Cup Success Measured Against Field Size

[Tweed]

I thought it would be fun to measure the "value" of a Stanley Cup, year-by-year, as determined by the number of teams competing for it. This idea came about when I was thinking about how the 1950s Habs 5-straight Cups weren't as impressive to me as say; the Hawks 3-in-6. The reason is that I don't personally find it "impressive" that 1 team wins a cup in a small field of 6 teams. I might be underestimating the difficulty in that, but it's moot, really.

So with that in mind, I set about weighting each Stanley Cup. I'm somewhat confident I didn't make any mathematical errors, but I certainly didn't go back through and double-check all of my work.

I started with the 1914-1915 season as it was the first season an NHL team could compete for the SC. Even though those early SCs were NHL champions battling against PCHA champions (or other leagues when applicable) for the Cup, I considered the total numbers of teams eligible to compete for the cup as part of a "greater unspoken league" of teams, and therefore the combined number of teams present in all the leagues, relevant.

I assigned each Stanley Cup a value in points as determined by the number of teams in the "league". Such that, 6 teams competing for the cup, gives the value of the cup that year "6 points". If a team won a cup in a year when the league had 12 teams, the cup was worth 12 points that year.

Here is the spreadsheet, for anybody that wants to view it, it's nothing special.
Winners listed in lowercase are long-defunct teams that I didn't care to track. Year is listed as the year culminating in the Cup victory. For example the 1956 Cup-winning Canadiens are the 1955-1956 Canadiens.

From there, I set about tallying the points for each Cup winner:
MON - 9,8,10,10,6,6,6,6,6,6,6,6,6,6,12,12,14,16,18,18,18,17,21,24 = 267
TOR - 7,7,8,7,6,6,6,6,6,6,6,6,6 = 83
DET - 8,8,6,6,6,6,6,26,26,30,30 = 158
BOS - 10,7,7,12,14,30 = 80
CHI - 9,8,6,30,30,30 = 123
EDM - 21,21,21,21,21 = 105
PIT - 21,22,30,30,30 = 133
NYR - 10,9,7,26 = 52
NYI - 21,21,21,21 = 84
NJD - 26,28,30 = 84
PHI - 16,16 = 32
LAK - 30,30 = 60
COL - 26,30 = 56
DAL - 27 = 27
CAL - 21 = 21
ANA - 30 = 30
CAR - 30 = 30
TBL - 30 = 30

And then I determined the number of points available to teams based on their founding date, or first NHL season where they were eligible to compete for the cup.

MON - 1914 = 1531 pts
TOR - 1917 = 1503 pts
BOS - 1924 = 1460 pts
CHI - 1926 = 1435 pts
DET - 1926 = 1435 pts
NYR - 1926 = 1435 pts
DAL - 1967 = 1148 pts
LAK - 1967 = 1148 pts
PIT - 1967 = 1148 pts
PHI - 1967 = 1148 pts
NYI - 1972 = 1084 pts
COL - 1972 = 1084 pts
CAL - 1972 = 1084 pts
NJD - 1974 = 1052 pts
CAR - 1979 = 963 pts
EDM - 1979 = 963 pts
TBL - 1992 = 689 pts
ANA - 1993 = 665 pts

I then applied the number of points earned against the number of points available to determine each team's success quotient, and then ranked them based on the results.

MON - 267 / 1531 = 0.1743
PIT - 133 / 1148 = 0.1158
DET - 158 / 1435 = 0.1101
EDM - 105 / 963 = 0.1090
CHI - 123 / 1435 = 0.0857
NJD - 84 / 1052 = 0.0798
NYI - 84 / 1084 = 0.0774
TOR - 83 / 1503 = 0.0552
BOS - 80 / 1460 = 0.0547
LAK - 60 / 1148 = 0.0522
COL - 56 / 1084 = 0.0516
ANA - 30 / 665 = 0.0451
TBL - 30 / 689 = 0.0435
NYR - 52 / 1435 = 0.0362
CAR - 30 / 963 = 0.0311
PHI - 32 / 1148 = 0.0278
DAL - 27 / 1148 = 0.0235
CAL - 21 / 1084 = 0.0193

I think this confirms what we all pretty much knew: The Montreal Canadiens are the Stanley Cuppiest Team of All-Time. But, it's neat to see how all the other teams fare, and to see how their Cup Success can be viewed in this light.

