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How do you calculate the group positions in a round-robin competition?

It's not as complicated as you might think, so let's take a closer look...

By
Martin Hughes

Owner and Editor

There are two basic competition and tournament systems of play for individual events - the **simple knock-out** system and the **group/round-robin** system.

In the simple knock-out system, players are drawn in pairs to compete against each other.

The loser of each pair is knocked-out whilst the winner continues to play in successive rounds until only one player is left as the overall winner.

In the group/round-robin system, players are allocated to groups and each member plays every other member of their group.

The results of these matches are then used to calculate a final ranking order for each group.

A pre-determined number of players may progress from each group into a knock-out competition, whilst the others are eliminated.

However, the calculation of group rankings are often misunderstood, so let's take a closer look at how to calculate the positions correctly.

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Let's start with the...

The basic principles are simple.

Results are always determined at the highest possible level - for example, by matches rather than by games - and that where, at any stage of the calculation, group members are equal, their relative positions are decided only by the matches played between them.

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So let's take a look at the process to be followed...

The first criteria used to calculate group rankings is - ** the overall result of each match**.

"Match Points" are awarded for every match.

The winner of each match earns 2 match points whether it is played or is a walkover/not played.

The loser receives 1 match point in a played match, but none for a match which is not played or is not completed.

Matches which are started but not finished are treated the same as those which are not played at all.

So let's use an example with 4 players (A,B,C,D) in a group where each match was the best of 5 games and the overall results were as follows...

A | B | C | D | Win/Loss | Match Points | Ranking | |
---|---|---|---|---|---|---|---|

A | 3-2 | 3-0 | 3-1 | 3/0 | 6 | 1 | |

B | 2-3 | 3-0 | 2-3 | 1/2 | 4 | 3 | |

C | 0-3 | 0-3 | 1-3 | 0/3 | 3 | 4 | |

D | 1-3 | 3-2 | 3-1 | 2/1 | 5 | 2 |

In this example, A has 6 match points, B has 4 match points, C has 3 match points and D has 5 match points, so it's easy to see that the final ranking order is A, D, B, C.

However, groups are seldom this clear-cut, so let's take a look at some different scenarios.

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First, let's see...

The final ranking of a group is seldom as clear-cut as shown in the previous example, and a more typical outcome is that two players have the same number of match points.

In the following example, B and D each have 5 match points and A and C each have 4 match points.

A | B | C | D | Win/Loss | Match Points | Ranking | |
---|---|---|---|---|---|---|---|

A | 1-3 | 3-0 | 1-3 | 1/2 | 4 | 3= | |

B | 3-1 | 3-2 | 0-3 | 2/1 | 5 | 1= | |

C | 0-3 | 2-3 | 3-1 | 1/2 | 4 | 3= | |

D | 3-1 | 3-0 | 1-3 | 2/1 | 5 | 1= |

So how do we determine the group rankings when faced with this scenario?

A common mistake made at this stage is to think that because all the positions have not been decided by match points alone, that we should calculate the ratio of games won to games lost, and/or points won to points lost, for all four players.

The correct procedure to be used is as follows...

It has already been established that, on the basis of match points, B and D are contenders for 1st place, whilst A and C are contenders for 3rd place.

So it is only necessary to distinguish between the two players who are tying for 1st and 2nd place (B and D), and between the two players who are tying for 3rd and 4th place (A and C).

So how do we do that?

Well, the relative positions of players who are equal at any stage will always depend ** only on the matches played between them** so as D beat B and A beat C the final order will be D, B, A, C, as shown here...

A | B | C | D | Win/Loss | Match Points | Ranking | |
---|---|---|---|---|---|---|---|

A | 1-3 | 3-0 | 1-3 | 1/2 | 4 | 3 | |

B | 3-1 | 3-2 | 0-3 | 2/1 | 5 | 2 | |

C | 0-3 | 2-3 | 3-1 | 1/2 | 4 | 4 | |

D | 3-1 | 3-0 | 1-3 | 2/1 | 5 | 1 |

However, even this scenario is rare, so let's take a look at another common scenario.

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Let's now look at...

Let's take a look at a scenario where C, with 3 match points, is clearly in 4th place but A, B and D are equal 1st with 5 match points each.

A | B | C | D | Win/Loss | Match Points | Ranking | |
---|---|---|---|---|---|---|---|

A | 3-2 | 3-0 | 1-3 | 2/1 | 5 | 1= | |

B | 2-3 | 3-2 | 3-0 | 2/1 | 5 | 1= | |

C | 0-3 | 2-3 | 1-3 | 0/3 | 3 | 4 | |

D | 3-1 | 0-3 | 3-1 | 2/1 | 5 | 1= |

As we saw earlier, the relative positions of players who are equal at any stage will always depend ** only on the matches played between them** so the next step is to eliminate the results of matches in which C took part (because C is already ranked solely in 4th place) and then recalculate the match points from the remaining matches.

