Peer Review Request : 'The Henderson-Lemieux-Crosby Trio' a.k.a. Canada's Greatest Goals.

[PrimumHockeyist]

Whenever I introduce an idea, I always assume that it is flawed somehow. The more significant the idea seems, the more I feel that I should ask if my understanding is correct. I would rather know that something is incorrect than leave a bad idea out there for others to get misled by.

So here's where I'm going.

A while back, on this board, I said that I believe that I had found data that proves, in a statistical way, that Canada's three greatest goals were subject to a non-random effect. Then I got sidetracked by another project that took a lot longer than I thought it would. At last, I am now ready to revisit this project and this subtopic in particular. I figure that if others can shred my findings on this subject, that I won't have to finish said project. I would be happy to, for the reasons mentioned.

My argument is/was that Paul Henderson's, Mario Lemieux's and Sidney Crosby's goals combine to produce three "significant and highly improbable" anomalies that defeat science's Null Hypothesis test. The NH test is the standard by that Science uses to determine if data is or is not random.

Since I've just resumed this other project, I thought that if I posted this particular finding here, for peer review, then somebody may come along before I've finished the project and show me the error of my ways. I am actually hoping that this information can be falsified, if it can be falsified. Private and public corrections or comments are both very welcome. In the meantime, I will move forward with said project, based on the assumption that my current conclusions are valid.

For the record, what I find intriguing about this is not whether individuals believe in chance or whatever. What interests me the most is that Canada's three greatest goals seem to crush the NH test, by providing significant and highly improbable data that NH test-takers won't be able to match when working with random trios of goals.

My data involves no swamp gas or possibly doctored videos. There is nothing "alleged" about it. I say this because, when one begins to reflect on the underlying improbabilities, no reasonable person would think that this kind of combined result could possibly appear when one works with randomly generated trios of hockey goals. And that is the point !!

That is the NH test here. If you can't match this combined Henderson-Lemieux-Crosby (HLC) data more than 1 in 3 times, then working with random trios of goals, then Science itself would say that we have what appears to be a non-random situation worthy of further investigation.

For a fuller discussion, click here.

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[PrimumHockeyist]

oops meant to post on the numbers board. please transfer there if possible.

 

[MadLuke]

oops meant to post on the numbers board. please transfer there if possible.

Maybe they would understand, because to the laymen hockey and goals will be obviously non-pure random event (and quite far from it), so it would be without any surprise that any particular goal would not respect rules regarding random events (like rolling a dice or flipping a coin).

If Mario Lemieux receiving past from Wayne Gretzky in the last minute of an hockey game in which Canada need absolutely a goal to win end up scoring a goal that a bunch of random player in a random situation was unlikely to score... ok yes ? And how many highly unlikely events occur during any game ?

 

[Cloned]

What does the null hypothesis test say about the conditions required for abiogenesis and the subsequent actual interactions required for life to start?

It’s the universe. Somewhere at some point in time everything and anything has happened, is happening, or will happen, no matter how random it seems.

 

[PrimumHockeyist]

Maybe they would understand, because to the laymen hockey and goals will be obviously non-pure random event (and quite far from it), so it would be without any surprise that any particular goal would not respect rules regarding random events (like rolling a dice or flipping a coin).

If Mario Lemieux receiving past from Wayne Gretzky in the last minute of an hockey game in which Canada need absolutely a goal to win end up scoring a goal that a bunch of random player in a random situation was unlikely to score... ok yes ? And how many highly unlikely events occur during any game ?

The main thing, as far as formal testing is concerned, is that we can isolate events, hockey goals, and test their rarity formally. It becomes beside the point, as far as testing is concerned, that other events occur in the game.

What interests me, is how the Henderson, Lemieux, Crosby Trio of goals defies formal scientific testing, to a degree that artificial intelligence says must be non random beyond a reasonable doubt.

I recorded my chats on this with AI and linked to it in my essay.

 

[PrimumHockeyist]

What does the null hypothesis test say about the conditions required for abiogenesis and the subsequent actual interactions required for life to start?

