This one is lengthy, but full of examples and related to the previous blog...
So, with all that said, here is a very simple 16 person tournament, so you can see how it all works out. To make it much easier on you, I'm going to use numbers instead of names, and the winner of the match will be determined by whichever number is lower (one beats two, two beats three, so on). Of course, to be fair, every number (or in the real situation, every girl) will start off at the same rank, meaning no one is better or worse than the other. All numbers are tied for 1st place. You can already assume that 1 will be 1st place, 2 will be 2nd, 3 will be 3rd, all the way to 16 will be 16th. But that isn't always the case, due to randomization. Once I randomize the 16 numbers, you could get possible pairings like this for Round 1:
15 vs 10
2 vs 12
11 vs 7
16 vs 13
8 vs 3
9 vs 14
5 vs 4
6 vs 1
The winners and losers are obvious in this pairing, but notice this: 5 vs 4 are both low numbers, but 5 will lose here, even though it can win the majority of matches. At the same time, 13 vs 16 is odd because 13, a high number, will win when it would lose to almost any other match up. This is just evidence that bad teams can still win, and good teams can still lose, which applies to several things. Either way, this is what Round 2 looks like:
10 vs 2
7 vs 13
3 vs 9
4 vs 1
14 vs 8
6 vs 5
12 vs 15
16 vs 11
The top half are winners, while the bottom half are losers. This is before round two is done, of course. Now notice this: 6 vs 5, the 6 will lose for the second time, and be eliminated from the tournament. At the same time, 7 vs 13, the 7 will win for the second time in a row. Does this mean 7 would beat a 6? Of course not, but that is what could happen with unlucky pairings, which is why I run this twice. Here is what round 3 looks like:
2 vs 7
3 vs 1
10 vs 8
13 vs 5
9 vs 12
4 vs 11
Eliminated:
15, 16, 6, 14 (tied for 13th place)
Before the winners face off, you would do the losers first. That is just the nature of the tournament. Here is the next round:
2 vs 7
3 vs 1
8 vs 5
9 vs 4
Eliminated:
15, 16, 6, 14 (tied for 13th place)
11, 12, 13, 10 (tied for 9th place)
According to this, 10, 13, 12, and 11 are all "better" than 6. Here's the next full round:
2 vs 1
3 vs 5
7 vs 4
Eliminated:
8, 9 (tied for 7th place)
And the next round, doing the losers first:
2 vs 1
3 vs 4
Eliminated:
5, 7 (tied for 5th place)
Keep in mind that the 2 and the 1 have never lost a single match yet. Here's the next full round:
1 vs ?
2 vs 3
Eliminated:
4 (4th place)
The ? will be the winner between 2 and 3. Here's the next round:
1 vs 2
Eliminated:
3 (3rd place)
And finally, the last round, which completes this double elimination tournament. I'll list them by ranking order:
Winner:
1 (1st place)
2 (2nd place)
3 (3rd place)
4 (4th place)
5, 7 (tied for 5th place)
8, 9 (tied for 7th place)
11, 12, 13, 10 (tied for 9th place)
15, 16, 6, 14 (tied for 13th place)
If the top eight were to move onto the next round, the 6 would get left behind due to being very unlucky. This is why I run it twice. Now that we have rankings assigned to each number, we can put them to use in the next double elimination tournament they will go through (just like how I explained in the previous blog in 4f). Same exact system, just more fair match-ups, and you'll find out why.
Here is round 1 of the second double elimination:
1 vs 14
9 vs 11
4 vs 15
5 vs 10
2 vs 6
8 vs 12
3 vs 16
7 vs 13
Here is round two:
1 vs 9
4 vs 5
2 vs 8
3 vs 7
12 vs 6
13 vs 16
11 vs 14
10 vs 15
Poor 6, already in the loser's bracket. Unlucky again? Technically not, considering it was doomed to get a tough opponent due to back luck from the previous tournament. So getting an unfavorable match up here was back luck carried over from earlier. But the luck will change. Round 3:
1 vs 4
2 vs 3
9 vs 6
5 vs 13
8 vs 11
7 vs 10
Eliminated:
15, 14, 16, 12 (tied for 13th)
Next round, losers only:
1 vs 4
2 vs 3
6 vs 5
8 vs 7
Eliminated:
10, 11, 13, 9 (tied for 9th)
Right here, at this point, you can see why this method works the majority of the time. The numbers that are still in the tournament are all numbers 1 through 8 (including 6, finally). All numbers eliminated are 9 through 16, where they technically belong. I'll fast forward to the end of this tournament and show you the new rankings.
1 (1st place)
2 (2nd place)
3 (3rd place)
4 (4th place)
5, 7 (tied for 5th place)
8, 6 (tied for 7th place)
9, 11, 13, 10 (tied for 9th place)
12, 15, 16, 14 (tied for 13th place)
This is much more accurate than before. The only thing that could be considered wrong is that 6 should be swapped with 7, and that 12 and 13 should also swap places. But considering that those numbers are only one digit apart, something like that is understandable and usually acceptable.
