Explaination of why the method on the right works.
This best explaining using a table. The table below has 4 rows (one for each player) and 4 columns (one for each player). This gives us 16 boxes in the table (4 x 4).
| |
1 Joe |
2 Bill |
3 Ken |
4 Jim |
| 1 Joe |
|
|
|
|
| 2 Bill |
|
|
|
|
| 3 Ken |
|
|
|
|
| 4 Jim |
|
|
|
|
Each box in the table above represents a possible match, but as you will soon see there are too many boxes at the moment.
As a player can't play himself we need to cross out some boxes. (see below)
| |
1 Joe |
2 Bill |
3 Ken |
4 Jim |
| 1 Joe |
X |
|
|
|
| 2 Bill |
|
X |
|
|
| 3 Ken |
|
|
X |
|
| 4 Jim |
|
|
|
X |
As you can see above 1 box has been crossed out for each player and now there are only 12 empty boxes representing 12 possible matches. So so far we have (4 x 4) - 4 = 12 boxes. The row of X ed out boxes divides the table exactly in half diagonally. There are 6 boxes above the X's and 6 boxes below the X's. We still have too many boxes in the table above though, so we need to cross out some more.
| |
1 Joe |
2 Bill |
3 Ken |
4 Jim |
| 1 Joe |
X |
|
X |
|
| 2 Bill |
|
X |
|
|
| 3 Ken |
X |
|
X |
|
| 4 Jim |
|
|
|
X |
In the table above you can see the red X is in Joe's row and Ken's column. It represents a match between Joe and Ken. If you look at the green X you will see it is in Ken's row and Joe's column. As we already have a box for the match between Ken and Joe we need to cross out the green X box. The same is true for all the boxes below the line of X's. (see below)
| |
1 Joe |
2 Bill |
3 Ken |
4 Jim |
| 1 Joe |
X |
|
|
|
| 2 Bill |
X |
X |
|
|
| 3 Ken |
X |
X |
X |
|
| 4 Jim |
X |
X |
X |
X |
The table above now correctly shows 1 empty box for each match. So what we did was, we started with 16 boxes (4 players x 4 players) then crossed out 1 box for each player. (16 - 4 = 12). And then we crossed out half the remaining boxes. (12 divided by 2 = 6) The six boxes remaining represent a match that must be played.
By looking at the table you can now make a list of games to be played. Start on the top row. You can see that Joe plays everyone after him on the list. On the second row you can see that Bill plays everyone after him on the list. On the third row you can see Ken plays every one after him on the list. The bottom row (4 Jim) only has X's in it so we can cross it out completly. (see below).
| |
1 Joe |
2 Bill |
3 Ken |
4 Jim |
| 1 Joe |
|
1 v 2 |
1 v 3 |
1 v 4 |
| 2 Bill |
|
|
2 v 3 |
2 v 4 |
| 3 Ken |
|
|
|
3 v 4 |
This now leaves one box for each of the six matches to be played.
((4x4)-4)/2 = number of matches
|
Working out a Round Robin.
A "Round Robin" is a points competition where each of the players involved play everybody else once. Players get a point for each leg they win and at the end, when everyone has played everone else, the player with the most points wins.
Print out a standard Round Robin scoresheet for ...
(4 players) (5 players) (6 players).
Round Robins are often used for regional competitions because all players have an equal chance, and generally the best player involved ends up with the most points and wins.
Many people have problems working out who plays who in a Round Robin, and working out how many matches need to be played. It is not difficult when you know how, so here's how you do it.
Start by writing down all the players in a list. I will use 4 players names as an example. For big RR's usually you assign each player a number.
- [1] = Joe.
- [2] = Bill.
- [3] = Ken.
- [4] = Jim.
Start with the first name and pair it up with the names that come after it. Thus:-
- Joe v Bill or (1 v 2)
- Joe v Ken or (1 v 3)
- Joe v Jim or (1 v 4)
Next move to the second name in the list and pair it with the names that come after it. Thus:
- Bill v Ken (2 v 3)
- Bill v Jim (2 v 4)
Next start at the third name in the list and pair it with the names that come after it. Thus:-
Keep going through the list till you get to the end. In my example list there is only 4 players. The last name in it is Jim. There is nobody after Jim to pair with so all the player combinations are already done. Thus the round robin would look As below. All you need to do next is work out the order of play depending on how many boards are available.
Thus finished round Robin play list for 4 players is:-
- Joe v Bill (1 v 2)
- Joe v Ken (1 v 3)
- Joe v Jim (1 v 4)
- Bill v Ken (2 v 3)
- Bill v Jim (2 v 4)
- Ken v Jim (3 - 4)
As you can see there will be six matches in this round robin.
It is often good to know how many matches need to be played in a round robin so you can decide if there is enough time to play one. The math is simple. As follows.
if N = number of players
N squared minus N divided by 2 = number of matches
For example with 4 players as above (N = 4) thus:-
((4 x 4) - 4 )/2 = number of matches
- 4 x 4 = 16
- minus 4 = 12
- divide by 2 = 6
thus for 4 players, 6 matches will be played
Example for 10 players (n = 10)
- 10 x 10 = 100
- minus 10 = 90
- divide by 2 = 45
45 matches need to be played for 10 players
To understand why this formula and method always works you can see the information in the left column. You don't really need to know why it works but some people might be interested.
Information about running a Darts Ladder using Round Robin format accross multiple boards can be found here.
|
