Speculation: The REAL probability of Leafs winning the lottery over X number of years

[Darth Milbury]

Forgive me for intruding guys, but I actually do teach statistics at a university.


The odds of independent events do not influence each other. If you toss a coin twice, the odds will be 50% each time. You could lose the coin toss nine times, and the odds will be no different the tenth time. Each coin toss is independent from the other.


Intuitively, it would seem logical that 9 tails would make a heads more likely on the tenth toss, but that is not correct.


Your odds only change if there is a dependency. So, the odds of getting a particular pick given that somebody else has already lost the lottery improve.


The Leafs odds of winning the lottery are exactly what their odds are given their position in the lottery.

 

[Man Bear Pig]

It's like saying because I bought a lottery ticket 4 years ago that if I buy one today, my odds have increased.

 

[colchar]

Precisely. Your luck doesn't just carry over from year to year.

OP seems to be a believer in karmic powers.

Maybe he is channeling Red Kelly and pyramid power.

 

[CHRoNiCWiLL]

Forgive me for intruding guys, but I actually do teach statistics at a university.


The odds of independent events do not influence each other. If you toss a coin twice, the odds will be 50% each time. You could lose the coin toss nine times, and the odds will be no different the tenth time. Each coin toss is independent from the other.


Intuitively, it would seem logical that 9 tails would make a heads more likely on the tenth toss, but that is not correct.


Your odds only change if there is a dependency. So, the odds of getting a particular pick given that somebody else has already lost the lottery improve.


The Leafs odds of winning the lottery are exactly what their odds are given their position in the lottery.

You are correct here, however I think what I was trying to address was the probability of winning the lottery at least once after 9 tries. Assuming the odds are the same each year. The calculations would be correct if we were still in 2006 and calculating our odds to win the lottery at least once in any year between 2006 and 2015.

 

[ACC1224]

It's like saying because I bought a lottery ticket 4 years ago that if I buy one today, my odds have increased.

I used to think that a quick pick ticket was less likely to win the lottery because those exact numbers would have to be randomly generated twice.

 

[Diatomic]

The leafs have missed the playoffs every year since the lockout except for 2013. The leafs have also never won the the draft lottery in any of those years missed. Now prior to 2014, a team who won the lottery could only move up a maximum of 4 spots. We will ignore this fact and only consider the 'act' of winning the lottery rather than obtaining 1st overall.
So looking at where we placed and regardless of whether we kept the pick or not:

2006 - 13th - 0.8%
2007 - 13th - 0.8%
2008 - 7th - 4.7%
2009 - 7th - 4.7%
2010 - 2nd -18.8%
2011 - 9th - 2.7%
2012 - 5th - 8.1%
2014 - 8th - 3.6%

Combining these odds we have 44.2% chance. Average that out over 8 years we have 5.525% chance to win the lottery each year.
So doing the math to calculate 1 success in 8 tries, we have
(8 choose 1)(.0525)^1(1-.0525)^7
= 8(.0525)(0.9475)^7 = 0.288
Thats 28.8% chance to win the lottery.

Lets say we finish 5th last, our chances are 8.5% combined with previous we have 8.5+44.2 = 52.7, average over 9 years 5.86% chance each year.
Doing the math again:
(9 choose 1)(0.0586)^1(1-0.0586)^8
=9(0.0586)(0.9414)^8 = 0.325.

OUR odds of winning the lottery on the 9th try is 32.5%!

"Let me just get out my crystal ball".

 

[Man Bear Pig]

I used to think that a quick pick ticket was less likely to win the lottery because those exact numbers would have to be randomly generated twice.

It's all random, as we all know. I'm curious as to know whether most lottery winners are people who have stuck by their same "lucky" numbers for decades vs people with random computer generated numbers. Maybe it'll get you an edge

 

[Stephen]

Chronic Math?

 

[Trapper]

"Let me just get out my crystal ball".

If you took all 14 current non playoff teams and gave them an additional .5% for every year out of the last 10 that they missed the playoffs, gave them an additional .5% for every year in the last 10 not in the top 3 and removed 1% for every 1st overall pick and what do the odds look like?

 

[666]

I have corrected my math.
You all can stop being so critical

Unfortunately, even allowing for what you meant to say, the math is still wrong.

One hint. You can't average probabilities like that.
0.6*0.4 does not equal 0.5*0.5

Try again.

 

[ACC1224]

It's all random, as we all know. I'm curious as to know whether most lottery winners are people who have stuck by their same "lucky" numbers for decades vs people with random computer generated numbers. Maybe it'll get you an edge

I stopped buying them. Got tired of throwing away tickets that I forgot to check.