I hope you all can read this. I really don't want to have to format it.

EDIT: Updated to omit 1919, 2005, and 2018 Cup Values in teams' Points Available (since the Cup couldn't be won in 1919 & 2005, and 2018 hasn't completed yet).

Click to read more...

 

[JackSlater]

Interesting to see the results, though I am confident that the difficulty of winning the Stanley Cup is not directly proportional to the number of teams. For instance, I don't think that the Stanley Cup became anywhere close to twice as difficult to win in 1968 (12 teams) compared with 1967 (6 teams). There is no perfect way to measure it. Overall due to basic randomness over a large sample I do agree that winning the Cup is more unlikely today for any given player, but it isn't nearly five times harder than it was in the 1950s.

The disparity between teams in the six team era is also difficult to reconcile. Did the 1950s Boston Bruins have a better chance of winning the Stanley Cup than this decade's Minnesota Wild? Those are two of the mediocre teams of their respective decades. Minnesota of the 2010s has to compete with a huge number of teams, absolutely. Boston of the 1950s had to compete with two absolutely loaded dynasty teams that couldn't realistically even exist in today's environment. I would say that each team had a pretty similar chance (pretty close to 0) and I may even think that Minnesota had a better chance overall. It's basically a choice between competing against several teams at relative parity and one or two teams with 5 or 6 (or more) HHOF players. Of course we must consider that a relatively large percentage of players and teams had the chance to participate in a dynasty and thus win a large number of Cups, and that is part of the reason that the comparison is challenging.

 

[Tweed]

Interesting to see the results, though I am confident that the difficulty of winning the Stanley Cup is not directly proportional to the number of teams. For instance, I don't think that the Stanley Cup became anywhere close to twice as difficult to win in 1968 (12 teams) compared with 1967 (6 teams). There is no perfect way to measure it. Overall due to basic randomness over a large sample I do agree that winning the Cup is more unlikely today for any given player, but it isn't nearly five times harder than it was in the 1950s.

The disparity between teams in the six team era is also difficult to reconcile. Did the 1950s Boston Bruins have a better chance of winning the Stanley Cup than this decade's Minnesota Wild? Those are two of the mediocre teams of their respective decades. Minnesota of the 2010s has to compete with a huge number of teams, absolutely. Boston of the 1950s had to compete with two absolutely loaded dynasty teams that couldn't realistically even exist in today's environment. I would say that each team had a pretty similar chance (pretty close to 0) and I may even think that Minnesota had a better chance overall. It's basically a choice between competing against several teams at relative parity and one or two teams with 5 or 6 (or more) HHOF players. Of course we must consider that a relatively large percentage of players and teams had the chance to participate in a dynasty and thus win a large number of Cups, and that is part of the reason that the comparison is challenging.

I totally hear ya... in the turbulence of team-decisions, yes, I agree with you 100%. For example, when the NHL expanded from 6 teams to 12 teams, the expansion teams were not given an equal starting position relative to the Original 6 teams.

The Original 6 teams had a less than 1-in-6 chance of winning the Cup, when the league expanded to 12 teams... but greater than 1-in-12 chance, due to their situations (they didn't have to gut their rosters to make a 12-even-team league). That said if you do the math on Original 6 teams with a 1-in-8 chance + Expansion teams with a 1-in-16 chance... you do end up with a mean of all teams having a 1-in-12 chance, from a league-wide perspective.

So here's the thing... this stuff is a look at the "base" difficulty from an "all things being equal" perspective. If all teams start the season with equal rosters (no players, or equal players across the board, however you want to put it), then it really is a 1-in-6 chance of winning the cup, in a 6-team league. The onus is on the management to assemble/alter the roster to stack the odds of winning in their favour, and obviously as you've pointed out, not all teams do that. Some make personnel mistakes, some make strategical mistakes, some teams have bad bounces (literally/figuratively)... and all that stuff plays into the outcome and results. At the end of the day, those decisions and approaches are all made outside of the vacuum (which of course, makes sense)... but that doesn't mean that in the vacuum, the work above doesn't represent a somewhat accurate way of weighting Cups, when measuring the league "as a whole", and not on a team-by-team situational basis.

