.


I don't think that's true - at least not from what I've read (please someone correct me if I'm wrong). I don't think disclosure is necessary, though it would be written in the contract.
This post is a good example of why hes not here... the guy clearly explains his models and others and goes in depth as to what the potential flaws or biases are... and then guys who clearly dont read that content make posts about how garrett thinks hes the be all end all.

Also i can tell you if you think peer review is unbiased you are mistaken... as a polar bear guide ive seen various agendas override science in that world.

Nothing is perfect but the guys making these models for hockey do not have a specific agenda except trying to make their models work.... they dont hate stan or pionk or scheif etc...
 
Used puck bag?
There is a past story of the future consideration being an equipment dryer, but not sure if that type of deal is allowed anymore. My understanding is future considerations is the minimal offer possible, because you can't trade nothing. It can be as vague as we will contact you first before we waive a player to see if you are interested. Most never come to anything and most times we have no idea what the future consideration was.
 
In statistics, data gathering and cleanliness is the single most important thing, so it's not an out of line question to ask.

And? Criminals often know what they are doing is a crime and it doesn't prevent them from doing it.

I like Garret - I miss him on these boards, but that doesn't mean his methodology is scientifically sound or peer reviewed (peer being an actual data scientist).

Who crowned him as the 'professional statistician'? Is it simply the product of him working and earning money in that role? If I called myself a doctor and started treating patients because I watched youtube videos, would that make me a doctor?

Hockey advanced stats are still in their infancy. There are a lot of people pushing a lot of 'their' metrics, some gimmicky and some not. There are tons of questions with these metrics:
  • How are they compiled?
  • How are they interpreted?
  • How are they weighted or used in calculations?
  • What is the background of the people doing this work?
  • Are they subjective or objective?
  • How likely is there to be bias?
I keep bringing this stuff up but those who use statistics as the bible or foundation of their understanding of hockey and players ignore the questions, it's almost like a cult.

I think what is happening in a lot of cases is that the NHL and teams use their own metrics and advanced stats to make determinations, and couple that with what they are seeing and hard outcomes. Those metrics are usually not what we see, and they aren't shared with the public.

That's why you see a lot of team and coaching moves that don't align with the advanced stats Garret, JFresh, whomever else are promoting.

I'm not saying that these stats are dereft of accuracy or value, but there are a TON of question marks, and when the stats don't match an experienced eye, it can call it in to question. Of course, eye test is very prone to bias as well.

In my profession, I see statistics compiled, bent, and manipulated to tell a story all the time. That's why you need a scientific method and peer review if you want accuracy.


I don't think that's true - at least not from what I've read (please someone correct me if I'm wrong). I don't think disclosure is necessary, though it would be written in the contract.
For data gathering and cleanliness - when you have nearly 5 million shot attempts in your dataset going back to 2007-08, any occasional mistakes are going to get washed out. There's nothing fundamentally wrong with the data. Even in a single game, if an extra shot attempt for or against gets counted, it's not going to change a lot...and it's not going to be consistently biased against anyone in particular.

Are you suggesting bias in terms of the Scoring Chance and xG models? They're just assigning probability values to shot attempts. Not sure what bias you could introduce to a model or what the goal would be - other than making the model worse and less predictive or descriptive (and no one wants that).

I usually stick to shot metrics (Corsi/shot-attempts, Fenwick/unblocked shot-attempts) and the publicly available xG and SC/HDSC used at Natural Stat Trick or Moneypuck.

RAPM, WAR, GAR and sG are tricky because they try to boil everything down and they're pretty complicated and possibly subject to bias, where their models are designed to like a certain type of player and dislike other types - but they have identified good under-the-radar players in past.

For the most part, the people behind the models have backgrounds in math, computer science, engineering, etc. Brad Timmins from NST has a comp sci and market research background. Peter Tanner from Moneypuck has a double major in Math and Comp Sci from Waterloo. McCurdy (Hockeyviz) has a math background. Patrick Bacon (Top Down Hockey - and where JFresh gets his stuff) has a MSc in Statistics.

If you think bias has more influence on the moves that Garret and JFresh are suggesting based on their stats based models, than it does on coaches who are mostly flying by the seat of their pants and basing personnel decisions on their gut and what they feel the team needs, then I think you're probably wrong there. If you think the black-box stats NHL teams are using are somehow vastly different in quality and more free of model bias than the public stuff, that's probably wrong as well.

If you're saying the bias is just when we present a stat and say "this guy sucks, look at his xGF%" - well I try not to do that. But we're all biased. Someone who loves that guy will complain, someone who doesn't love that guy will agree and the HFBoards Circle of Life continues...
 