It’s the universe. Somewhere at some point in time everything and anything has happened, is happening, or will happen, no matter how random it seems.

Thanks for your input. I kind of answered this in my reply to Mad Luke. If I understand your point correctly, here's where I bring it up in the essay...

"Translation: Mario Lemieux's 1987 goal does indeed share that same trait that Henderson's does. Both feature significant and highly improbable anomalies that appear independently of these goals' noted cultural significance.
By being confined to details that hockey people consider significant, Henderson's and Lemieux's anomalies enable us to weed out all trivial associations. Our ability to limit the discussion to details that hockey people deem significant is based on our direct evidence. We demand similar evidence because we can provide the same. This alone undermines all suggestions that meaningful data can be found everywhere."

 

[rubenflamshep]

Hey, this is a very ambitious work! I think you're what you're looking to apply is a poisson distribution to determine the likelihood of those three goals happening in that time span. You'll get a specific likelihood which would likely be very low as you suspect.

On a separate note, don't laugh but I've found The Cartoon Guide to Statistics to be really helpful re: my understanding of a lot of this stuff.

 

[MadLuke]

What interests me, is how the Henderson, Lemieux, Crosby Trio of goals defies formal scientific testing, to a degree that artificial intelligence says must be non random beyond a reasonable doubt.

I am just lost, no one ever suggested that any goal ever at hockey were a random event too ? So it is not that surprising that those goals at non-random beyond a reasonable doubt.


A non-random event is an event that occurs with a certain degree of predictability and is not subject to chance. In other words, the outcome of a non-random event can be determined or influenced by known factors or conditions. Non-random events are governed by specific causes, rules, or patterns, making their occurrence more predictable compared to random events, which occur without any discernible pattern or predictability.

Would hockey goal be random events (like say a roll dice), we would be quite stupid to watch hockey game or try to talk anything about their results... I must be missing something.

 

[PrimumHockeyist]

I am just lost, no one ever suggested that any goal ever at hockey were a random event too ? So it is not that surprising that those goals at non-random beyond a reasonable doubt.

I think that a lot of people would say that hockey goals unfold randomly based on a mixture of skill and chance. the mixture is what makes the outcome random. Can skill determine when the second in which a goal is scored? Can skill determine if a goal is a third straight game winner? My take is that any goal that is based on a mixture of randomness and skill, and is therefore random to some degree. I'm not concerned with the complex things that led to the final goal, but the final result, the goal itself and what we can say about it in particular: like a third straight winning goal in Henderson's case. This is an outcome that is perfect for testing, because a hockey goal is a hockey goal is a hockey goal. How often do such goals occur. How unique was Henderson's Goal of the Century really, when we ferret out all of the emotional attachments?

A non-random event is an event that occurs with a certain degree of predictability and is not subject to chance. In other words, the outcome of a non-random event can be determined or influenced by known factors or conditions. Non-random events are governed by specific causes, rules, or patterns, making their occurrence more predictable compared to random events, which occur without any discernible pattern or predictability.

Would hockey goal be random events (like say a roll dice), we would be quite stupid to watch hockey game or try to talk anything about their results... I must be missing something.

"A non-random event is an event that occurs with a certain degree of predictability and is not subject to chance. "

For me, the question becomes if we can formally decide when an outcome is random, the outcome in this case being a hockey goal. And we can, apparently. We all know that Henderson's result is extraordinarily rare, when recognized as a 'hockey goal' that was also a third straight game winner. That we might find three goals with such independent data like that, in a row, is virtually impossible.. It is why science itself rules chance out as a plausible explanation, through the Null Hypothesis test.

 

[PrimumHockeyist]

Hey, this is a very ambitious work! I think you're what you're looking to apply is a poisson distribution to determine the likelihood of those three goals happening in that time span. You'll get a specific likelihood which would likely be very low as you suspect.

On a separate note, don't laugh but I've found The Cartoon Guide to Statistics to be really helpful re: my understanding of a lot of this stuff.

