Math Is Fun Forum

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