What if the Sabres win the lottery?

[JujuFish]

I don't know what the numbers are, but if it's 5% in the first draw and ~5.4% in the second draw, then Buffalo's odds of winning one of the two draws is 10.13%.

[SDS]

1 hour ago, JujuFish said:

I don't know what the numbers are, but if it's 5% in the first draw and ~5.4% in the second draw, then Buffalo's odds of winning one of the two draws is 10.13%.

Since it’s two separate draws, it doesn’t work that way. It’s like flipping a coin twice.

[woods-racer]

1 hour ago, JujuFish said:

I don't know what the numbers are, but if it's 5% in the first draw and ~5.4% in the second draw, then Buffalo's odds of winning one of the two draws is 10.13%.

On 5/6/2022 at 2:41 PM, woods-racer said:

@SDS turned me on to a book a few years back called A Drunkards' Walk-How Randomness Rules Our Lives. 

Talks all about math-probabilities-statistics and how swayed they are or can be. Quite eye opening.

Read it. You'll understand why it doesn't work that way.

[JujuFish]

2 hours ago, SDS said:

Since it’s two separate draws, it doesn’t work that way. It’s like flipping a coin twice.

Since you're not providing me an alternative answer, I can't explain why you're wrong, so I'll try to explain why I'm right.

Let's start with your coin flip analogy.  What are the odds of getting heads on a coin flip? 50%.  Flip it again.  What are the odds of getting heads on the second flip?  50%.  Now I tell you I'm going to flip it twice in a row.  What are the odds I get heads on either flip?  It seems to me like you think it's 50%, but it's 75%.  With a coin flip, this is particularly easy to see, because it's very easy to enumerate the results.  We have HH, HT, TH, TT. Three out of four results have heads, AKA 75%.

 

Let's go with a more complicated example, closer to the draft but nowhere near as complex.  Let's say there are 6 teams eligible for the draft, and they all have equal odds.  Now we're looking at two rolls of a die.  Let's call the Sabres 1 (because we're #1!).  On the first roll, everyone has a 1/6 chance.  After the die is rolled once, we have a winner and that number now becomes a re-roll, making the remaining teams have a 1/5 chance.  This is still simple enough to enumerate.  We have the following possibilities:

1-2 1-3 1-4 1-5 1-6 = 5/5 results with Buffalo winning
2-1 2-3 2-4 2-5 2-6 = 1/5 results with Buffalo winning
3-1 3-2 3-4 3-5 3-6 = 1/5 results with Buffalo winning
4-1 4-2 4-3 4-5 4-6 = 1/5 results with Buffalo winning
5-1 5-2 5-3 5-4 5-6 = 1/5 results with Buffalo winning
6-1 6-2 6-3 6-4 6-5 = 1/5 results with Buffalo winning
------------------------------------------------------
                     10/30 = 33.3% chance Buffalo wins

As you can see, the odds of Buffalo winning are how I'm attempting to describe.  When there are 1001 draws like the NHL, with over 1 million combinations, it's infeasible (for me) to write them all out, but the principle remains the same.

If you know the individual odds of something happening in two different setups, it's easy to calculate the odds of it happening at least once by calculating the odds of it not happening either time and subtracting that from 100%.  In the coin flip example, the odds of not getting heads either time is 50%, so 1-(.5)(.5) = .75 or 75%.  In the die roll example, it's 1-(5/6)(4/5) = 1-(20/30) or 33.3%.  Assuming the numbers upthread are accurate, for the draft lottery it's 1-(.95)(.946) = 10.13%.

2 hours ago, woods-racer said:

Read it. You'll understand why it doesn't work that way.

See above.  Hopefully you'll understand why you're wrong.

[North Buffalo]

On 5/6/2022 at 5:19 PM, woods-racer said:

I wouldn't call it being fooled, just not understanding in this case.

If you get 2 shots moving up in the draft one at 5% and one at 5.2% it is very easy to assume that their odds are 10.2%. Some would assume that they are much better but maybe not a total of 10.2%.

The reality is when the first lottery is played and you lose the odds of winning the second lottery are still just 5%. Getting more chances does not increase the % chance you will win.

Called independent variables... 

[MattPie]

Juju has it. In two draws without the odds changing, you just add the probability winning if you only care if you win once. In this scenario it is more complex because the first draw changes the odds of the second, but it's still in the neighborhood of 10% that the Sabres win one of the two.

If it were 5% each draw, after 20 draws (5 * 20 == 100) you'd expect that you'd win one of the draws. If you're using the 6-sided die, each number comes up 1/6 of the time (16.6667%), so if you roll the die 6 times you "should" see each number come up, even though any particular roll the odds don't change.

