Cup Success Measured Against Field Size

[Tweed]

August 2017 NHL betting line for the 2018 SC:

Odds to win the 2018 Stanley Cup

Seems that the 31 NHL teams were not viewed as "equal".

I'm not completely sure of the context of your post... but if you're addressing my OP, I wasn't suggesting that all teams are "equal".

My claim was that a team's chance of winning the cup is impacted by the structure of the league. The math was intended to show the severity in which a team's chances are impacted, on a year by year basis... and then to arrive at mathematical proof as to the value of success earned against those probabilities.

If you weren't addressing my OP, then my apologies... please clarify further.

 

[Canadiens1958]

I'm not completely sure of the context of your post... but if you're addressing my OP, I wasn't suggesting that all teams are "equal".

My claim was that a team's chance of winning the cup is impacted by the structure of the league. The math was intended to show the severity in which a team's chances are impacted, on a year by year basis... and then to arrive at mathematical proof as to the value of success earned against those probabilities.

If you weren't addressing my OP, then my apologies... please clarify further.

Simply an example of "unequalness" illustrated by one perspective that is numerical.

Can provide O6 era previews by columnists that illustrate "unequalness" but are not numerical.

 

[Tweed]

Simply an example of "unequalness" illustrated by one perspective that is numerical.

Can provide O6 era previews by columnists that illustrate "unequalness" but are not numerical.

I'm open to the idea that I'm totally misunderstanding the point you keep trying to make... because you're speaking in clipped phrases, and truncated sentences... but it seems to me all you're saying is "Life isn't fair"... as a counterpoint to my saying "All things being equal".

Either way, I'm not sure what that has to do with anything. You're making fragmented points that deal in the realm of perspective and subjectivity... in a discussion of structure and math. They're totally two different beasts. There is absolutely zero element of subjectivity to the OP. It's the very reason I didn't post this on the main board. Our "opinions" don't mean anything, with this... because they don't factor into calculating the results.

I'll give you some examples of how far down the rabbit-hole we can go with the subjective... Do we start increasing the value of cups in years where there was flu/measles/mumps outbreaks in North America, because those teams defied greater odds by virtue of staying healthy? Because you can totally make a case for it. And you can go to the other extreme and diminish the value of each successive Habs Cup, by showing that they overcame very easy odds simply because they had all the best players, and had a psychological advantage.

This is an example of the objective: For all intents-and-purposes... nothing was preventing the Expansion 6 teams from wheeling and dealing with the Original 6 teams in '67, and building themselves into a cup-contender from Day 1. There was nothing about the structure of the league that prevented them from doing that. Circumstances, Luck, Decisions, etc... are what prevented them from doing it.

My point is, none of any of what I'm showing, deals with any of that, because you can't calculate it. What we can calculate is the base probability of success, and relative values of successes between years.

 

[Tweed]

This is a math thing that I think some readers will overlook when they're taking issue with me saying that odds of winning multiple cups in the Original 6 era were pretty high. My math shows 1-in-6 chance for a single cup. 16.7% chance.

I get the sense that people who don't agree with that sentiment, feel that the level and quality of competition affects the odds.

So let's say we do the math on it. Let's say those people that feel the odds of a teaming winning the cup back then was closer to 1-in-10 (10% chance), and it was more difficult than I am claiming it to be.

What happens when you add up 6 teams with a 10% chance of winning the cup. You get a 60% chance that "somebody" will the cup (6x10%). That means there's a 40% chance of somebody not winning the cup.

That's obviously wrong. Whatever value you assign to each team, the sum total of all the teams HAS to come out to 100%.

Using Canadians1958 link to the vegas odds this year... I would wager everything I own, that if somebody were to total up the odds on all of those betting lines... they will come out to somewhere just under 1:1 odds (aka 100%).

Why "just under"? Because of "The House", they gotta make money. Otherwise, we'd all just go out and put $100 down on every single team winning the cup, and be guaranteed that we'll make money no matter who wins the cup.

 

[Canadiens1958]

^^^ Two previous posts. On the road visiting friends in the province. Will respond. I get back early this coming week.

 

[Canadiens1958]

This is a math thing that I think some readers will overlook when they're taking issue with me saying that odds of winning multiple cups in the Original 6 era were pretty high. My math shows 1-in-6 chance for a single cup. 16.7% chance.

I get the sense that people who don't agree with that sentiment, feel that the level and quality of competition affects the odds.