Another way of looking at it is to imagine that all teams make perfect managerial decisions, and have perfect players on their rosters, and play their games perfectly. The odds of any one team winning the Cup are 1-in-6, in a 6-team-league. Anything a team does to give themselves an advantage towards success over the rest of the league, is DEFINITELY a credit to them, but it doesn't change the hard math that, at the core, and technically, their odds of winning are just the same. The very fact that teams do practice, or juggle lines, or move players is a pure testament to the idea that they are trying to tilt the odds in their favour, and away from a base "even chance".

We can actually see this effect more readily nowadays where we have a league, full of teams, where the disparity between the 1st line players and the 4th line players is much smaller than back in the "old days". It's the reason why we have such tight playoff races, and point-differentials in the standings. Almost all teams are becoming proficient at maximizing their chances for success, which is returning the field to even odds.

To your point, dare I say that it might have been even easier to win a Cup two years in a row back-in-the-day, regardless of how many teams were in the league, when good teams were able to retain their rosters and winning strategies, much easier than today, in the Cap Era (for example).

I think the point I'm trying to make is that more often than not, mediocre teams are mediocre because they themselves have sailed their ships in the wrong direction, away from the mean probability, OR, conversely, the great teams have navigated in the right direction and the consequences of that, are that the other teams become below-average/mediocre, by law.

So really, I think the point that you're making addresses a different scenario, where you'd want to measure Cup Value in terms of "odds of overcoming individual situations". The 1950s Bruins had little chance of winning the Cup over stacked Habs' teams, because... credit to the Habs for building their rosters to maximize their probabilities of success, and perpetuating that success. But that doesn't make the value of their Cup wins, any greater or less than the value of the Cup to the Bruins if they had won them in those years. The 2010's Minnesota Wild had very little chance of winning the Cup with their roster, not because there was a juggernaut in the league, but because there were just soooo many other barely better teams. We agree on that. Is it a difference of being 5x less-likely? In a vacuum, absolutely. In reality... probably not quite, once we introduce the "rules of change" that affected roster make-up, appropriate for the eras. Again, that's on a team-by-team basis.

I understand your point though, and it did occur to me as I was doing this stuff, that it would be neat to measure the value of "induced change", across all eras, and introduce it into the calculations as way of buffing/nerfing teams Cup Values on "repeats". A "Difficulty of Sustained Success" modifier of sorts. But... that would be a completely different measurement, because it turns the whole thing into an exercise in subjectivity.

 

[Tweed]

It's actually just occurred to me that, while in most years a team's odds of winning the cup, are directly reflective of the number of teams in the league (ie. Original 6 Era & '67 Expansion 12 Team League)... there are years where the divisional alignment is imbalanced due to an odd number of teams in the league. For example, the '82-'83 Season where the Islanders came from the 6-team Patrick Division, as opposed to the Oilers out of the 5-team Smythe.

Since the Stanley Cup isn't won in a Battle Royale Fashion... where all teams in the league compete for the Cup for the entirety of the season, and there's a culling process (aka "The Playoffs")... a team's odds of qualifying for the playoffs impacts their overall probability of success, with the disparity surfacing in the divisional format.

Quick example:
"1982-83" 21 team league
Oilers 4/5 chance of making the playoffs x 1/2^4 of succeeding in each PO Round = 0.050 = 1/20 chance of winning the Cup
Islanders 4/6 chance of making the playoffs x 1/2^4 of succeeding in the each PO Round = 0.042 = 1/24 chance of winning the Cup

I suspect reworking all the numbers to accommodate each team's format situation would be time-consuming, and wouldn't probably impact my previous calculations to any great extent... but it's an interesting thought, nevertheless.

 

[Habs Icing]

Actually, an argument can be made that it was harder to win 5 straight in the old 6 team league than in a 31 team league.

Imagine spreading the talent over 6 teams instead of 31 teams. The difference in quality from one team to another was practically nil. The counter argument to that is that more nations play hockey these days so the talent pool is larger. I can think of other pros and cons to the question but I don't want to hijack your thread.

 

[bambamcam4ever]

Actually, an argument can be made that it was harder to win 5 straight in the old 6 team league than in a 31 team league.