Thank you.

I could use help from people who understand stats, the language, the approach and all that.
One of the challenges in this work is trying to balance the math with the simplicity of the statement.

For example, I got A.I. to admit that "the reasonable person' would likely find it unreasonable, beyond a reasonable doubt, to think that one could be dealt three Full Houses in a row with just five cards. each full house is 1 in 694. being dealt three full houses in a row is like 1 in 340 million (1 x 694 x 694 x 694.)

Transferring that idea, I got A.I. to tell me how often we would have to look at NHL goals, if it was exactly as hard to find a third straight game-winning goal as a full house AND if the NHL averaged six goals per game. A I told me that one in 200 goals would have to be third straight game winners on average. (198 x 3.5 = 694) . At this rate, third straight game winning goals would happen about once every two weeks. Hat tricks might be more common!

My point is that this, once every two weeks, is the frequency that all three of these HLC feats would have to occur at, in order to be ONLY as rare as getting three straight random full houses. The sketch data I am pulling seems to prove that each feat must be much, much rarer, so the compounding ought to be much rarer than 1 in 340 mill.... I think!

This is simply not the kind of data that should appear in any random trios of goals, ever. Yet it does, and does so in relation to one's nation's three most cherished goals.

Going back to something that I said in my essay, we could probably confirm the trending with ten random NHL goals. But I can't make the list, otherwise, people will think I've rigged it. If a list like that were out there, that others could look at, then we should soon be able to determine if my personal framing is somehow wrong. Until shown, that would mean that the HLC Trio is at least a 1 in 1000 kind of trio.

Edit - curiously, with 87 fails the HLC Trio becomes as officially rare as a Royal Flush. 86 doesn't quite get one there . . .

 

[MadLuke]

That we might find three goals with such independent data like that, in a row, is virtually impossible.. It is why science itself rules chance out as a plausible explanation, through the Null Hypothesis test.

Yes I have little doubt science would say it was almost impossible to be totally random, that maybe the same team winning 3 games in a row could mean one was better, could mean a coach did put on the ice the players with the last 2 game winners, late in a game where he need a game winners, that someone that scored 2 game winners has more chance than pure randomness to be the next one to do so (he is a forward for examples, he is good at scoring..)

The question, is more, how could it be possibly actually pure randomness to even have the question if it is ?

 

[PrimumHockeyist]

Yes I have little doubt science would say it was almost impossible to be totally random, that maybe the same team winning 3 games in a row could mean one was better, could mean a coach did put on the ice the players with the last 2 game winners, late in a game where he need a game winners, that someone that scored 2 game winners has more chance than pure randomness to be the next one to do so (he is a forward for examples, he is good at scoring..)

The question, is more, how could it be possibly actually pure randomness to even have the question if it is ?

Hi Luke.

Thanks for staying with me on this. I'm thinking that maybe I should note that we are talking about two kinds of randomness here. I completely agree with you that hockey goals are derived from a mixture of factors. If I understand you correctly, we agree that hockey goals are based on a mixture of skill and luck and coaching decisions et.

The other kind of randomness that I am bringing up here is how hard it will be to match the HLC Trio with "randomly generated" trios of NHL goals.

To your point, it turns out there are a number of 'significant and improbable' considerations that we cannot attribute to human cause. One such case, wouldn't you agree, would concern the exact second in which a goal was scored.

So, let's suppose that we have three goals, ABC, and that the first goal, A, just happens to encode the jersey numbers of the other two scorers in a given random trio. That would be very improbable, and the timing of a goal is certainly significant (noted always by the NHL).

After I thought about this, at first I wondered, "How long will it take to find a random trio whose first goal does this? Then I though, "I would mention the same thing if the third goal did the same, or if the second goal did. So, there would be three chances to make a 'comparable' match.

So, I'm saying that we have this impossibly rare Trio. I've also just said that some hockey goal outcomes can't really be attributed to human intervention, such as the exact second when a hockey goal is scored.

Here is the goal that many of us have probably thought about far too much!