Looking for a formula for 1st round matches (Winners & Loser) when there are byes

bye chart

http://www.playcsipool.com/uploads/7/3/5/9/7359673/bcapl_bye_placement_chart.pdf

Byes are assigned to the charts evenly from top to bottom.
For example; 16 player bracket. only 14 players, one bye gets spot 16 and the other gets 8. if someone shows up in time, they are assigned the last number, in this example it would be number 8

If the number of players is not a multiple of 2 (i.e., not 4, 8, 16, 32, 64, etc.), then go up to the next higher multiple of 2. The number of byes is that next higher multiple of 2 minus the actual number of players.

Examples:

• 9 players. Next-higher multiple of 2 is 16. Number of first-round byes is 16 - 9 = 7. So the number of first-round players is 9 - 7 = 2, and the number of first-round matches is 2 ÷ 2 = 1. The winner of that match will join the 7 byes to create a full winners'-side next round of 8 players.

• 19 players. Next-higher multiple of 2 is 32. Number of first-round byes is 32 - 19 = 13. So the number of first-round players is 19 - 13 = 6, and the number of first-round matches is 6 ÷ 2 = 3. The winners from those 3 matches will join the 13 byes to create a full winners'-side next round of 16 players.

• 87 players. Next-higher multiple of 2 is 128. Number of first-round byes is 128 - 87 = 41. So the number of first-round players is 87 - 41 = 46, and the number of first-round matches is 46 ÷ 2 = 23. The winners from those 23 matches will join the 41 byes to create a full winners'-side next round of 64 players.

calcuttaman said:

I don't need 9 person brackets. Just want the formula. Something like...

9 players - 8 = 1 (number of 1st rnd matches)

That's a very simplified version and of course doesn't work for all scenarios.

Click to expand...

Let's see if this attachment works. If it doesn't, I'll send it to you.


And if you want a formula, the first number should always be the next base-2 number above the number of players.

E.g.

For 9 players, the next base-2 number is 16 (2^4).

16 - 9 = 7 byes. There is a logical method on how to put the byes in the chart. NEVER draw in the byes.

Freddie <~~~ can beat the bye... sometimes

For a second here I was hoping this was created my my local LO!

But that would have been too forward thinking. The ol' pull names from a baseball hat and write them in on crate paper will work forever, just like Social Security.

calcuttaman said:

I'll give this a shot....

(Total players - (Next highest chart size - Total Players)) / 2

(87 - (128-87)) / 2 = 23

Click to expand...

Formulae

For 9-16 players:

P= Number of Players

[(16/2 -(16-P)] = N (Number of 1st round Matches)

Edit - I'm incorrect on losers formula
And there should always be the same amount of matches (23) in the first round of the losers side.

Apparently its pretty easy to figure out the winners side matches. But, how do you figure out the 1st side of the losers bracket?

Check this example out http://ctsondemand.com/mobilebracketviewer.aspx?BracketID=710ecc1a-53c0-4de1-8f1a-d309efd31f64

64 person bracket, 9 byes with 7 matches in the 1st round of the losers side. How do you formula that?

Click to expand...

1st round loser's side? You can only have 1st round loser-side matches if you have two adjacent filled (no byes) 1st round brackets (we can call them couplets or whatever) that the losers play each other in the 1st round of the loser side.

In the original case:

B = # of byes

(16/4 - B) = LSFR (loser round first round), Minimum=0

and in your recent example

(64/4 - B) = 16 - 9 = 7 matches in the first round of loser's side

calcuttaman said:

In the example in my post from Ctsondemand there is a 64 person bracket, 55 teams. Using yours and At Large's formula its easy to come up with 23 winners side matches.

But what I really want is how to determine those 7 matches in the first round of the losers side.

Click to expand...

Check my edit with formula

64 bracket
9 byes


Bracket size/4 - Byes

or

64/4 - 9

= 7


Once a 1/4 of the field are byes, there will be no 1st round loser's matches.

calcuttaman said:

Thank you.

Click to expand...

This assumes that the byes were distributed evenly per my or TomCincy's post (or any other post that had an even distribution of byes).


Good luck,

Freddie