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**Commissioner_rumY****Member**- Registered: 2013-04-19
- Posts: 5

Hello.

I have an update to a question that I've gotten an answer to here before (cannot post links, but the thread was called "Probability with draft lottery" if it helps). Our league is expanding to 12 teams now, so I need to update our odds for each pick with a new "ticket" distribution, shown below.

**I'm trying to figure out each team's odds of receiving each of the 11 lottery picks in our draft.** It's much like the NBA's lottery draft, but there are no limitations as to how much a team can move up or down and we use all 1001 tickets (the NBA drops one).

Can anyone help me figure this out, or point me to where I could learn to simulate the results myself?

Finish Tickets Odds of first Pick

12th 300 30.0%

11th 250 25.0%

10th 175 17.5%

9th 100 10.0%

8th 75 7.5%

7th 50 5.0%

6th 25 2.5%

5th 15 1.5%

4th 7 0.7%

3rd 3 0.3%

2nd 1 0.1%

1st No tickets, picks last (12th) automatically

Total Tickets 1001

To perhaps better explain, here is what the results were for the draft when it was only 10 teams (below is what I'm hoping to figure out for the new distribution of tickets).

Odds

Standings Tickets 1st Pick 2nd Pick 3rd Pick 4th Pick 5th Pick 6th Pick 7th Pick 8th Pick 9th Pick

10th 400 40.0% 30.5% 18.7% 8.0% 2.4% 0.4% <0.1% <0.1% <0.1%

9th 300 30.0% 30.3% 22.5% 12.2% 4.2% 0.9% 0.1% <0.1% <0.1%

8th 150 15.0% 18.5% 26.0% 22.7% 12.5% 4.3% 0.8% 0.1% <0.1%

7th 75 7.5% 10.2% 15.6% 25.7% 23.4% 13.0% 4.1% 0.6% <0.1%

6th 40 4.0% 5.5% 8.8% 15.9% 27.0% 23.9% 11.8% 2.8% 0.2%

5th 20 2.0% 2.8% 4.7% 8.5% 16.2% 29.2% 25.2% 10.5% 1.1%

4th 10 1.0% 1.4% 2.3% 4.4% 8.7% 17.3% 33.5% 26.5% 4.7%

3rd 5 0.5% 0.7% 1.2% 2.2% 4.5% 9.1% 20.1% 47.7% 13.9%

2nd 1 0.1% 0.1% 0.3% 0.4% 0.9% 1.8% 4.3% 11.8% 80.2%

1st 0 Champion picks last (10th) automatically

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi;

Your link is over here,

http://www.mathisfunforum.com/search.ph … 1393459055

but your chart was more readable. This one I am having problems with.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Commissioner_rumY****Member**- Registered: 2013-04-19
- Posts: 5

Yeah that didn't post as legibly as I'd hoped. Here's the new ticket distribution, laied out as it was in the old post (hoping that's more clear):

Out of 1001 tickets (all of the 4/14 possible combos):

Team 1: 300 tickets

Team 2: 250 tickets

Team 3: 175 tickets

Team 4: 100 tickets

Team 5: 75 tickets

Team 6: 50 tickets

Team 7: 25 tickets

Team 8: 15 tickets

Team 9: 7 tickets

Team 10: 3 tickets

Team 11: 1 ticket

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Are the rules the same as the other thread?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Commissioner_rumY****Member**- Registered: 2013-04-19
- Posts: 5

Correct. Nothing but the number of picks (was 9, is now 11) and ticket distribution (as above) has changed.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

One more thing, math is newfangled to me so I really only believe in one thing. Did the calculations I provided work last time?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Commissioner_rumY****Member**- Registered: 2013-04-19
- Posts: 5

Yes, the calculations from your simulation last time worked perfectly. That's why I came back here

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Okay, then I am going to do them the exact same way and hope for the best. I will post the answers here.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Commissioner_rumY****Member**- Registered: 2013-04-19
- Posts: 5

Sweet thanks so much

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

The chance that a team comes up with the first pick:

The chance that a team comes up with the second pick:

The chance that a team comes up with the third pick:

The chance that a team comes up with the fourth pick:

The chance that a team comes up with the fifth pick:

The chance that a team comes up with the sixth pick:

The chance that a team comes up with the seventh pick:

The chance that a team comes up with the eighth pick:

The chance that a team comes up with the ninth pick:

The chance that a team comes up with the tenth pick:

The chance that a team comes up with the eleventh pick:

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 303

Hi bobbym;

Did you ever come up with an exact method for this problem? Thank you for making me E!:)

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi;

Hmmm, you will not be thanking me after you have read them all...

Nope, he was happy in the past with a computer solution so I just went with that.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Is the other thread deleted? What are the rules?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi gAr;

I am looking for it. I do not see it. I can only presume that the OP has deleted it.

I can provide the rules if you need them.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Yes please, I'd like to have a look..

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Here are the exact values for the second pick, I think, if I got the rules correctly:

bobbym wrote:

I am looking for it. I do not see it. I can only presume that the OP has deleted it.

Members cannot delete threads.

*Last edited by anonimnystefy (2013-05-02 06:46:54)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

It appears to be gone. The link in post #2 is going nowhere. I did not touch it, so...

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Have you looked at the table in post #16?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Yes I have.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

It looks very nasty. I haven't tried to get it for latter draws, because it would involve too many summations.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Edward Morbius: All very interesting young man, except for one...

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

We have a simpler answer which is good enough for current intents and purposes?

*Last edited by anonimnystefy (2013-05-02 07:06:02)*

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

A question? A statement? What?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

bobbym wrote:

Edward Morbius: All very interesting young man, except for one...

I was answering that with a question.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Not exactly, you stated:

It looks very nasty. I haven't tried to get it for latter draws, because it would involve too many summations.

I have not even seen the simpler summations you have done!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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