Bowling League Schedule for 7 Teams

[filip]

We have small league with 7 teams.
I need to write schedule for this league.
There must be there rules:
7 teams play 1 game with each others, american style (one game on the pair of lanes 1-2 or 3-4 or 5-6).
Each team plays once on the one line.
Pair must be change after each game.
If team has break they must return to different pair also.

My best solution is this:
7 - 5 3 - 4 1 - 2 6
4 - 2 7 - 1 3 - 6 5
3 - 7 5 - 6 4 - 1 2
1 - 6 2 - 7 5 - 3 4
2 - 3 4 - 5 6 - 7 1
6 - 4 1 - 3 2 - 5 7
5 - 1 6 - 2 7 - 4 3

There is one mistake in last round, team 7 will return to same line.
Do you have any ideas how to solve it?
Maybe "perfect" schedule is not exists but who knows?
Is somewhere some generator for league schedule?
Thank you.

[bowl1820]

Not exactly following what your trying to do, if your wanting to run just a regular league or something different.

this shows regular league schedules:
http://usbcongress.http.internapcdn....eschedules.pdf


This lists has already made schedules for 4 up to 48 teams.

Since you have 7 teams you need to use a bye also, then Just use the 8 team schedule.

Also here's a standing sheet for 8 or less teams:
http://usbcongress.http.internapcdn....ms or Less.pdf

There must be there rules:
7 teams play 1 game with each others, american style (one game on the pair of lanes 1-2 or 3-4 or 5-6).
Each team plays once on the one line.
Pair must be change after each game.
If team has break they must return to different pair also.

By this do you mean you want them to change lanes after each game?

if so you would use the above schedule for the nights starting positions and the teams would just move one pair right after each game.

example:
Game 1- teams 1&2 would bowl on Lanes 1&2
Game 2- teams 1&2 would move right and bowl on Lanes 3&4
Game 3- teams 1&2 would move right and bowl on Lanes 5&6

(Teams on lanes 7&8 would move to lanes 1&2 for game 2 then 3&4 for game 3)

OR

By this do you mean a team bowls each of the other 6 teams the same night, plus have them switching lanes also?

Example:
Game 1-Team 1 plays team 2
Game 2-Team 1 plays team 3
Game 3-Team 1 plays team 4
Game 4-Team 1 plays team 5
Game 5-Team 1 plays team 6
Game 6-Team 1 plays team 7

If so each team will have to bowl one bye game also, for a total of 7 games for the night. You could still use the 8 team schedule, by just using the different week lineups as the game lineups for that night. (this gives you the lane switches)

example: Weeks 1-7 would become Games 1-7 (you would need 4 pairs of lanes ex: lanes 1-8)

Or

each team (the one playing the bye position that game) would have to sit out that game, so each team played 6 games for the night. using Weeks 1-6 which would become Games 1-6 (you would need 3 pairs of lanes ex: lanes 1-6)

[filip]

We play league by "American style", it means that team playing on the pair of the lanes.
It means that first round (for example) 1-2.
I want to change pair after each game because this is small advantage for team which stay on the same pair.
If you lock to schema for 8 teams - it is exactly same- team is playing once on the one lane and pair is also changed after each game.

7 teams. It means that all teams will play 6 games and one game will be break.
For these 6 games i need to use (1,2,3,4,5,6 line).
It must be like this because left team start write ordering of player first.

I just try to find "fair" league schedule for 7 teams.
For even count of teams it is possible to use from usb pages but I need 7 teams.

[bowl1820]

If I understand you.

Your limited to six lane (3 pairs of lanes)

And Not only do you want teams to move a pair of lanes and play a different team each game. You want them to change their starting lane from Left to Right each game.

If so, you have multiple mistakes in your solution not just one.
Beside team 7 staying on the right the last two rounds
Team 7 starts on the left lane rounds 3&4&5
Teams 1 & 6 don't change pairs the first two rounds
Team 5 doesn't change pairs in rounds 4 & 5
Team 4 doesn't change pairs in rounds 5 & 6
and others

Also teams 7 & 5 play each other twice

My best solution is this:
7 - 5 3 - 4 1 - 2 6
4 - 2 7 - 1 3 - 6 5
3 - 7 5 - 6 4 - 1 2
1 - 6 2 - 7 5 - 3 4
2 - 3 4 - 5 6 - 7 1
6 - 4 1 - 3 2 - 5 7
5 - 1 6 - 2 7 - 4 3

There is one mistake in last round, team 7 will return to same line.

As far as I can see You just can't do it with those restrictions. You'll always have either a team not moving a pair of lane and/or start on the same side the next game.

[Mike White]

I don't think you can achieve the results you are looking for with that set of restrictions.

If however you remove the restriction where after sitting out a game, you can come back to the same pair, then there is a solution.

The restrictions are:
1) bowl on each lane once
2) don't bowl on the same pair two games in a row
3) bowl each opponent once

1 - 2 / 3 - 4 / 5 - 6 / 7 - x
3 - 5 / 1 - 6 / 2 - 7 / 4 - x
2 - 6 / 7 - 3 / 4 - 1 / 5 - x
4 - 7 / 5 - 1 / 3 - 2 / 6 - x
6 - 3 / 4 - 2 / 7 - 5 / 1 - x
5 - 4 / 6 - 7 / 1 - 3 / 2 - x
7 - 1 / 2 - 5 / 6 - 4 / 3 - x

[bowl1820]

I don't think you can achieve the results you are looking for with that set of restrictions.