I just went through this talking about Lindgren. The stats said he was ok with Fox, worse without him. Which is fine, but dig deeper. How bad was the Trouba effect. It was bad. Fox was better without Lindgren, but the player replacing him was a better player. The last stat you see is Lindgren is really good with Schneider. This was very similar to arguments used against Pionk last year. That he was worse away from Dillon, but the results with Samberg were kind of glossed over. In the end the Jets chose to follow the analytics of that pairing, which was the Jets best d-pairing to start the year. I always ask questions about stats, even when Garret was on here he was crusading against Pionk, but he had some stats at his disposal that showed that Pionk was an effective puck mover, they weren't stats he provided in his original argument. Sometimes you have to dig deeper. Sometimes the stats work, where Garret's crusade against Mark Stuart probably helped the Jets turn a corner by buying him out. His anti-Stanley stance may still hold water. But the picture is so wide in the stats that I am sure that they are not as isolated as statisticians try to make them. In hockey every single player has an impact on the stats. Where you start from has an impact on the stats. What the score is has an impact on the stats.

I became real skeptical of stats when the government was locking people down based on stats, which if you did quick math meant that 0.01% of the population posed a legitimate public health risk, and the number of beds available was a direct result of government policy that closed two emergency care facilities.
This is bias in action - you like Lindgren, and you've hunted through the numbers I posted until you found a straw to grasp.

I said Lindgren is not good away from Fox (a Norris-caliber partner with whom he's played over 75% of his 5v5 minutes with).

You said "Take away Trouba" because he's so bad the Rags got rid of him - so I did. In total, Lindgren was still not good...but not as bad as he was with Trouba...but still...not good.

There were 3 other partners he played with when not with Fox or Trouba. Gustafsson, Miller and Schneider. Out of those three, he was only good with Schneider (another solid partner) in 104 minutes (the least minutes out of his non-Fox partners) over 3 seasons.

(You had also just posted that Fox's better numbers without Lindgren were because then Fox played with Miller - who's NYR's best RD. But Lindgren + Miller put up terrible numbers...hmmm).

So your takeaway from all that is that "Lindgren is good"?

I don't really have a dog in this fight (other than I don't want the Jets to spend assets on a defenseman whose rep might be boosted by his all-star partner).

You also mentioned Lindgren's PK abilities. He kills penalties alright...just not very effectively.

TOIFA/60GA/60xGA/60SCA/60HDCA/60
Lindgren-Trouba219:0385.196.579.1661.3624.93
Lindgren-Fox177:4872.557.098.1057.7129.36
Trouba-Miller166:5970.074.677.1749.9517.25
Fox-Miller98:3560.257.305.9543.8218.87
Miller-Schneider78:1551.373.074.6330.6713.80

I didn't think personnel were the problem on last year's powerplay, and I don't think it's a personnel problem for the Jets PK this year either. And even if it is, it doesn't look like Lindgren's any kind of answer.
 
This is bias in action - you like Lindgren, and you've hunted through the numbers I posted until you found a straw to grasp.

I said Lindgren is not good away from Fox (a Norris-caliber partner with whom he's played over 75% of his 5v5 minutes with).

You said "Take away Trouba" because he's so bad the Rags got rid of him - so I did. In total, Lindgren was still not good...but not as bad as he was with Trouba...but still...not good.

There were 3 other partners he played with when not with Fox or Trouba. Gustafsson, Miller and Schneider. Out of those three, he was only good with Schneider (another solid partner) in 104 minutes (the least minutes out of his non-Fox partners) over 3 seasons.

(You had also just posted that Fox's better numbers without Lindgren were because then Fox played with Miller - who's NYR's best RD. But Lindgren + Miller put up terrible numbers...hmmm).

So your takeaway from all that is that "Lindgren is good"?

I don't really have a dog in this fight (other than I don't want the Jets to spend assets on a defenseman whose rep might be boosted by his all-star partner).

You also mentioned Lindgren's PK abilities. He kills penalties alright...just not very effectively.

TOIFA/60GA/60xGA/60SCA/60HDCA/60
Lindgren-Trouba219:0385.196.579.1661.3624.93
Lindgren-Fox177:4872.557.098.1057.7129.36
Trouba-Miller166:5970.074.677.1749.9517.25
Fox-Miller98:3560.257.305.9543.8218.87
Miller-Schneider78:1551.373.074.6330.6713.80

I didn't think personnel were the problem on last year's powerplay, and I don't think it's a personnel problem for the Jets PK this year either. And even if it is, it doesn't look like Lindgren's any kind of answer.
Great post.

However i would like to ask for an analysis of the jets powerplay this year... because its so effective that its essentially an anomaly.

I personally give ehlers presence the credit because its rhe obvious difference... ie we have had many other pp coaches make a difference short term and then the knives eventually come out - see brad lauer.