[PASabreFan]

[carpandean]

Sigh ... odds <> probability.  Most of y'all are talking about the latter.

As for the actual probability of being selected once, it will be close to two independent draws, but not quite.  It's a little higher ...

If the Sabres don't win the first draw, then the winning combinations for the team that was picked first become redraws.  As such, it's as though they are removed from the draw.  So, for example, if a team with a 10% chance originally (i.e., 100/1000 combinations) were picked first, then the Sabres' probability of being picked in the second draw would become 50/(1000-100) = 0.0556 (5.56%). 

In total, the Sabres probability of being picked once:

0.05 + sum over all other teams{Pr[that team being picked first]*(0.05/(1-Pr[that team being picked first]))} = 10.319%

 

[woods-racer]

In the simplest of terms..

 

If I play the Mega Millions lottery and the draw is once a week the odds of the lottery are 300 million to one for me this week.

If I play again next week, the odds are still 300 million to one for me again.

If I play once a week every week for 10 years, in 10 years the odds are still 300 million to one when I play.

Increasing the number of times I play does not increase the chances I win, but the only way to win is to play.

The odds are still the same odds no mater how many times you play, there is no increase in the probability of winning because you play more. It doesn't sound logical, but Mlodinow explains why.

 

[Curt]

6 minutes ago, woods-racer said:

In the simplest of terms..

 

If I play the Mega Millions lottery and the draw is once a week the odds of the lottery are 300 million to one for me this week.

If I play again next week, the odds are still 300 million to one for me again.

If I play once a week every week for 10 years, in 10 years the odds are still 300 million to one when I play.

Increasing the number of times I play does not increase the chances I win, but the only way to win is to play.

The odds are still the same odds no mater how many times you play, there is no increase in the probability of winning because you play more. It doesn't sound logical, but Mlodinow explains why.

 

The odds remain the same each time, but of course increasing the number of times that you play increases the chances that you win.

With the league drawing two lottery winners, the Sabres have a greater chance of winning a lottery draw than if there was only one drawing, and they have a lesser chance of winning than they would if the league was still drawing three lottery winners.

[woods-racer]

21 minutes ago, Curt said:

The odds remain the same each time, but of course increasing the number of times that you play increases the chances that you win.

With the league drawing two lottery winners, the Sabres have a greater chance of winning a lottery draw than if there was only one drawing, and they have a lesser chance of winning than they would if the league was still drawing three lottery winners.

That's what the book discusses in great detail. It's not true. The odds remain the same, but you can't win unless you play.

Edit.

In the case of the Sabres and the NHL the second lottery is effected by taking one team off of the Lottery draw as explained by TaroT. He then states the given odds for the second lottery.

Edited May 8, 2022 by woods-racer

[ddaryl]

the Sabres do not have a 10% chance of winning the lottery. You cannot add the odds of draw 1 and draw 2 together. That's not how it works. It wil depend on whom wins the 1st draw and has their chances removed, but the 2nd draw odds will not vary much from the 5.4% posted above. 

This is not rocket science





 

[Curt]

43 minutes ago, woods-racer said:

That's what the book discusses in great detail. It's not true. The odds remain the same, but you can't win unless you play.

Edit.

In the case of the Sabres and the NHL the second lottery is effected by taking one team off of the Lottery draw as explained by TaroT. He then states the given odds for the second lottery.

So if I play the lottery 10,000 in my life, the probability of me winning a lottery drawing are no greater than someone who played the lottery only once in their life?  I haven’t read the book, but I disagree.

In this case, it’s not even like playing an entirely new lottery a second time.  It’s one lottery in which two winning numbers are drawn.  In a lottery with two winners drawn, there is a greeting chance of winning than in the same lottery with only one winner drawn.

Lets not throw all common sense out the window.

[Curt]

41 minutes ago, ddaryl said:

the Sabres do not have a 10% chance of winning the lottery. You cannot add the odds of draw 1 and draw 2 together. That's not how it works. It wil depend on whom wins the 1st draw and has their chances removed, but the 2nd draw odds will not vary much from the 5.4% posted above. 

This is not rocket science





 

This is correct.

[woods-racer]

10 minutes ago, Curt said:

So if I play the lottery 10,000 in my life, the probability of me winning a lottery drawing are no greater than someone who played the lottery only once in their life?  I haven’t read the book, but I disagree.

In this case, it’s not even like playing an entirely new lottery a second time.  It’s one lottery in which two winning numbers are drawn.  In a lottery with two winners drawn, there is a greeting chance of winning than in the same lottery with only one winner drawn.

Lets not throw all common sense out the window.

Exactly. That is randomness.