Imagine spreading the talent over 6 teams instead of 31 teams. The difference in quality from one team to another was practically nil. The counter argument to that is that more nations play hockey these days so the talent pool is larger. I can think of other pros and cons to the question but I don't want to hijack your thread.

History would say differently.

 

[Tweed]

Actually, an argument can be made that it was harder to win 5 straight in the old 6 team league than in a 31 team league.

Imagine spreading the talent over 6 teams instead of 31 teams. The difference in quality from one team to another was practically nil. The counter argument to that is that more nations play hockey these days so the talent pool is larger. I can think of other pros and cons to the question but I don't want to hijack your thread.

To your point, I agree, and once you introduce factors such as quantity of talent, and talent pool... combined with induced change, or lack thereof (salary cap vs non-cap)... it really does alter a team's probability of success in overcoming their "situation".

But again, on an "all things being equal basis"... where you have 6 teams with no players (or equal players), or 30 teams with no players (or equal players)... we can say for certain, that the odds of prevailing are directly reflective of the number of teams in the field. 1 white marble in a bag with 5 black marbles, and it's a 1-in-6 chance you draw the white marble. Much lower odds of drawing the white marble in a bag of 30 black marbles. That's really all I'm trying to show, and evaluate here.

Don't worry about hijacking the thread though bro, nobody really seems to be discussing this stuff, so I'm happy to go down some rabbit holes with you if you wanna go back and forth over stuff with me.

 

[Tweed]

History would say differently.

I think he means the difference in quality between teams nowadays, in reference to the 31 team league... as opposed to the dynastic eras of the O6 days.

Edit: Scratch that... I read it wrong. I agree with you.

 

[Canadiens1958]

History would say differently.

To your point, I agree, and once you introduce factors such as quantity of talent, and talent pool... combined with induced change, or lack thereof (salary cap vs non-cap)... it really does alter a team's probability of success in overcoming their "situation".

But again, on an "all things being equal basis"... where you have 6 teams with no players (or equal players), or 30 teams with no players (or equal players)... we can say for certain, that the odds of prevailing are directly reflective of the number of teams in the field. 1 white marble in a bag with 5 black marbles, and it's a 1-in-6 chance you draw the white marble. Much lower odds of drawing the white marble in a bag of 30 black marbles. That's really all I'm trying to show, and evaluate here.

Don't worry about hijacking the thread though bro, nobody really seems to be discussing this stuff, so I'm happy to go down some rabbit holes with you if you wanna go back and forth over stuff with me.

Fair coins, dice, marbles, lottery draws are a probability abstraction.

Sports are never "fair".

 

[Michael Farkas]

Yeah, I remember having an argument/discussion with a co-worker once upon a time about an imbalanced division and he goes "yeah, it's easier for such and such because there's only five teams in it and four make it...it's harder to make it for the team in the six-team division where only four make it..."

I didn't think that made any sense. It's not a lottery. I'd want to be in the six-team division because I can control more points of my opponents...the only thing more valuable than me earning two, is taking two from them in the process...why you'd want to limit your "earning power", if you will, is odd...

I'd wonder what kind of adjustments could be made to factor in strength of teams/opponents as opposed to counting all teams as equal and a smaller-league win to be considered weaker...

 

[Doctor No]

I didn't think that made any sense. It's not a lottery. I'd want to be in the six-team division because I can control more points of my opponents...the only thing more valuable than me earning two, is taking two from them in the process...why you'd want to limit your "earning power", if you will, is odd...

Hypothetically, would you prefer to be in a five-team division where four teams make the playoffs, or a 100-team division where four teams make the playoffs?

 

[Tweed]

Yeah, I remember having an argument/discussion with a co-worker once upon a time about an imbalanced division and he goes "yeah, it's easier for such and such because there's only five teams in it and four make it...it's harder to make it for the team in the six-team division where only four make it..."

I didn't think that made any sense. It's not a lottery. I'd want to be in the six-team division because I can control more points of my opponents...the only thing more valuable than me earning two, is taking two from them in the process...why you'd want to limit your "earning power", if you will, is odd...

There is no greater value in taking two, than earning two. Both are "equally" advantageous. When the Pens take 2 from the Flyers, they're also helping their own division rivals, Rags, Devs and Caps at the same time. The effect is a wash, and is the same in a 5-team division.