Now, each of the players has 3 match points, so in order to resolve their group ranking positions it is necessary to consider next the ratios of games won to games lost.

A has a win/loss ratio in games of 4/5, B's is 5/3 and D's is 3/4, which means that the final group ranking order will be B, A, D, C as shown below...

A | B | C | D | Win/Loss | Match Points | Games | Ranking | |
---|---|---|---|---|---|---|---|---|

A | 3-2 | 1-3 | 1/1 | 3 | 4/5 | 2 | ||

B | 2-3 | 3-0 | 1/1 | 3 | 5/3 | 1 | ||

C | 4 | |||||||

D | 3-1 | 0-3 | 1/1 | 3 | 3/4 | 3 |

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However, if the results had been slightly different (as in the example below) A, B and D would each have had 3 match points AND a games won/lost ratio of 5/5 ... so this would not have been decisive.

A | B | C | D | Win/Loss | Match Points | Games | Ranking | |
---|---|---|---|---|---|---|---|---|

A | 3-2 | 2-3 | 1/1 | 3 | 5/5 | 1= | ||

B | 2-3 | 3-2 | 1/1 | 3 | 5/5 | 1= | ||

C | 4 | |||||||

D | 3-2 | 2-3 | 1/1 | 3 | 5/5 | 1= |

In these circumstances, the next step is to consider the ratios of points won to points lost.

Eliminating C's results as before, and substituting points scores for games scores, the table will now be as follows...

A | B | C | D | Games | Points | Ranking | |
---|---|---|---|---|---|---|---|

A | 9, -7, 8, -7, 6 | 9, -4, -6, 7, -10 | 5/5 | 89/95 | 3 | ||

B | -9, 7, -8, 7, -6 | 12, -9, 6,-8, 11 | 5/5 | 100/98 | 2 | ||

C | 4 | ||||||

D | -9, 4, 6, -7, 10 | -12, 9, -6, 8, -11 | 5/5 | 101/97 | 1 |

The points won/lost ratios for A, B and D are 89/95, 100/98 and 101/97 respectively, so the final group ranking order is D, B, A, C.

If it is not possible to resolve the final group rankings by the above procedure (for example, the points ratio is also equal), the relative group positions are decided by lot (for example, tossing a coin).

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Finally, let's take a look at some...

Let's use the same results table that we used previously where two players (B and D) each had 5 match points and two players (A and C) each had 4 match points, but let's suppose that D had been injured during play and had conceded the match to C, 1-3*.

*Remember we discovered earlier that - Matches which are started but not finished are treated the same as those which are not played at all. And that the loser receives 1 match point in a played match, but none for a match which is not played or is not completed.*

This means that there is no change (from the previous example) in the numbers of match points won by A, B and C - but now, D will no longer receive any match points from the match with C, which means that D now only has a total of 4 match points and will be in equal 2nd place as shown below...

A | B | C | D | Win/Loss | Match Points | Ranking | |
---|---|---|---|---|---|---|---|

A | 1-3 | 3-0 | 1-3 | 1/2 | 4 | 2= | |

B | 3-1 | 3-2 | 0-3 | 2/1 | 5 | 1 | |

C | 0-3 | 2-3 | 3-1* | 1/2 | 4 | 2= | |

D | 3-1 | 3-0 | 1-3* | 2/1 | 4 | 2= |

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We saw earlier that when three players are equal on match points, we must eliminate the results involving the 4th player (B).

So, when we eliminate the results of B's matches and recalculate the results for A, C and D ...

A and C now have three match points, whilst D now has 2 match points (as shown below).

And as A beat C, this gives the final ranking order of B, A, C, D.

A | B | C | D | Win/Loss | Match Points | Ranking | |
---|---|---|---|---|---|---|---|

A | 3-0 | 1-3 | 1/1 | 3 | 2 | ||

B | 1 | ||||||

C | 0-3 | 3-1* | 1/1 | 3 | 3 | ||

D | 3-1 | 1-3* | 1/1 | 2 | 4 |

So that the effect of the unfinished match was to drop D from 1st to 4th (compared to the previous example).

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If a match is unplayed or unfinished, the player who is declared the winner is awarded enough game points to decide the match.

So the winner of an unplayed match is regarded as having won by 3-0 (or 4-0 in best-of-7) in games and 11-0 in each game.

However, if a match has been partly played when it is abandoned in favour of one player, all points already scored are counted. For example, if a player is injured and has to retire when leading 5-3 in the final game of a best-of-5, the winner's score will be recorded as 11-5 in the final game, and the actual scores in the first 4 games will remain unaltered.

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*Source: ITTF Handbook for Tournament Referees*

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