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

[CHRoNiCWiLL]

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%!

Click to read more...

 

[Shwaguy*]

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%

If we combine this, we have should have had a total of 44.2% chance to at least win the lottery once. Now since we didnt, we can include our 2015 odds.

Let's say we finish 5th last, with the new odds, this is 8.5%. Combine with before and we should expect to have a 52.7% chance to finally win the lottery for 2015.

That's not how odds and probability works.

Each set (Or case) has it's own individual probability.

Now, if you said the Leafs were going to finish with the 13th, 13th, 7th, 7th, 2nd, 9th, 5th, 8th, 5th, over the next 9 drafts (Assuming the probabilities for a lotto win were the same each time. You could say the Leafs would have a 52.7% chance of winning A single Lottery over the next 9 years.

 

[Duke Silver]

That's not how odds and probability works.

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

OP seems to be a believer in karmic powers.

 

[The Legend]

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%

If we combine this, we have should have had a total of 44.2% chance to at least win the lottery once. Now since we didnt, we can include our 2015 odds.

Let's say we finish 5th last, with the new odds, this is 8.5%. Combine with before and we should expect to have a 52.7% chance to finally win the lottery for 2015.

Using this theory, eventually we will be over 100%.

 

[Clip68]

Unfortunately the math doesn't work like that. If you had a 50% chance at winning something, you wouldn't be guaranteed to get it on the 2nd attempt (50%+50%=100%).

Under your scenario, it would still be an 8.5% chance to win the lottery.

 

[Pi]

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

 

[Mess]

Unfortunately you can't accumulate odds by adding years thinking it increases your odds. One year has no relevance to the next.

That is like saying if I flip a coin the odds of heads is 50% and I lose and its ends tails

Then we flip it again and I add the 50% of last flip adding it to the 50% of this pick and my odds become 100% after 2 flips and 150% after 3. When really its only ever 50% each flip (independent event) each time its tossed.

 

[Northern Dancer]

Using this theory, eventually we will be over 100%.

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

 

[waingr0]

I beleaf!!

 

[pooleboy]

using this logic flipping a coin twice should guarantee a head and a tail.

50%+50%=100%

 

[CHRoNiCWiLL]

Actually I found the correct formula to calculate this
(100*0.008)+(100-(100*0.008)*0.008)+(100-(100-(100*0.008)*0.008)*0.047)+...... and so on.
Much harder to calculate then I thought (its pretty much recursive).

Let's just pretend we have a 50% chance to expect to finally win.

 

[TheLeastOfTheBunch]

That's not how that works, but let's just say we're long due for a lucky break

C'mon hockey gods

 

[Warden of the North]

Take an average of those figures for an accurate look. Excluding the Seguin draft Id guess its about 2%

 

[WilliamNylander]

Dont you learn this is wrong in like...grade 5 math?

 

[ACC1224]

Probability works different when it comes to the Leafs.
The least desirable outcome is the likeliest.

 

[Northern Dancer]

Actually I found the correct formula to calculate this
(100*0.008)+(100-(100*0.008)*0.008)+(100-(100-(100*0.008)*0.008)*0.047)+...... and so on.
Much harder to calculate then I thought (its pretty much recursive).

Let's just pretend we have a 50% chance to expect to finally win.

I concur

 

[PuckMagi]

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%

Chances that we would have drafted #1 at least once:

1 - (.992 x .992 x .953 x .953 x .812 x .973 x .919 x .964)
= 1 - (0.625562289396830834671616)
= 0.374437710603169165328384
= ~ 37.44% chance

(it's easier to solve if you try to calculate the chances of not drafting #1, and then subtract that number from 1).

 

[666]

Wow, just wow.

 

[Ruski]

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%

Chances that we would have drafted #1 at least once:

1 - (.992 x .992 x .953 x .953 x .812 x .973 x .919 x .964)
= 1 - (0.625562289396830834671616)
= 0.374437710603169165328384
= ~ 37.44% chance

(it's easier to solve if you try to calculate the chances of not drafting #1, and then subtract that number from 1).

Except that we could have only drafted #1 in 2010 and 2012, because in the past you could only move up a max of 4 positions from your spot (after winning the lottery), so its a mess to calculate and doesn't mean much at all to us in present day

 

[PuckMagi]

Except that we could have only drafted #1 in 2010 and 2012, because in the past you could only move up a max of 4 positions from your spot (after winning the lottery), so its a mess to calculate and doesn't mean much at all to us in present day

gotcha. didn't know that. i was just doing the calculation that the OP butchered.

 

[Trapper]

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

I believe the lottery should also take into consideration your past 10 years when calculating odds. So for example, the Leafs are sitting with a 6.5% chance. However, every year missing the playoffs, every year not in the top 3 etc. should be calculated. Edmonton with 3 1sts should not have better odds because we constantly finish 8-12. Does it matter if you miss the playoffs every year in last place or every year in 7th? A team like Colorado who can draft Duchene,Landy and then MacKinnon while we draft Gauthier (no offense) needs to be addressed.

 

[member 147413]

What the hell kind of education are taxes being put towards?

 

[Havoq]

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%

If we combine this, we have should have had a total of 44.2% chance to at least win the lottery once. Now since we didnt, we can include our 2015 odds.

Let's say we finish 5th last, with the new odds, this is 8.5%. Combine with before and we should expect to have a 52.7% chance to finally win the lottery for 2015.

 

[CHRoNiCWiLL]

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

 

[Shimso]

The lottery chances are based on our finish this year - the previous years outcomes have zero impact on the future. Its like how I've had all 8 of my Tim Hortons cups (plus the 2 or 3 I've bought for others) say "PLEASE PLAY AGAIN" - even though the odds are 1:6 it doesn't mean I'm destined for a Camry with my next coffee.