So, with all that said, here is a very simple 16 person tournament, so you can see how it all works out. To make it much easier on you, I'm going to use numbers instead of names, and the winner of the match will be determined by whichever number is lower (one beats two, two beats three, so on). Of course, to be fair, every number (or in the real situation, every girl) will start off at the same rank, meaning no one is better or worse than the other. All numbers are tied for 1st place. You can already assume that 1 will be 1st place, 2 will be 2nd, 3 will be 3rd, all the way to 16 will be 16th. But that isn't always the case, due to randomization. Once I randomize the 16 numbers, you could get possible pairings like this for Round 1:
15 vs 10
2 vs 12
11 vs 7
16 vs 13
8 vs 3
9 vs 14
5 vs 4
6 vs 1
The winners and losers are obvious in this pairing, but notice this: 5 vs 4 are both low numbers, but 5 will lose here, even though it can win the majority of matches. At the same time, 13 vs 16 is odd because 13, a high number, will win when it would lose to almost any other match up. This is just evidence that bad teams can still win, and good teams can still lose, which applies to several things. Either way, this is what Round 2 looks like:
10 vs 2
7 vs 13
3 vs 9
4 vs 1
14 vs 8
6 vs 5
12 vs 15
16 vs 11
The top half are winners, while the bottom half are losers. This is before round two is done, of course. Now notice this: 6 vs 5, the 6 will lose for the second time, and be eliminated from the tournament. At the same time, 7 vs 13, the 7 will win for the second time in a row. Does this mean 7 would beat a 6? Of course not, but that is what could happen with unlucky pairings, which is why I run this twice. Here is what round 3 looks like:
2 vs 7
3 vs 1
10 vs 8
13 vs 5
9 vs 12
4 vs 11
Eliminated:
15, 16, 6, 14 (tied for 13th place)
Before the winners face off, you would do the losers first. That is just the nature of the tournament. Here is the next round:
2 vs 7
3 vs 1
8 vs 5
9 vs 4
Eliminated:
15, 16, 6, 14 (tied for 13th place)
11, 12, 13, 10 (tied for 9th place)
According to this, 10, 13, 12, and 11 are all "better" than 6. Here's the next full round:
2 vs 1
3 vs 5
7 vs 4
Eliminated:
8, 9 (tied for 7th place)
And the next round, doing the losers first:
2 vs 1
3 vs 4
Eliminated:
5, 7 (tied for 5th place)
Keep in mind that the 2 and the 1 have never lost a single match yet. Here's the next full round:
1 vs ?
2 vs 3
Eliminated:
4 (4th place)
The ? will be the winner between 2 and 3. Here's the next round:
1 vs 2
Eliminated:
3 (3rd place)
And finally, the last round, which completes this double elimination tournament. I'll list them by ranking order:
Winner:
1 (1st place)
2 (2nd place)
3 (3rd place)
4 (4th place)
5, 7 (tied for 5th place)
8, 9 (tied for 7th place)
11, 12, 13, 10 (tied for 9th place)
15, 16, 6, 14 (tied for 13th place)
If the top eight were to move onto the next round, the 6 would get left behind due to being very unlucky. This is why I run it twice. Now that we have rankings assigned to each number, we can put them to use in the next double elimination tournament they will go through (just like how I explained in the previous blog in 4f). Same exact system, just more fair match-ups, and you'll find out why.
Here is round 1 of the second double elimination:
1 vs 14
9 vs 11
4 vs 15
5 vs 10
2 vs 6
8 vs 12
3 vs 16
7 vs 13
Here is round two:
1 vs 9
4 vs 5
2 vs 8
3 vs 7
12 vs 6
13 vs 16
11 vs 14
10 vs 15
Poor 6, already in the loser's bracket. Unlucky again? Technically not, considering it was doomed to get a tough opponent due to back luck from the previous tournament. So getting an unfavorable match up here was back luck carried over from earlier. But the luck will change. Round 3:
1 vs 4
2 vs 3
9 vs 6
5 vs 13
8 vs 11
7 vs 10
Eliminated:
15, 14, 16, 12 (tied for 13th)
Next round, losers only:
1 vs 4
2 vs 3
6 vs 5
8 vs 7
Eliminated:
10, 11, 13, 9 (tied for 9th)
Right here, at this point, you can see why this method works the majority of the time. The numbers that are still in the tournament are all numbers 1 through 8 (including 6, finally). All numbers eliminated are 9 through 16, where they technically belong. I'll fast forward to the end of this tournament and show you the new rankings.
1 (1st place)
2 (2nd place)
3 (3rd place)
4 (4th place)
5, 7 (tied for 5th place)
8, 6 (tied for 7th place)
9, 11, 13, 10 (tied for 9th place)
12, 15, 16, 14 (tied for 13th place)
This is much more accurate than before. The only thing that could be considered wrong is that 6 should be swapped with 7, and that 12 and 13 should also swap places. But considering that those numbers are only one digit apart, something like that is understandable and usually acceptable.