This is what it looks like when 6 teams in the same division, do exactly that which you describe:

1987-88 NHL Standings | Hockey-Reference.com Be sure to compare their point toals to the teams that made the playoffs in the other divisions.

 

[Tweed]

I'd wonder what kind of adjustments could be made to factor in strength of teams/opponents as opposed to counting all teams as equal and a smaller-league win to be considered weaker...

That's when it gets subjective. A team's strength can only be determined through judgement. That wasn't something I wasn't prepared to do, nor knowledgeable enough (going way back) to do. The part that I knew I could calculate objectively, with accuracy was the probabilities based on format.

That said, I'd be super interested to see the results of what you're describing.

 

[Michael Farkas]

Hypothetically, would you prefer to be in a five-team division where four teams make the playoffs, or a 100-team division where four teams make the playoffs?

Hmm, interesting point. Maybe there is a math or maths out there using the schedule as a limit that would determine where that advantage ends. Because in an 82 game schedule, the 100-team division must create all the more points that you cannot control and therefore the advantage is lost (much like the quality of the league with all these teams........)

I should not assume that you disagree with my premise despite this hypothetical, right? Or "not so fast my friend"? :pencil:

 

[Michael Farkas]

That's when it gets subjective. A team's strength can only be determined through judgement. That wasn't something I wasn't prepared to do, nor knowledgeable enough (going way back) to do. The part that I knew I could calculate objectively, with accuracy was the probabilities based on format.

That said, I'd be super interested to see the results of what you're describing.

Maybe not even subjectively, maybe based on regular season standings or some such...? Like the 1975 Capitals and 1992 Sharks were not even a speed bump for teams...in fact, they ably helped opponents play hockey better...the Caps winning seven games one year make them a nothingburger...the 1959 Habs faced no such opponent...

 

[Doctor No]

Hmm, interesting point. Maybe there is a math or maths out there using the schedule as a limit that would determine where that advantage ends. Because in an 82 game schedule, the 100-team division must create all the more points that you cannot control and therefore the advantage is lost (much like the quality of the league with all these teams........)

I should not assume that you disagree with my premise despite this hypothetical, right? Or "not so fast my friend"? :pencil:

My opinion - and it's only provable in the hypothetical sense, since we can't do this experiment in the real world - is that if you have a fixed number of playoff spots, each additional team in the division lowers your chances of making the playoffs.

Now, if the added team is terrible, then the effect may be zero - suppose you have a five-team NHL division, and you add to that division an average Toronto beer league team. That team probably isn't going to win any games. However, the five existing teams play that team the same number of times, so they'll each benefit equally (which puts them relatively on the same footing).

Things would change with the introduction of wild cards, of course - since now those five teams would benefit by playing the new team more times (and teams in other divisions would not).

So now let's assume that the new sixth team belongs in the division, and would win some games. Each of the other five teams would benefit equally (roughly) from playing that new team. To the extent that the new team can win some games and has a non-zero playoff chance, whatever that playoff chance is has to be taken away from the other teams (since there's still only four playoff positions).

So that's my stance.

 

[Michael Farkas]

Hmm, I can feel when I'm about to get out-mathed. But I'll stand in there and take a few punches...

I look at it from the perspective of:
a) I believe in my team
b) I can benefit from controlling the points of my opponents

So if you're a five-team division and you play each team four times in an 82-game schedule (meaning that 16 of your 82 games and therefore 32 of your 164 points are against the direct opponents that you're competing for a playoff spot with) -- on top of that, you control 8 points of each of your opponents in the process. So you ultimately control 32 of yours, 32 of theirs...64 points of 820 total division points (this isn't removing points impossible to attain by way of the intra-divisional scheduling...as it's too early in the morning for me to figure that out and even if it was the middle of the day, I'm not smart enough...).

So that's 64 of 820 =- 7.8%

If you're in a six-team division at four games each. So...

20 games, 40 points of 164 plus 40 of theirs. So that's 80 out of 964 = 8.3%.

If you scale up the schedule, not the division...

Five-team division, eight times each. 64 points of 164 points, plus 64 of theirs. 15.6%

Six-team division at eight games each...

