sinewav wrote:[...] those numbers don't make any sense. Let me go brush up on Bayes' theorem and see if I can calculate something more meaningful.
But they do make sense for that specific and simplified situation. If you can improve the numbers or make it more flexible, that's great!
What I wanted to show was that the difference between 0 seeds and 2 seeds when it comes to getting an unlucky draw, is not big at all. The main difference is that with 0 seeds there's a small (0 - 5%) chance of a lopsided final due to randomization, and with 2 seeds the 2 previous finalists will always be in either semi final (assuming they do show up and win previous matches)
Since we mentioned
Ladle 34, which did have completely lopsided brackets: 1/20 (or 2/39) chance for that to happen according to my math. We started getting ~16 teams in
Ladle 18 (15 teams.
Ladle 17 had only 9 teams). The first seeded ladle was Ladle 38. So in ladles 18 to 37 we had
20 unseeded ladles with around 16 teams. The completely lopsided bracket happened once: 1/20 times.
Just to be super clear, and because it's fun, let's apply my math to Ladle 34 while following Team uNk.
The average team (back then) - Team uNk
The 4 pro teams (back then) - CT, ~*SP*~, Jalapeños, TX.
The 11 noob teams (back then) - uNa, Anesthetized, DS, CAT, EC, PRU, Open Team, ID, _~R~_, ~bye1~, ~bye2~
(since the premise is that noob teams never make upsets, the byes are equal to noob teams in this example. heh)
Opening Round:
1. Besides uNk there's 15 teams of which 11 are noob teams.
2. 11/15 = 0.733333333333 - this means there's a 73.3% chance Team uNk would face one of the noob teams in the Opening Round. Pretty much 3 out of 4 times.
Quarter Finals:
1. For uNk to face another noob team in the quarters, the opening match next to them must have been between 2 noob teams.
2. In addition to the 11/15 chance of uNk's first opponent being noobs, and since noob teams never beat pro teams, there's a 10/14 (14 teams left, 10 of them noobs) and 9/13 (since another noob team is gone, there's only 9 noob teams out of 13 total teams left) chance the other quarter finalist is a noob team as well.
3. (11/15)*(10/14)*(9/13) = 0.362637362637 - this means there's a 36.3% chance uNk would be better off in the Quarter Final as well. Pretty much 1 out of 3 times.
Semi Finals:
1. Same thing as the #1 above, except it covers uNk's entire half of the brackets. All 7 teams besides uNk must have been noob teams.
2. Same idea as with the #2 above, except it's longer.
3. (11/15)*(10/14)*(9/13)*(8/12)*(7/11)*(6/10)*(5/9) = 0.0512820512821 - there's a 5.12% chance uNk would be fine in the semi final and proceed to the finals.
4. 2/39 = 0.0512820512821 = 5.12% (actually 5.13%, oops!). So in 1 out of 20 ladles (since you can't rly say 19.5 ladles) there's going to be something like this if it's unseeded and there's around 16 teams. There were 20 unseeded ladles with around 16 teams, and it happened once.
Finals:
1. With all 4 of the "pro teams" on the other side of the brackets it's likely you're going to face the best of them in the finals. Good luck.
orion wrote:Cosidering all this discussion, yes, 2 seeds helps both arguments
Newbies teams get the chance to have a little better bracket than with 4 seeds but it guarantee they should face a hard enemy in semi-finals.
Orion was right on page 4. Well done.
asdfasdf wrote:The numbers pretty much make sense in the context that he puts them; there are a couple errors, though.
Any serious errors? Share it here if it's relevant to the thread or pm it if you feel like educating a math noob a little