If you could do a deep dive into our pp adv stats - it would be interesting because my cursory glance is that while all the players contribute ehlers is the individual changing our pp performance...
 
This post is a good example of why hes not here... the guy clearly explains his models and others and goes in depth as to what the potential flaws or biases are... and then guys who clearly dont read that content make posts about how garrett thinks hes the be all end all.

Also i can tell you if you think peer review is unbiased you are mistaken... as a polar bear guide ive seen various agendas override science in that world.

Nothing is perfect but the guys making these models for hockey do not have a specific agenda except trying to make their models work.... they dont hate stan or pionk or scheif etc...
Quite right. No one is bias-free but the math-savvy folks who do it for a living are very well versed in the limits of their models and risks of bias, much more so than the common fan who has an ax to grind.

Peer review is an interesting thing. Expert reviewers are great, but are often small in number and not completely bias-free, as you say. The internet is actually a democratic, open-access peer review platform and statisticians whose models aren't reliable will be discovered very quickly. Among the hundreds of thousands of readers of these forums there are, statistically speaking, likely to be enough good minds to separate the good from the bad.

"Statsnerds" and other pejorative terms are mostly just mudslinging, used by people who don't really understand/respect the stats experts or their process. To them, I would say, channeling my inner kanadalainen, they "doth protest too much, methinks".
 
This is bias in action - you like Lindgren, and you've hunted through the numbers I posted until you found a straw to grasp.

I said Lindgren is not good away from Fox (a Norris-caliber partner with whom he's played over 75% of his 5v5 minutes with).

You said "Take away Trouba" because he's so bad the Rags got rid of him - so I did. In total, Lindgren was still not good...but not as bad as he was with Trouba...but still...not good.

There were 3 other partners he played with when not with Fox or Trouba. Gustafsson, Miller and Schneider. Out of those three, he was only good with Schneider (another solid partner) in 104 minutes (the least minutes out of his non-Fox partners) over 3 seasons.

(You had also just posted that Fox's better numbers without Lindgren were because then Fox played with Miller - who's NYR's best RD. But Lindgren + Miller put up terrible numbers...hmmm).

So your takeaway from all that is that "Lindgren is good"?

I don't really have a dog in this fight (other than I don't want the Jets to spend assets on a defenseman whose rep might be boosted by his all-star partner).

You also mentioned Lindgren's PK abilities. He kills penalties alright...just not very effectively.

TOIFA/60GA/60xGA/60SCA/60HDCA/60
Lindgren-Trouba219:0385.196.579.1661.3624.93
Lindgren-Fox177:4872.557.098.1057.7129.36
Trouba-Miller166:5970.074.677.1749.9517.25
Fox-Miller98:3560.257.305.9543.8218.87
Miller-Schneider78:1551.373.074.6330.6713.80

I didn't think personnel were the problem on last year's powerplay, and I don't think it's a personnel problem for the Jets PK this year either. And even if it is, it doesn't look like Lindgren's any kind of answer.
I'm going to try a lot harder this year to stay out of arguments that drag down the experience for other posters.

So I'll try like this.

Lindgren's GA/60 on the Rangers PK is 6.9/60 vs. De Melo (8.5) and Pionk (8.1), both of whom have suffered from the Stanley effect (13.5). Now Samberg is 5.6/60 and Fleury 6.5 (Josh is even lower at 5.9), but Fleury has shown some struggles as a regular, and provides depth at the very least, and Morrissey is best in the reserve role if you want his best legs 5 on 5.

So that's a significant improvement in one position.

It's hard to say that a guy who went to Eastern Conference Finals 2 of the last 3 years as a top 4 d-man is not capable of improving the team, maybe some stats skew it, but you look at some positive results in there too (with Fox and Schneider). Why doesn't he work with K'Andre Miller, maybe because they are both lefties and neither are comfortable on their offside? I can't answer that one, I just go by what I have seen, and yes it is a bias.

That's still I think the best avenue for Chevy. Because it balances 3 pairs and leaves some different options, like potentially putting Samberg on his offside (without Stanley) if a top 4 d-man was called upon on the right side. I think there is more confidence in Miller to step up too, than there is in Fleury, Heinola, or Stanley in bigger minute situations.

Sun is shining, we're in no danger of wildfires, or hurricanes, ice is pretty good in some spots. Enjoy your day.
 
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Quite right. No one is bias-free but the math-savvy folks who do it for a living are very well versed in the limits of their models and risks of bias, much more so than the common fan who has an ax to grind.

Peer review is an interesting thing. Expert reviewers are great, but are often small in number and not completely bias-free, as you say. The internet is actually a democratic, open-access peer review platform and statisticians whose models aren't reliable will be discovered very quickly. Among the hundreds of thousands of readers of these forums there are, statistically speaking, likely to be enough good minds to separate the good from the bad.

