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#1 2013-04-19 08:52:48

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

Fantasy League Draft Lottery Question

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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#2 2013-04-19 09:01:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-04-19 09:07:24

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

Re: Fantasy League Draft Lottery Question

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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#4 2013-04-19 09:14:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

Are the rules the same as the other thread?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2013-04-19 09:19:36

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

Re: Fantasy League Draft Lottery Question

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

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#6 2013-04-19 09:24:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#7 2013-04-19 09:36:48

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

Re: Fantasy League Draft Lottery Question

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

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#8 2013-04-19 09:51:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

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


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9 2013-04-19 10:00:46

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

Re: Fantasy League Draft Lottery Question

Sweet thanks so much

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#10 2013-04-19 10:12:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

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:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11 2013-04-30 23:29:56

ElainaVW
Member
Registered: 2013-04-29
Posts: 279

Re: Fantasy League Draft Lottery Question

Hi bobbym;

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

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#12 2013-04-30 23:36:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

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.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#13 2013-05-01 16:11:10

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Fantasy League Draft Lottery Question

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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#14 2013-05-01 21:51:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

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.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#15 2013-05-02 00:56:09

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Fantasy League Draft Lottery Question

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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#16 2013-05-02 02:04:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,859

Re: Fantasy League Draft Lottery Question

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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#17 2013-05-02 05:57:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

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


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#18 2013-05-02 06:47:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,859

Re: Fantasy League Draft Lottery Question

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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#19 2013-05-02 06:49:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

Yes I have.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#20 2013-05-02 06:57:14

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,859

Re: Fantasy League Draft Lottery Question

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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#21 2013-05-02 07:04:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

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


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#22 2013-05-02 07:05:31

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,859

Re: Fantasy League Draft Lottery Question

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.

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

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#23 2013-05-02 07:08:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

A question? A statement? What?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#24 2013-05-02 07:08:52

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,859

Re: Fantasy League Draft Lottery Question

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.

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

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#25 2013-05-02 07:10:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Fantasy League Draft Lottery Question

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!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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