Your are dealing with numbered balls popping up into a tube. Randomness. You can't put a linear equation into that and say that randomness will adhere to it.

You are saying that if your odds are 5% if you play the lottery 100 times you will win 5 of them. It's not how randomness works.

You can play it a 1000 times and not win, then win the next 10 in a row. Each time your odds of winning will be 5%.

[Curt]

29 minutes ago, woods-racer said:

Exactly. That is randomness.

Your are dealing with numbered balls popping up into a tube. Randomness. You can't put a linear equation into that and say that randomness will adhere to it.

You are saying that if your odds are 5% if you play the lottery 100 times you will win 5 of them. It's not how randomness works.

You can play it a 1000 times and not win, then win the next 10 in a row. Each time your odds of winning will be 5%.

Ok.  That’s not actually what I’m saying, but forget about you or I playing the lottery.  I suppose it’s a useless tangent.

The NHL draft lottery isn’t that.  It’s one single lottery with two drawings.  A lottery in which two winning numbers are drawn must have a higher probability of any single number(or set of numbers in this case) winning than the same lottery with just one winner drawn.  No?

Are you saying that the Sabres have just a 5% chance of moving up in the draft?

EDIT:  ok, reading back I do see what you are saying.  The probability of winning the 2nd drawing does increase, but not that much.  

Edited May 8, 2022 by Curt

[JujuFish]

2 hours ago, woods-racer said:

In the simplest of terms..

 

If I play the Mega Millions lottery and the draw is once a week the odds of the lottery are 300 million to one for me this week.

If I play again next week, the odds are still 300 million to one for me again.

If I play once a week every week for 10 years, in 10 years the odds are still 300 million to one when I play.

Increasing the number of times I play does not increase the chances I win, but the only way to win is to play.

The odds are still the same odds no mater how many times you play, there is no increase in the probability of winning because you play more. It doesn't sound logical, but Mlodinow explains why.

 

It's like you're aware of Gambler's Fallacy and you're overcorrecting.  The odds don't change between plays, but if you buy 10 tickets right now, for 10 consecutive lottery wins, your odds of winning at least one of them are significantly greater than 1 in 300 million.

[Sabres Fan in NS]

[sabresparaavida]

3 hours ago, woods-racer said:

In the simplest of terms..

 

If I play the Mega Millions lottery and the draw is once a week the odds of the lottery are 300 million to one for me this week.

If I play again next week, the odds are still 300 million to one for me again.

If I play once a week every week for 10 years, in 10 years the odds are still 300 million to one when I play.

Increasing the number of times I play does not increase the chances I win, but the only way to win is to play.

The odds are still the same odds no mater how many times you play, there is no increase in the probability of winning because you play more. It doesn't sound logical, but Mlodinow explains why.

 

This differs from the way the NHL draft lottery works though. After the first winner has been picked, the rest of the teams’ chances increase proportionally to their chances of winning the lottery in the first draw. The amount each team increases depends on which team wins the lottery (if Montreal wins the first, then their 18.5% chance of winning is no longer there and so gets split among the other lottery teams)

[irregularly irregular]

Here are my $0.02 on this subject.

Does it really matter? Do you have any control over the outcome? So sit back, enjoy the ride and hope for the best possible outcome while expecting the most likely outcome. 

And yes, Tom Webster nailed it. 

[GASabresIUFAN]

And now back to the show?

What if the Sabres win the lottery and take Mr. Wright.  I see him kind of in the same vain as Reinhart. I don't think he is NHL ready, but should be in another year.  

How does that change this lineup? Does it change the organization's view of Mitts or Krebs or even JJP?  At some point, management is going have to make some hard choices on some of these talented young forwards.

Here is the forwards under control breakdown (Current age) arb = arbitration eligible

1. KO (34) - 1 year left - UFA

2. Skinner (29) - 5 years left  - UFA

3. Girgensons (28) - 1 year left - UFA

4. Olofsson (26) - RFA (arb)

5. Tuch (25) - 4 years left - UFA

6. Bjork (25) - 1 year left - RFA (arb)

7. Thompson (24) - 1 year left - RFA (arb)

8. Asplund (24) - 1 year left - RFA (arb)

9. Routsalainen (24) - RFA (arb)

10. Mittelstadt (23) - 2 years left - RFA (arb)

11. Murray (23) - RFA (arb)

12. Cozens (21) - 1 year left - RFA

13. Krebs (21) - 2 years left - RFA

14. Quinn (20) - 3 years left - RFA

15. JJP (20) - 3 years left - RFA

At some point you can't keep everyone.  After next season KO, Girgensons, Thompson, Asplund and Cozens will all need new contracts, with Krebs, and Mitts (plus Dahlin and Jokiharju) the following year. Tough decisions are coming and if you add a Wright to the mix, someone is going to left without a chair.