So let's say we do the math on it. Let's say those people that feel the odds of a teaming winning the cup back then was closer to 1-in-10 (10% chance), and it was more difficult than I am claiming it to be.

What happens when you add up 6 teams with a 10% chance of winning the cup. You get a 60% chance that "somebody" will the cup (6x10%). That means there's a 40% chance of somebody not winning the cup.

That's obviously wrong. Whatever value you assign to each team, the sum total of all the teams HAS to come out to 100%.

Using Canadians1958 link to the vegas odds this year... I would wager everything I own, that if somebody were to total up the odds on all of those betting lines... they will come out to somewhere just under 1:1 odds (aka 100%).

Why "just under"? Because of "The House", they gotta make money. Otherwise, we'd all just go out and put $100 down on every single team winning the cup, and be guaranteed that we'll make money no matter who wins the cup.

Have bolded a few passages. You are dancing between "pure abstract probabilities" and "odds" which are not one and the same.

From your seminal post in this thread where you include a look at the O6 era and though you do not overtly say so you compare the the act of 0ne of six teams winning the SC to the act of rolling one of six numbers on a "fair die".

Linked is a reasonable discussion of "Fair dice", standards, agreed upon criteria,unfair dice etc. Everything is well defined verifiable and measurable before the start of the trial.

Dice - Wikipedia

I have yet to see from you or anyone such an extensive and exhaustive discourse of this concept being put forth of a "fair team". Having observed and participated in team sports for over 60 years, I have yet to see a satisfactory explanation, definition or criteria of this mythical "fair team" .

Consequently you have a major credibility gap between "pure abstract probabilities" and actual on ice outcomes. To the extent that unlike other activities - 6/49 format lotteries :



Every aspect,feature and result may be verified for fairness.
This becomes an issue with scheduling in a league with an odd number of teams(not touching the issue of whether the teams are fair or not).

Odd number of league teams cannot be compared to an odd number of lottery balls since in a lottery none of the numbers is ever excluded. In a schedule at least one or an odd number of teams are always excluded.

So define "fair team" and work around the scheduling problem to re-enforce your point.

 

[Canadiens1958]

I'm open to the idea that I'm totally misunderstanding the point you keep trying to make... because you're speaking in clipped phrases, and truncated sentences... but it seems to me all you're saying is "Life isn't fair"... as a counterpoint to my saying "All things being equal".

Either way, I'm not sure what that has to do with anything. You're making fragmented points that deal in the realm of perspective and subjectivity... in a discussion of structure and math. They're totally two different beasts. There is absolutely zero element of subjectivity to the OP. It's the very reason I didn't post this on the main board. Our "opinions" don't mean anything, with this... because they don't factor into calculating the results.

I'll give you some examples of how far down the rabbit-hole we can go with the subjective... Do we start increasing the value of cups in years where there was flu/measles/mumps outbreaks in North America, because those teams defied greater odds by virtue of staying healthy? Because you can totally make a case for it. And you can go to the other extreme and diminish the value of each successive Habs Cup, by showing that they overcame very easy odds simply because they had all the best players, and had a psychological advantage.

This is an example of the objective: For all intents-and-purposes... nothing was preventing the Expansion 6 teams from wheeling and dealing with the Original 6 teams in '67, and building themselves into a cup-contender from Day 1. There was nothing about the structure of the league that prevented them from doing that. Circumstances, Luck, Decisions, etc... are what prevented them from doing it.

My point is, none of any of what I'm showing, deals with any of that, because you can't calculate it. What we can calculate is the base probability of success, and relative values of successes between years.

As explained you have not described, defined or set any criteria to examine your claim of a "fair team" or equal teams.Yet in all the analogies to date you rely on readily available definitions of "fair coin", "fair die", "fair lottery".

There is no "rabbit hole" either. Lewis Carroll -the mathematician Charles Dodgson. Lewis Carroll - Wikipedia

1959-60 preview by DinkCarroll(minor scroll left required):

The Montreal Gazette - Recherche d'archives de Google Actualités

Your attempts at distinguishing the objective from the subjective do not work. All you have are situations where the translations from words to numbers have not taken place. Specifically in the Carroll column King Clancy's claim that the difference between the Leafs and Canadiens are Harvey and Plante, today could be explained with numbers.Likewise Lynn Patrick's indirect admission that the Bruins are effectively 14 seasons behind setting up a farm system may be measured numerically today.

