Tonight I ran a simulation of the N=31 case. I ran 1,000,000 seasons. I assumed that all 31 teams are evenly matched and that every game is a 50/50 coin flip.
Here is a table showing for each possible number of team wins (0-60), how many team-seasons with that number of wins finished in the Top 16, how many total team-seasons had that number of wins, and the percentage.
Season Wins | Seasons in Top 16 | Total Seasons | Percentage |
---|
0 | 0 | 0 | NA |
1 | 0 | 0 | NA |
2 | 0 | 0 | NA |
3 | 0 | 0 | NA |
4 | 0 | 0 | NA |
5 | 0 | 0 | NA |
6 | 0 | 0 | NA |
7 | 0 | 0 | NA |
8 | 0 | 0 | NA |
9 | 0 | 0 | NA |
10 | 0 | 3 | 0.0 |
11 | 0 | 8 | 0.0 |
12 | 0 | 39 | 0.0 |
13 | 0 | 142 | 0.0 |
14 | 0 | 436 | 0.0 |
15 | 0 | 1,446 | 0.0 |
16 | 0 | 3,972 | 0.0 |
17 | 0 | 10,485 | 0.0 |
18 | 0 | 24,790 | 0.0 |
19 | 0 | 55,096 | 0.0 |
20 | 0 | 112,649 | 0.0 |
21 | 0 | 215,012 | 0.0 |
22 | 0 | 379,352 | 0.0 |
23 | 0 | 630,141 | 0.0 |
24 | 0 | 969,453 | 0.0 |
25 | 0 | 1,398,184 | 0.0 |
26 | 0 | 1,877,680 | 0.0 |
27 | 16 | 2,364,937 | 0.0 |
28 | 12,559 | 2,787,012 | 0.5 |
29 | 741,520 | 3,078,943 | 24.1 |
30 | 2,852,740 | 3,181,515 | 89.7 |
31 | 3,075,207 | 3,077,451 | 99.9 |
32 | 2,786,552 | 2,786,553 | 100.0 |
33 | 2,366,145 | 2,366,145 | 100.0 |
34 | 1,880,792 | 1,880,792 | 100.0 |
35 | 1,394,519 | 1,394,519 | 100.0 |
36 | 969,793 | 969,793 | 100.0 |
37 | 628,476 | 628,476 | 100.0 |
38 | 380,651 | 380,651 | 100.0 |
39 | 214,351 | 214,351 | 100.0 |
40 | 113,046 | 113,046 | 100.0 |
41 | 55,344 | 55,344 | 100.0 |
42 | 25,101 | 25,101 | 100.0 |
43 | 10,433 | 10,433 | 100.0 |
44 | 3,927 | 3,927 | 100.0 |
45 | 1,490 | 1,490 | 100.0 |
46 | 462 | 462 | 100.0 |
47 | 127 | 127 | 100.0 |
48 | 34 | 34 | 100.0 |
49 | 8 | 8 | 100.0 |
50 | 2 | 2 | 100.0 |
51 | 0 | 0 | NA |
52 | 0 | 0 | NA |
53 | 0 | 0 | NA |
54 | 0 | 0 | NA |
55 | 0 | 0 | NA |
56 | 0 | 0 | NA |
57 | 0 | 0 | NA |
58 | 0 | 0 | NA |
59 | 0 | 0 | NA |
60 | 0 | 0 | NA |
You will see that the Pcts are very knife-edgy. They go directly from 0% to 100% with little in between. I am not sure if that is an artifact of "only" running 1 million seasons. Since this simulation took several hours to complete, I am not keen on running significantly larger simulations.
Last edited by whosnext; 04-27-2018 at 06:43 AM.