"Statsnerds" and other pejorative terms are mostly just mudslinging, used by people who don't really understand/respect the stats experts or their process. To them, I would say, channeling my inner kanadalainen, they "doth protest too much, methinks".
Trust me, I understand research, data collection, peer review, etc. I have no problem with any of it... I DO have an issue with people who misuse it to make grandiose conclusions in the absence of other inputs

There are people who have never played hockey at a competitive level looking at the game almost solely through stats and they think they not only have an understanding of the sport, but a superior one to people who have actually played/coached AND look at the numbers
 
For data gathering and cleanliness - when you have nearly 5 million shot attempts in your dataset going back to 2007-08, any occasional mistakes are going to get washed out. There's nothing fundamentally wrong with the data. Even in a single game, if an extra shot attempt for or against gets counted, it's not going to change a lot...and it's not going to be consistently biased against anyone in particular.

Are you suggesting bias in terms of the Scoring Chance and xG models? They're just assigning probability values to shot attempts. Not sure what bias you could introduce to a model or what the goal would be - other than making the model worse and less predictive or descriptive (and no one wants that).

I usually stick to shot metrics (Corsi/shot-attempts, Fenwick/unblocked shot-attempts) and the publicly available xG and SC/HDSC used at Natural Stat Trick or Moneypuck.

RAPM, WAR, GAR and sG are tricky because they try to boil everything down and they're pretty complicated and possibly subject to bias, where their models are designed to like a certain type of player and dislike other types - but they have identified good under-the-radar players in past.

For the most part, the people behind the models have backgrounds in math, computer science, engineering, etc. Brad Timmins from NST has a comp sci and market research background. Peter Tanner from Moneypuck has a double major in Math and Comp Sci from Waterloo. McCurdy (Hockeyviz) has a math background. Patrick Bacon (Top Down Hockey - and where JFresh gets his stuff) has a MSc in Statistics.

If you think bias has more influence on the moves that Garret and JFresh are suggesting based on their stats based models, than it does on coaches who are mostly flying by the seat of their pants and basing personnel decisions on their gut and what they feel the team needs, then I think you're probably wrong there. If you think the black-box stats NHL teams are using are somehow vastly different in quality and more free of model bias than the public stuff, that's probably wrong as well.

If you're saying the bias is just when we present a stat and say "this guy sucks, look at his xGF%" - well I try not to do that. But we're all biased. Someone who loves that guy will complain, someone who doesn't love that guy will agree and the HFBoards Circle of Life continues...
Specifically, I asked who gathers Garrett's zone exit data since he obviously has a bias against Stanley since before he was drafted. It's a more than fair question, and anyone in research/data understands bias and would want to guard against it by having someone else either collect or analyze their results

I also brought up the concept of blinding as it relates to bias (there's a reason the DBRCT is the gold standard in testing interventions). Mardybum posted all the data for thr Jets D men and I asked that if you replaced their names with "Defender A", "Defender B", etc... would any dataset warrant the amount of hatred that Stanley receives here... I don't think his results would stand out that poorly. Someone might look at them and say "well, that guy is a borderline #6/7"... which is exactly what he is
 
Quite right. No one is bias-free but the math-savvy folks who do it for a living are very well versed in the limits of their models and risks of bias, much more so than the common fan who has an ax to grind.

Peer review is an interesting thing. Expert reviewers are great, but are often small in number and not completely bias-free, as you say. The internet is actually a democratic, open-access peer review platform and statisticians whose models aren't reliable will be discovered very quickly. Among the hundreds of thousands of readers of these forums there are, statistically speaking, likely to be enough good minds to separate the good from the bad.

"Statsnerds" and other pejorative terms are mostly just mudslinging, used by people who don't really understand/respect the stats experts or their process. To them, I would say, channeling my inner kanadalainen, they "doth protest too much, methinks".
If i could double heart love a post thus would be it

Specifically, I asked who gathers Garrett's zone exit data since he obviously has a bias against Stanley since before he was drafted. It's a more than fair question, and anyone in research/data understands bias and would want to guard against it by having someone else either collect or analyze their results

I also brought up the concept of blinding as it relates to bias (there's a reason the DBRCT is the gold standard in testing interventions). Mardybum posted all the data for thr Jets D men and I asked that if you replaced their names with "Defender A", "Defender B", etc... would any dataset warrant the amount of hatred that Stanley receives here... I don't think his results would stand out that poorly. Someone might look at them and say "well, that guy is a borderline #6/7"... which is exactly what he is
Read his original post. There is no bias he just says we should look at debrincat or girard instead.

He also clearly explains how he defines zone exits and actually how hes probably leaning towards the benefit of the doubt for stan.
 
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