1967 expansion. Sponsorship era. The expansion teams did deal with the O6 teams but since there were six expansion teams the results tended to wash. 2017 expansion-only one expansion team. Did not have to compete with other expansionteams for the same players.Huge and measurable difference.

 

[Tweed]

Have bolded a few passages. You are dancing between "pure abstract probabilities" and "odds" which are not one and the same.

I'm just using those words, interchangeably, in the context of my OP. Same thing when I use the words "chance" and "probability". It's all in the context of "on-paper... as the league is structured".

I have yet to see from you or anyone such an extensive and exhaustive discourse of this concept being put forth of a "fair team". Having observed and participated in team sports for over 60 years, I have yet to see a satisfactory explanation, definition or criteria of this mythical "fair team" .

I'm not sure where I've used the term "fair", let alone the words "fair team".... without reading back through everything I posted, but I don't think I did. Forgive me if I'm wrong. I spoke about "all things being equal", and very specifically, in terms of the layout/format of the league. I think you're the only person talking about "fair", and then when you do, you're citing factors such as scheduling to evidence unfairness.

I also really don't feel like my OP requires an extensive/exhaustive discourse. I think it's pretty simple.

I'm really not sure what there is to discuss, unless you are suggesting we should put the time/energy in, to further refine the exact values for each season, by examining each team's schedule, and modifying (buffing/nerfing) the probability values on a team-by-team basis. I honestly wouldn't spend my time like that unless I was getting paid to, because it would be a monumental task... and it's not going to affect the numbers any noticeable way, such that the results I posted would differ much. Honestly.

In other words, you're splitting hairs where I already know the results aren't affected by... hairs.

Further to that... everybody here, and everywhere else in the world, already knows that no two teams have ever been matched exactly, or have identical situations beyond the very first decision a team has made.

1967 expansion. Sponsorship era. The expansion teams did deal with the O6 teams but since there were six expansion teams the results tended to wash. 2017 expansion-only one expansion team. Did not have to compete with other expansionteams for the same players.Huge and measurable difference.

This is a perfect example of just how "on paper" I'm talking about. The very moment the NHL approved both Pittsburgh and Philadelphia for expansions teams... those two teams were "equal"... in that they both had "the exact same odds" of winning the cup. That's it. Go no further, than that moment. Because nothing more matters. Just the on-paper part. As soon as you introduce a schedule, you're tilting the odds in favour of one team, over the other. But not enough to show any fault in the math of my OP.

 

[Canadiens1958]

I'm just using those words, interchangeably, in the context of my OP. Same thing when I use the words "chance" and "probability". It's all in the context of "on-paper... as the league is structured".




I'm not sure where I've used the term "fair", let alone the words "fair team".... without reading back through everything I posted, but I don't think I did. Forgive me if I'm wrong. I spoke about "all things being equal", and very specifically, in terms of the layout/format of the league. I think you're the only person talking about "fair", and then when you do, you're citing factors such as scheduling to evidence unfairness.

I also really don't feel like my OP requires an extensive/exhaustive discourse. I think it's pretty simple.

I'm really not sure what there is to discuss, unless you are suggesting we should put the time/energy in, to further refine the exact values for each season, by examining each team's schedule, and modifying (buffing/nerfing) the probability values on a team-by-team basis. I honestly wouldn't spend my time like that unless I was getting paid to, because it would be a monumental task... and it's not going to affect the numbers any noticeable way, such that the results I posted would differ much. Honestly.

In other words, you're splitting hairs where I already know the results aren't affected by... hairs.

Further to that... everybody here, and everywhere else in the world, already knows that no two teams have ever been matched exactly, or have identical situations beyond the very first decision a team has made.




This is a perfect example of just how "on paper" I'm talking about. The very moment the NHL approved both Pittsburgh and Philadelphia for expansions teams... those two teams were "equal"... in that they both had "the exact same odds" of winning the cup. That's it. Go no further, than that moment. Because nothing more matters. Just the on-paper part. As soon as you introduce a schedule, you're tilting the odds in favour of one team, over the other. But not enough to show any fault in the math of my OP.

Yet in your opening post you give the 1967 SC, the last O6 SC 6 points based on 6 teams. Then you give the 1968 SC 12 points based on 12 teams yet claim that Pittsburgh and Philadelphia are equal,by extension equal to the O6 teams.

This is the same flawed population argument that Bill James debunked (William Shakespeare/Topeka KS). Talent is a function of population. Only your version is that difficulty of winning(coming out on top as a writer) is a function of league size(population).