40 games, 80 points of 164 plus 80 of theirs. So that's 16.6%.

That's my stance...as disorganized as it is, I look at it from a 'control direct opponents points' perspective...and I hope that you are overwhelmed by the science and cannot form a response haha

 

[Canadiens1958]

Olympic Marathon Standards:

Olympic Marathon Trials Qualifiers

Boston Marathon Standards:

Qualifying

Olympic Marathon has a much smaller field.

Putting the top 10 marathoners from the Olympics in the Boston Marathon would not decrease their chances of winning or medaling in a fair race unless they collide at the start with one of the weekend warriors.

Not a question of judgement but objective qualifying standards.

Using the division range, 6 vs 100. Hyperbolic example. Making things sound more impressive or difficult than they really are.

Just like in the marathon example it is a question when participants or teams no longer have a chance of winning. Some are eliminated by the first mile,others miles 2- 25, along the way. One hand finger count remain in contention the last mile.

Bringing all this back to NHL hockey. First 25 seasons you had two repeat winners - Canadiens 1930 and 1931, Red Wings 1936 and 1937. Last 25 seasons you also have two repeat winners Red Wings 1997 and 1998 and Penguins 2016 and 2017. First 25 seasons you had at most 10 realistically eligible teams until the "challenge" rule was eliminated. Last 25 seasons you have upwards of 31 eligible teams.

Ironically in the 1893 to 1917 era, mainly a challenge era, with well over 31 amateur teams eligible for Stanley Cup play you regular repeat winners over 2 or 3 seasons.

List of Stanley Cup champions - Wikipedia

Like population not having a direct correlation with hockey talent development(debunked previously), league size does not have a direct correlation on winning the SC.

 

[Canadiens1958]

There is no greater value in taking two, than earning two. Both are "equally" advantageous. When the Pens take 2 from the Flyers, they're also helping their own division rivals, Rags, Devs and Caps at the same time. The effect is a wash, and is the same in a 5-team division.

This is what it looks like when 6 teams in the same division, do exactly that which you describe:

1987-88 NHL Standings | Hockey-Reference.com Be sure to compare their point toals to the teams that made the playoffs in the other divisions.

Would a goal in a high scoring era be worth the same as a goal in a low scoring era?

Basically, more so with the introduction of the "loser point", the 4-point game has been eliminated from impacting standings.

At the core this is MF's point.

 

[Doctor No]

Hmm, I can feel when I'm about to get out-mathed. But I'll stand in there and take a few punches...

I look at it from the perspective of:
a) I believe in my team
b) I can benefit from controlling the points of my opponents

So if you're a five-team division and you play each team four times in an 82-game schedule (meaning that 16 of your 82 games and therefore 32 of your 164 points are against the direct opponents that you're competing for a playoff spot with) -- on top of that, you control 8 points of each of your opponents in the process. So you ultimately control 32 of yours, 32 of theirs...64 points of 820 total division points (this isn't removing points impossible to attain by way of the intra-divisional scheduling...as it's too early in the morning for me to figure that out and even if it was the middle of the day, I'm not smart enough...).

So that's 64 of 820 =- 7.8%

If you're in a six-team division at four games each. So...

20 games, 40 points of 164 plus 40 of theirs. So that's 80 out of 964 = 8.3%.

If you scale up the schedule, not the division...

Five-team division, eight times each. 64 points of 164 points, plus 64 of theirs. 15.6%

Six-team division at eight games each...

40 games, 80 points of 164 plus 80 of theirs. So that's 16.6%.

That's my stance...as disorganized as it is, I look at it from a 'control direct opponents points' perspective...and I hope that you are overwhelmed by the science and cannot form a response haha

Everything you've got here is correct as far as my opinion is concerned, but I'll add two things:

Each of the other division opponents also controls more points against the new opponent, so have a similar advantage to the one you enumerate.

And to the extent that the new team has any chance of winning at all (even a very small one), that chance has to come from somewhere in the division (or to put it in your terminology, if the new team has any ability at all, then they also control more points against their opponents).

Even if the added team has a 0.1% chance to make the playoffs, that means that someone has a lesser chance.