 

 

 

[pi2000]

4 hours ago, carpandean said:

Sigh ... odds <> probability.  Most of y'all are talking about the latter.

As for the actual probability of being selected once, it will be close to two independent draws, but not quite.  It's a little higher ...

If the Sabres don't win the first draw, then the winning combinations for the team that was picked first become redraws.  As such, it's as though they are removed from the draw.  So, for example, if a team with a 10% chance originally (i.e., 100/1000 combinations) were picked first, then the Sabres' probability of being picked in the second draw would become 50/(1000-100) = 0.0556 (5.56%). 

In total, the Sabres probability of being picked once:

0.05 + sum over all other teams{Pr[that team being picked first]*(0.05/(1-Pr[that team being picked first]))} = 10.319%

 

Normally this would be true.

However, there exists a set of numbers that do not belong to any team.  If those numbers are drawn, they immediately redraw. 

Now, consider there are infinite parallel universes (there are).  In at least one of those universes, the lottery results in an unassigned number over and over and over again for infinity... in which case no team ever wins the lottery... ever.   

I'm just hoping we don't live in that universe.

 

[ddaryl]

On 5/6/2022 at 10:48 AM, GASabresIUFAN said:

There are two lottery slots.  What do the Sabres do if they win the No 1 slot?  What if they win the No 2 slot?  How does it change KA’s off-season game plan?  Are any of the prospects NHL ready?  Is Wright the dynamic center the forward group needs? Would KA consider trading down a slot or two to add more draft capital or a player?

IMO it changes nothing short term outside of having another top prospect re-tooling the pool.  You grab the highest ranking prospect on your board
I don't think Trading down is wise as the top picks in any NHL draft are almost always a solid step above the rest. If anything you eventually move another lesser piece from your organization when needed to make room for the new prospect. The lesser piece being moved can still net a player / draft pick/ or both

Edited May 8, 2022 by ddaryl

[kas23]

2 hours ago, woods-racer said:

Exactly. That is randomness.

Your are dealing with numbered balls popping up into a tube. Randomness. You can't put a linear equation into that and say that randomness will adhere to it.

You are saying that if your odds are 5% if you play the lottery 100 times you will win 5 of them. It's not how randomness works.

You can play it a 1000 times and not win, then win the next 10 in a row. Each time your odds of winning will be 5%.

Let’s use an extreme example. Suppose you have 2 people. Person 1 plays the lottery only once and has an odds of winning 1 in 300M. Now, suppose Person 2 lives for over 900M years (or better yet, has an infinite lifespan) and plays the same lottery once per day for their whole life. Person 2 does not have the same odds of winning over their lifespan (that’s the key here) than person 1. 

[French Collection]

46 minutes ago, GASabresIUFAN said:

And now back to the show?

What if the Sabres win the lottery and take Mr. Wright.  I see him kind of in the same vain as Reinhart. I don't think he is NHL ready, but should be in another year.  

How does that change this lineup? Does it change the organization's view of Mitts or Krebs or even JJP?  At some point, management is going have to make some hard choices on some of these talented young forwards.

Here is the forwards under control breakdown (Current age) arb = arbitration eligible

1. KO (34) - 1 year left - UFA

2. Skinner (29) - 5 years left  - UFA

3. Girgensons (28) - 1 year left - UFA

4. Olofsson (26) - RFA (arb)

5. Tuch (25) - 4 years left - UFA

6. Bjork (25) - 1 year left - RFA (arb)

7. Thompson (24) - 1 year left - RFA (arb)

8. Asplund (24) - 1 year left - RFA (arb)

9. Routsalainen (24) - RFA (arb)

10. Mittelstadt (23) - 2 years left - RFA (arb)

11. Murray (23) - RFA (arb)

12. Cozens (21) - 1 year left - RFA

13. Krebs (21) - 2 years left - RFA

14. Quinn (20) - 3 years left - RFA

15. JJP (20) - 3 years left - RFA

At some point you can't keep everyone.  After next season KO, Girgensons, Thompson, Asplund and Cozens will all need new contracts, with Krebs, and Mitts (plus Dahlin and Jokiharju) the following year. Tough decisions are coming and if you add a Wright to the mix, someone is going to left without a chair.

 

 

 

Interesting that we are getting nearer to a time when they have to move talent out or let them walk. I view that as a good thing, it means no JAGs.

Middle 6 prospects barely make the 4th line, 1st round draft picks spend 1-2 years in the AHL and we don’t sweat over whether a NCAA guy goes back for another year.

I can see it happening, a team we can enjoy watching, year after year.