The actual math is not flawed, after all it is basic grade school stuff. What is flawed is the link you are trying to make with success of any given trial and the population size of eligible elements.

 

[Tweed]

Yet in your opening post you give the 1967 SC, the last O6 SC 6 points based on 6 teams. Then you give the 1968 SC 12 points based on 12 teams yet claim that Pittsburgh and Philadelphia are equal,by extension equal to the O6 teams.

This is the same flawed population argument that Bill James debunked (William Shakespeare/Topeka KS). Talent is a function of population. Only your version is that difficulty of winning(coming out on top as a writer) is a function of league size(population).

The actual math is not flawed, after all it is basic grade school stuff. What is flawed is the link you are trying to make with success of any given trial and the population size of eligible elements.

I'm not giving anybody anything. I'm just calculating the obvious basic grade school stuff. It's not meant to dissect it any further than that.

Here's the thing... you understand the premise of my OP, so I'm not clear on what it is you're taking issue with. Can you please either state, in a single sentence, exactly what you take issue with. Or better yet, bang out some really rough numbers using the same format I did in the OP... to illustrate what you're seeing that I'm not seeing... I won't hold you to your math, but at the very least I might begin to understand your point.

 

[Canadiens1958]

I'm not giving anybody anything. I'm just calculating the obvious basic grade school stuff. It's not meant to dissect it any further than that.

Here's the thing... you understand the premise of my OP, so I'm not clear on what it is you're taking issue with. Can you please either state, in a single sentence, exactly what you take issue with. Or better yet, bang out some really rough numbers using the same format I did in the OP... to illustrate what you're seeing that I'm not seeing... I won't hold you to your math, but at the very least I might begin to understand your point.

Problem is the lack of logical coherence going from the basic math to the conclusion.

Similar to the fallacies generated by the population arguments in all their glory.

Simple counting illustrates that the population of Shakespeare's London, England may have been the equivalent of Topeka, KS at a given point in time.

Does this in any way imply that Topeka, Kansas should have produced another William Shakespeare? Or a great playright/author/wordsmith the quality of Shakespeare?

Does this imply that a population centre with a population of "x" times Shakespeare's London would produce "x" Shakespeares.

Greatness, winning, success is never a function in any way of simple population ratios. Does not matter if you are looking at people, teams, coins or what strikes your fancy.

 

[Bear of Bad News]

Problem is the lack of logical coherence going from the basic math to the conclusion.

Please find a nicer way to say these sorts of opinions of yours.

 

[Canadiens1958]

I'm not giving anybody anything. I'm just calculating the obvious basic grade school stuff. It's not meant to dissect it any further than that.

Here's the thing... you understand the premise of my OP, so I'm not clear on what it is you're taking issue with. Can you please either state, in a single sentence, exactly what you take issue with. Or better yet, bang out some really rough numbers using the same format I did in the OP... to illustrate what you're seeing that I'm not seeing... I won't hold you to your math, but at the very least I might begin to understand your point.

CFL vs the NHL. CFL since 1954 has been a two conference league featuring mainly 9 teams with a blip to 16 teams in 1994 and 1995. Schedule grew from 12 to 18 RS games,interlocking since 1961. Salary Cap since 2007.

Grey Cup winners linked:

List of Grey Cup champions - Wikipedia.

Compare the number of repeat winners and the string lengths(n-peats).

Likewise for the NBA since the start in 1947:

List of NBA champions - Wikipedia

Compare the number of repeat winners and the string length(n-peats).

Likewise NFL Super Bowl winners:

Super Bowl Winners and Results - Super Bowl History - National Football League - ESPN

Compare the number of repeat winners and the string length(n-peats).

MLB World series winners:

List of World Series champions - Wikipedia

Compare the number of repeat winners and the string length(n-peats).

Never a direct correlation to league size in the CFL,MLB, NBA or NFL. What makes the NHL different?

 

[Canadiens1958]

Re-visiting Bill James, William Shakespeare and the Stanley Cup.

Shakespeare and Verlander | Articles | Bill James Online

The article is a must read. Applied to this thread and topic it raises the key question. What type of league and competition is desired? Do we want a league NHL,NFL,MLB,NBA,CFL, etc where dominance is encouraged and structured to best attract eyeballs and the resulting dollars? Or is the league model based on maximizing eyeballs and dollars via parity?

Regardless, at no time is league size the determining factor. Just like population is never the determining factor.