 

[Shwaguy*]

I have corrected my math.
You all can stop being so critical

You're still wrong though, you can't look at this as the "9th try" this is try number one

and if you do this calculation again next year? It'll still be try #1

 

[StuckOutHere]

We'd still ******* it up somehow.

We'd get Daigle'd

 

[Shwaguy*]

Forgive me for intruding guys, but I actually do teach statistics at a university.


The odds of independent events do not influence each other. If you toss a coin twice, the odds will be 50% each time. You could lose the coin toss nine times, and the odds will be no different the tenth time. Each coin toss is independent from the other.


Intuitively, it would seem logical that 9 tails would make a heads more likely on the tenth toss, but that is not correct.


Your odds only change if there is a dependency. So, the odds of getting a particular pick given that somebody else has already lost the lottery improve.


The Leafs odds of winning the lottery are exactly what their odds are given their position in the lottery.

Your a stats prof at a university? Which one if you don't mind my asking. I'm a stats major at a University lol

 

[Woodman19]

Flipping 3 straight heads on a coin doesn't change the odds of landing a tails on the 4th try, it is still 50/50.

 

[Darth Milbury]

You are correct here, however I think what I was trying to address was the probability of winning the lottery at least once after 9 tries. Assuming the odds are the same each year. The calculations would be correct if we were still in 2006 and calculating our odds to win the lottery at least once in any year between 2006 and 2015.

That's not correct. Your odds do not improve on the 10 try because you lost 9 times before. Your odds on the 9th try and exactly what they are on that try, because the events are not dependent.


If you were to say "What are odds of winning at least once in 10 years" - that is a joint probability and it has an entirely different distribution than the probability on any independent role. That probability would not help you to understand the odds on any individual trial and it would be nowhere near 32%.

Your probability of winning the lottery will be exactly your odds on the day of the lottery - no better or worse.

 

[PuckMagi]

I have corrected my math.
You all can stop being so critical

it's still not correct. see my post for the correct answer.

 

[Shwaguy*]

Man could you imagine the ****storm if we got McDavid and he Daigle'd on us?

 

[BlueBaron]

That's not correct. Your odds do not improve on the 10 try because you lost 9 times before. Your odds on the 9th try and exactly what they are on that try, because the events are not dependent.


If you were to say "What are odds of winning at least once in 10 years" - that is a joint probability and it has an entirely different distribution than the probability on any independent role. That probability would not help you to understand the odds on any individual trial and it would be nowhere near 32%.

Your probability of winning the lottery will be exactly your odds on the day of the lottery - no better or worse.

Probability Stats are really hard for most people to wrap their heads around because the reality is kind of counter intuitive. I think the OP's mistake is understandable for the average person.

 

[Kubus]

I see the OP never took stats.

 

[BlueBaron]

Man could you imagine the ****storm if we got McDavid and he Daigle'd on us?

This is the problem with stats, they don't factor in our curse

 

[Woodman19]

That's not correct. Your odds do not improve on the 10 try because you lost 9 times before. Your odds on the 9th try and exactly what they are on that try, because the events are not dependent.


If you were to say "What are odds of winning at least once in 10 years" - that is a joint probability and it has an entirely different distribution than the probability on any independent role. That probability would not help you to understand the odds on any individual trial and it would be nowhere near 32%.

Your probability of winning the lottery will be exactly your odds on the day of the lottery - no better or worse.

Would the Hypergeometric Probability Distribution not be used to do that?

 

[The Legend]

As someone with a stats background, I'm just going to leave this here in case OP actually wants to learn about probabilities.

Monty Hall problem.

 

[Al14]

The lottery doesn't have memory so wherever we finish in the standings will determine our chances to win.

Not with Bettman in charge!

He'll see to it that the best players go to his American based teams as he sees fit!

 

[666]

That's not correct. Your odds do not improve on the 10 try because you lost 9 times before. Your odds on the 9th try and exactly what they are on that try, because the events are not dependent.


If you were to say "What are odds of winning at least once in 10 years" - that is a joint probability and it has an entirely different distribution than the probability on any independent role. That probability would not help you to understand the odds on any individual trial and it would be nowhere near 32%.

Your probability of winning the lottery will be exactly your odds on the day of the lottery - no better or worse.

The OP appears to be asking, given the probabilities listed (which are incorrect due to the draft rules ) what is the probability that the Leafs should have won the lottery in the last 8 years, and his math is wrong. Then he's assuming this years probability and incorrectly adding it in.

it's still not correct. see my post for the correct answer.

This is the correct way to do what the OP appears to be trying to do but he also want's to add in the 9th year.