Fantasy League Draft Lottery Question

Commissioner_rumY · 2013-04-19 08:52:48

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

bobbym · 2013-04-19 09:01:26

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.

Commissioner_rumY · 2013-04-19 09:07:24

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

bobbym · 2013-04-19 09:14:52

Are the rules the same as the other thread?

Commissioner_rumY · 2013-04-19 09:19:36

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

bobbym · 2013-04-19 09:24:17

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

Commissioner_rumY · 2013-04-19 09:36:48

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

bobbym · 2013-04-19 09:51:09

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

Commissioner_rumY · 2013-04-19 10:00:46

Sweet thanks so much

bobbym · 2013-04-19 10:12:26

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:

ElainaVW · 2013-04-30 23:29:56

Hi bobbym;

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

bobbym · 2013-04-30 23:36:59

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.

gAr · 2013-05-01 16:11:10

Hi bobbym,

Is the other thread deleted? What are the rules?

bobbym · 2013-05-01 21:51:42

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.

gAr · 2013-05-02 00:56:09

Hi bobbym,

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

anonimnystefy · 2013-05-02 02:04:19

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)

bobbym · 2013-05-02 05:57:19

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

anonimnystefy · 2013-05-02 06:47:12

Have you looked at the table in post #16?

bobbym · 2013-05-02 06:49:30

Yes I have.

anonimnystefy · 2013-05-02 06:57:14

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

bobbym · 2013-05-02 07:04:49

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

anonimnystefy · 2013-05-02 07:05:31

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

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

bobbym · 2013-05-02 07:08:04

A question? A statement? What?

anonimnystefy · 2013-05-02 07:08:52

bobbym wrote:

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

I was answering that with a question.

bobbym · 2013-05-02 07:10:30

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!

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Fantasy League Draft Lottery Question

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