Probability of a team going 82-0

[Steerpike]

So I'm super intrigued by this thread:

http://hfboards.mandatory.com/showthread.php?t=1717823

For those who didn't see it, the game is to produce a lineup of players that would win all 82 games in a season. To make it simpler, assume that even if you decide to have Crosby on your team, the Penguins still have him as well or are just as good without him.

For example my fictional team looked like:

Ovechkin—Crosby—Malkin
Benn—Seguin—Stamkos
Hall—Getzlaf—Perry
Toews—Kopitar—Bergeron

Suter—Weber
Karlsson—Pietrangelo
Doughty—Keith

Rask
Lundqvist


You could qualitatively debate the merits of a team but I think it's much more interesting to think of this problem mathematically and try to figure out what Goals for and Goals against rates would result in a team having a decent probability of winning all 82 games.


I think the most logical way to approach this is to look at goals for and goals against per game as Poisson distributions to calculate the probability of winning a game. Multiply that by itself 82 times to get the probability of of winning all 82 games.

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[Tarasenko]

Short answer : 0%
Long answer : Impossible.

 

[Catamo]

I think the most logical way to approach this is to look at goals for and goals against per game as Poisson distributions to calculate the probability of winning a game. Multiply that by 82 to get the probability of of winning all 82 games.

Actually, You would multiply the odds winning each game (Say it was 94%) by itself 82 consecutive times.

which would make the odds of winning all 82 games 0.6%

Goaltending plays too big of a factor for any superstar team to go 82-0 against any NHL calibre teams. Rask and Lundqvist are capable of laying an egg, and alternatively the opposing goalie is capable of being red hot.

 

[Steerpike]

So I did the math and realized it's way easier to change it to "go 82 games without a loss" as I don't want to work out what happens in the event of ties.

All you have to do is score 7.8 goals per game while holding your opponent to 1.5 goals per game and you have a 50% chance of going the entire season without a loss.


The amusing thing is that you end up needing a 0.9963 probability of not losing any particular game to end up with this 50% chance. 82 is a lot of games.

 

[Steerpike]

Actually, You would multiply the odds winning each game (Say it was 94%) by itself 82 consecutive times.

which would make the odds of winning all 82 games 0.006%

Goaltending plays too big of a factor for any superstar team to go 82-0 against any NHL calibre teams. Rask and Lundqvist are capable of laying an egg, and alternatively the opposing goalie is capable of being red hot.

Yeah I got that number out and realized I was being Pejorative Slured

 

[Arno Dorian*]

And honestly, the .0006% number is assuming you have a 50% chance of winning every game. In theory, the further on in the season you get (say game 60 or 70), the less likely you are to win (after getting the huge lead in the conference, it's better to rest players for the playoffs, where a one seed is a one seed whether you win 55 games or 82).

 

[kmad]

It would go beyond basic statistics.

If a team was even 20-0 at some point, it would become the ultimate goal of every other team in the league to knock that team down. No team would be able to withstand every team in the league bringing their A game for 62 games afterwards.

 

[BraveCanadian]

Zero

 

[No Fun Shogun]

It's technically not impossible, but I'd happily give you odds and bet that it'll never happen.

 

[Mystifo]

Short answer : 0%
Long answer : Impossible.

Improbable not impossible.


But yeah I would not bet a whole lot on it happening.

 

[JoeCool16]

It would go beyond basic statistics.

If a team was even 20-0 at some point, it would become the ultimate goal of every other team in the league to knock that team down. No team would be able to withstand every team in the league bringing their A game for 62 games afterwards.

I agree, after becoming veterans, lots of games probably start looking pretty similar to players in the regular season. They take moments like that to rev themselves back up. A team on a long winning streak definitely garners a better effort against than a middling team going nowhere.

 

[Adityase]

The answer is 0%, but how could you now have Zetterberg on the 3rd line LW over Hall? I mean, in a pure shut down role, I would expect a Penguins fan to appreciate that opportunity!

 

[Steerpike]

The answer is 0%, but how could you now have Zetterberg on the 3rd line LW over Hall? I mean, in a pure shut down role, I would expect a Penguins fan to appreciate that opportunity!

A) What led you to believe I'm a penguin's fan?
B) It's not really about the roster, it's about how scoring goals leads to win probability and the necessary win probability to have a chance at 82-0
C) Injury concerns over Zetterberg.
D) Getzlaf and Perry scored at the highest rate in the NHL even strength. Every line needs to score. Hall has shown he's pretty good at that.
E) Just make your own roster if you want to complain about mine.

 

[Constable]

Would it be possible to add the numbers of points and other stats to reach a ultimatum? for example:

Pittsburgh scores 362 goals in a season. They got 41-31-10 (idk random numbers) add up so that pittsburgh is at least 1 goal higher in each game than the opponent, and lets say the number of goals is 402. With this, I can guess somewhat reasonably that pittsburgh, in order to win 82 games, this team needed to reach atleast 402 goals.

Of course, all the numbers here are random, and we still do have unpredictability, but the point still stands; if this figurative team during this figurative season wanted to go 82 and 0; they would need 402 goals scored, and 201 goals against.

The number of points they would need to put up in the end would be anywhere between 402-1206.


Once again, these are random numbers used to show a concept.

 

[Steerpike]

Would it be possible to add the numbers of points and other stats to reach a ultimatum? for example:

Pittsburgh scores 362 goals in a season. They got 41-31-10 (idk random numbers) add up so that pittsburgh is at least 1 goal higher in each game than the opponent, and lets say the number of goals is 402. With this, I can guess somewhat reasonably that pittsburgh, in order to win 82 games, this team needed to reach atleast 402 goals.