 

[Canadiens1958]

Super Bowl Champions:

List of Super Bowl champions - Wikipedia

Last 25 seasons the NFL has been a stable 32 team league -other than franchise moves. Four teams distributed over eight divisions. In division play is balanced,outside division play is weighed - strong team schedule/weak team schedule based on the previous season's standings.NFLis a Salary Cap league

NHL over its last 25 seasons has never had 32 teams. Mathematical abstraction dictates(using fair numbers) that as a result it should be harder to repeat as champions in the NFL with 32 teams than in the NHL approaching 31 teams. Especially given that NFL playoffs are one game eliminations vs best of 7 series.

Yet as the list shows the NFL has produced more repeat champions and long term contenders over 25 seasons than the NHL. Why?

Likewise the NBA -30 team league/Salary Cap over 25 seasons, has produced more repeat champions. Why?

List of NBA champions - Wikipedia

 

[Michael Farkas]

Hmm, that's fair. To be clear, I'm not adding an expansion team (non-Vegas), I'm just assuming a generic, regular, whatever you want to call it division.

I think we're looking at it through a slightly different lens...you're looking at it from a "insert an also-ran" perspective. I'm looking at it from a "I'm a 100-point team, get out of my way" perspective.

I guess maybe it's philosophical for me (which may be at odds with statistics)...but is there such a thing as a "chance" of making the playoffs? Does the fact that the Islanders play in the Patrick actually drain on the Penguins "chance" of making the playoffs...? The Penguins control their own destiny in every game. The only time the Islanders can really affect the Penguins is if they beat them in head to head games I feel like...

 

[Doctor No]

I'll try and run some Monte Carlo simulations later today which will (hopefully) illuminate the situation.

 

[Tweed]

Maybe not even subjectively, maybe based on regular season standings or some such...? Like the 1975 Capitals and 1992 Sharks were not even a speed bump for teams...in fact, they ably helped opponents play hockey better...the Caps winning seven games one year make them a nothingburger...the 1959 Habs faced no such opponent...

I think the closest we could possibly come to "objectively" measuring a team's strength would be to factor in their winning percentage for the season over/under 0.500, and then calculate it against their base-probability of success.

Correct me if I'm wrong, but I'm under the impression that you are advocating for O6 teams that saw great success, and taking the position that their chance of winning the cup was not 5x greater than a single team in modern day 30-team NHL.

That would have the opposite effect of what you're hoping to show though. A team like the '59 Habs, who were a powerhouse, had an extremely high chance of success, given their situation (roster, chemistry, previous success). What that really means is, them winning the Cup that year, is less of an accomplishment for them, than it would be for a lesser team in the league, to have overcome the Habs.

That's how the math would flesh out, when you start to inject things like "team strength" into the equation.

 

[Tweed]

Especially given that NFL playoffs are one game eliminations vs best of 7 series.

True, in the context of "stronger teams beat weaker teams, more often than not"... and therefore will succeed more often in a Best-of-7 format than they would in a Best-of-1 format.

But not true, in the context of "both teams have an equal chance of winning, based purely on the format". There's not one thing that favours one team over another, in either format. Both teams have an equal chance of succeeding in a Best-of-1, as they do in a Best-of-7.

To the rest of your point, I think this video addresses most of it:



And then when we factor in things like how much change is induced either by a cap system, or roster makeup... we're able to start to identify why some teams in some sports are able to perform repeats. For example, the Pens repeat last year was almost certainly a byproduct of their ability to keep nearly their entire championship roster intact, which consisted of many of their premier players in their prime, on contracts that were conducive to additional managerial decision-making opportunities for improvement and/or compensation of weaknesses (Fleury in for Murray, Hainsey in for Letang, addition of Guentzel).

Additional reading: https://arxiv.org/pdf/1701.05976.pdf

6.1. Summary. We propose a modied Bayesian state-space framework that can
be used to estimate both time-varying strength and variance parameters in order to
better understand the underlying randomness in competitive organizations. We apply
this model to the NBA, NFL, NHL, and MLB.

Our first finding relates to the relative equivalence of the four leagues. At a single
point in time, team strength estimates diverge substantially more in the NBA and
NFL than in the NHL and MLB. In the latter two leagues, contests between two
randomly chosen teams are closer to a coin-flip, in which each team has a reasonable
shot at winning.