If however you remove the restriction where after sitting out a game, you can come back to the same pair, then there is a solution.

The restrictions are:
1) bowl on each lane once
2) don't bowl on the same pair two games in a row
3) bowl each opponent once

1 - 2 / 3 - 4 / 5 - 6 / 7 - x
3 - 5 / 1 - 6 / 2 - 7 / 4 - x
2 - 6 / 7 - 3 / 4 - 1 / 5 - x
4 - 7 / 5 - 1 / 3 - 2 / 6 - x
6 - 3 / 4 - 2 / 7 - 5 / 1 - x
5 - 4 / 6 - 7 / 1 - 3 / 2 - x
7 - 1 / 2 - 5 / 6 - 4 / 3 - x

Is that a example of what you purpose?

Team 7 is bowling the same pair two games in a row (The 1st & 2nd also the 3rd&4th and 5th&6th games)

Team 3 has the same problem games 3&4 6&7

Team 4 has the same problem 5&6

Like I said You'll always have either a team not moving a pair of lanes and/or starting on the same side the next game.

The best you can do is Have each team bowl 3 games on the left lane and 3 on the right lane.
and bowl 2 games on each pair of lanes.

And just not worry about if they bowled on the same pair the last or same side the last game.


A slight improvement IMO would be this:



While it still has teams bowl on the same pair two games in a row.

Each team gets to bowl on the same pair (5&6) two games in a row once (except team 2)

instead of team 7 getting to do it 3 times.

[Mike White]

Is that a example of what you purpose?

Team 7 is bowling the same pair two games in a row (The 1st & 2nd also the 3rd&4th and 5th&6th games)

Team 3 has the same problem games 3&4 6&7

Team 4 has the same problem 5&6

Like I said You'll always have either a team not moving a pair of lanes and/or starting on the same side the next game.

The best you can do is Have each team bowl 3 games on the left lane and 3 on the right lane.
and bowl 2 games on each pair of lanes.

And just not worry about if they bowled on the same pair the last or same side the last game.


A slight improvement IMO would be this:



While it still has teams bowl on the same pair two games in a row.

Each team gets to bowl on the same pair (5&6) two games in a row once (except team 2)

instead of team 7 getting to do it 3 times.

Yes, there is something wrong, but you assume it's what I wrote, rather than how you read it.

1 - 2 / 3 - 4 / 5 - 6 / 7 - x
3 - 5 / 1 - 6 / 2 - 7 / 4 - x
2 - 6 / 7 - 3 / 4 - 1 / 5 - x
4 - 7 / 5 - 1 / 3 - 2 / 6 - x
6 - 3 / 4 - 2 / 7 - 5 / 1 - x
5 - 4 / 6 - 7 / 1 - 3 / 2 - x
7 - 1 / 2 - 5 / 6 - 4 / 3 - x

The first line is team 1 vs team 2, team 3 vs team 4, team 5 vs team 6, and team 7 vs nobody.

[bowl1820]

Yes, there is something wrong, but you assume it's what I wrote, rather than how you read it.

1 - 2 / 3 - 4 / 5 - 6 / 7 - x
3 - 5 / 1 - 6 / 2 - 7 / 4 - x
2 - 6 / 7 - 3 / 4 - 1 / 5 - x
4 - 7 / 5 - 1 / 3 - 2 / 6 - x
6 - 3 / 4 - 2 / 7 - 5 / 1 - x
5 - 4 / 6 - 7 / 1 - 3 / 2 - x
7 - 1 / 2 - 5 / 6 - 4 / 3 - x

The first line is team 1 vs team 2, team 3 vs team 4, team 5 vs team 6, and team 7 vs nobody.

Okay yes the formatting of your schedule did cause me to look at the wrong way.

But it does bear out what I said in a earlier post to the O.P. (and you restated in yours)

That you can't do it with his (the O.P.) restrictions. Because you'll always have either a team not moving a pair of lanes and/or starting on the same side the next game.

In your case while you don't have any teams bowling the same pair two games in a row.

You have teams starting on the same side two games in a row.

So if the O.P. just removes the restriction on starting lane, it would solve it.


(Note for those that wonder why it matters whether or not your starting on the left or right lane . I know you already know MW

It's because on some match point leagues, The team scheduled on the odd lane gets enter its lineup first. Then the team on the even lane gets to enter their lineup. This is so the team on the even lane can pick who they want to go against in that position on the other team. You can find it under 100k. Match Point in the USBC rule book)

[filip]

Thank you guys, but the schedule:
1 - 2 / 3 - 4 / 5 - 6 / 7 - x
3 - 5 / 1 - 6 / 2 - 7 / 4 - x
2 - 6 / 7 - 3 / 4 - 1 / 5 - x
4 - 7 / 5 - 1 / 3 - 2 / 6 - x
6 - 3 / 4 - 2 / 7 - 5 / 1 - x
5 - 4 / 6 - 7 / 1 - 3 / 2 - x
7 - 1 / 2 - 5 / 6 - 4 / 3 - x
There is same mistake like in my solution.
Team 2, round 5 pair 3-4
Team 2, round 6, free
Team 2, round 7, pair 3-4
I will continue try to find better solution (maybe it is not possible... I'm not sure).

And also team 6, rounds 3,4,5

Regards
Filip

[bowl1820]

I will continue try to find better solution (maybe it is not possible... I'm not sure).

As Mike and I both have said it's "not" possible with the restrictions you want to use.

You either have to drop the starting lane requirement or add a another pair of lanes and use a bye.

Well good luck.