Of course, all the numbers here are random, and we still do have unpredictability, but the point still stands; if this figurative team during this figurative season wanted to go 82 and 0; they would need 402 goals scored, and 201 goals against.

The number of points they would need to put up in the end would be anywhere between 402-1206.


Once again, these are random numbers used to show a concept.

Yeah I think I see what you mean. I think a better way of thinking about it though is looking at their GF/60 rates with them on the ice. All of these forwards play 20ish minutes a game and now they would be playing 15ish minutes. This would substantially decrease their points but it might increase their GF/60 as they would be more rested.

 

[Big Phil]

I'll say 1%. In other words, virtually impossible. The way I look at it, some of the greatest teams ever iced lost a game once. The 1976 Canadian Canada Cup team. The Russians losing to the Americans in 1980. Canada in the last couple of Olympics with a loaded roster not unlike the one you have there other than 2014 of course, but 2002 and 2010 lost one game.

You have to take into account fatigue, and the fact that they'll never be going 100 miles an hour all season. As someone said, the other team constantly giving you their "A" game. Think of it this way, when a player get a scoring streak such as Crosby had a couple of years ago with 25, look at how hard that was to maintain. Every team wanted to be the one to shut him down. Imagine facing that every game with this team.

 

[Steerpike]

I'll say 1%. In other words, virtually impossible. The way I look at it, some of the greatest teams ever iced lost a game once. The 1976 Canadian Canada Cup team. The Russians losing to the Americans in 1980. Canada in the last couple of Olympics with a loaded roster not unlike the one you have there other than 2014 of course, but 2002 and 2010 lost one game.

Olympic teams aren't given as much time to gain chemistry together so they don't operate like a normal NHL team would after playing together for a season. They also aren't made out of all of the best players in the world. +they play on an international ice surface that most players aren't used to and it throws a curve ball of randomness into the situation.

You have to take into account fatigue, and the fact that they'll never be going 100 miles an hour all season. As someone said, the other team constantly giving you their "A" game. Think of it this way, when a player get a scoring streak such as Crosby had a couple of years ago with 25, look at how hard that was to maintain. Every team wanted to be the one to shut him down. Imagine facing that every game with this team.

The team certainly won't be going at 100% all the time but neither are NHL players on their current teams so it might be a wash. There would obviously have to be some great incentive for the players and the team to win 82 games or they would start mailing in their performance after crushing everyone for a while.

 

[Halibut]

Your biggest problem off the bat is you are over the cap with that lineup.

 

[Steerpike]

Oh **** really? By how much?

 

[Brainiac]

The amusing thing is that you end up needing a 0.9963 probability of not losing any particular game to end up with this 50% chance. 82 is a lot of games.

I think your number is a little off. I do get 0.99163. But at this point, it's already beyond ridiculous anyways.

The bolded is key. 82 games is a whole freaking lot of games. Numbers do tend to become hard to conceptualize at that point. Especially as the 82 will be used as an exponent in many formulas.

A good team could go 15-0 or 20-0, it happens. A super duper crazy stacked team could go 30-0 or 40-0. But from there to 82-0 is just too much. They will run into a goalie that will give an out of this world performance and it's all over.

A great team winning the playoffs with a 16-0 record is much more realistic, even though the level of play is higher. Some teams actually came close.

 

[Rebuilt]

Well if you dummy it down some you can come up with the odds.

If a team either wins or loses -because of the shoot out winning is possible every game.

If you count OT/shoot out loss as a loss then there is only wins and losses.

Take a coin, flip it heads or tails. Say its heads.

What are the odds you can flip a coin to come up heads 82 times in a row ?

Those are the odds.

 

[Theokritos]

Take a coin, flip it heads or tails. Say its heads.

What are the odds you can flip a coin to come up heads 82 times in a row ?

Those are the odds.

Not sure if serious. You think a team with a line-up like the following has the same 50:50 chance to win or lose than a coin has to come up heads or tail?

Ovechkin—Crosby—Malkin
Benn—Seguin—Stamkos
Hall—Getzlaf—Perry
Toews—Kopitar—Bergeron

Suter—Weber
Karlsson—Pietrangelo
Doughty—Keith

Rask
Lundqvist

If anything that's like flipping a coin where one side is much heavier than the other.

 

[OilerPensfan97]

That will never happen. Teams always have their ups and downs no matter how good they are.

 

[Number54]

If we're counting OT and SO losses as losses, then this is tractable as a binomial probability of N choose R, where N is the total number of games and R is the number of wins. The formula for calculating this is:
n! / (n-k)! * p^(n-k) * q^k
Assuming wins and losses are equiprobable (which they must be if every game has a winner and a loser), we obtain:
82! / (0!) * 0.5^(0) * 0.5^(82) = 82! *0.5^82 = 9.830304 * 10^-97

If you're not partial to scientific notation, that's a probability of about 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001; so, basically, ZERO.

 

[Brainiac]

If we're counting OT and SO losses as losses, then this is tractable as a binomial probability of N choose R, where N is the total number of games and R is the number of wins. The formula for calculating this is:
n! / (n-k)! * p^(n-k) * q^k
Assuming wins and losses are equiprobable (which they must be if every game has a winner and a loser), we obtain:
82! / (0!) * 0.5^(0) * 0.5^(82) = 82! *0.5^82 = 9.830304 * 10^-97

If you're not partial to scientific notation, that's a probability of about 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001; so, basically, ZERO.

There's a little bit of a fallacy right there. The expected outcome of a hockey game is not 50-50. Depends on the teams involved.

It's like all those guys that say anything is possible come playoffs time because you've got 16 teams involved and thus a 1/16 chance of winning it all.