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Before discussing specific tiebreaker rules, it is mentioned that breaking ties in round-robin tournaments is certainly not a new problem and there are many possible approaches. (For example, the group stage is quite similar in Ultimate Frisbee.) Furthermore, any team that is left behind after a multi-team tie will be disappointed, regardless of the tiebreakers used. For this reason, the primary purpose of this webpage is not to claim that one approach to breaking multi-team ties is

- (a) Most Wins.
- (b) Most Rocks used.
- (c) Most Papers used.

Contestant | Wins | Rocks | Papers |
---|---|---|---|

Ron | 1 | 2 |
0 |

Peg | 1 | 0 | 2 |

Sam | 1 | 0 | 0 |

Ron | Peg | Sam | |||

Sam | Ron | Peg |

What are the final standings for this tournament? All three contestants won a single match, so all three are tied by rule (a). Since rule (b) is based on the number of Rocks used, then Ron finishes in first-place from using 2 Rocks (above in bold), while Peg and Sam remain tied. However, determining second-place is not as simple. Roughly speaking, we have a

- Ron.
- Peg.
- Sam.

Contestant | Wins | Rocks | Papers |
---|---|---|---|

Peg | 0 | 0 | 1 |

Sam | 1 |
0 | 0 |

Sam | |

Peg |

In this case Sam has 1 win (in bold), and since there are no other matches between these contestants, then Sam would finish ahead of Peg by rule (a). That is, the final standings would be:

- Ron.
- Sam.
- Peg.

"The ranking of each team in each group will be determined as follows:

- a) greatest number of points obtained in all group matches;
- b) goal difference in all group matches;
- c) greatest number of goals scored in all group matches.

- d) greatest number of points obtained in the group matches between the teams concerned;
- e) goal difference resulting from the group matches between the teams concerned;
- f) greater number of goals scored in all group matches between the teams concerned;
- g) drawing of lots by the FIFA Organising Committee."

Notice that the above rules are actually quite simple. The first three rules separate teams based on points, goal difference, and then goals scored. These initial three rules a)-c) are then repeated as rules d)-f) for any teams that remain tied. Finally, the last rule g) resolves ties that cannot be broken by using these three criteria. To test the rules, consider the following scenario for Group C in the 2010 World Cup:

Country | Pts | W | D | L | GF | GA | GD |
---|---|---|---|---|---|---|---|

Algeria | 6 | 2 | 0 | 1 | 7 | 4 | +3 |

USA | 6 | 2 | 0 | 1 | 7 | 4 | +3 |

England | 6 | 2 | 0 | 1 | 7 | 4 | +3 |

Slovenia | 0 |
0 | 0 | 3 | 2 | 11 | -9 |

Algeria | 2 | USA | 5 | England | 4 | Algeria | 3 | USA | 2 | England | 3 | ||||||

Slovenia | 1 | Slovenia | 1 | Slovenia | 0 | USA | 0 | England | 0 | Algeria | 2 |

(Pts = points, W = wins, D = draws, L = losses, GF = goals for, GA = goals against, GD = goal differential)

Notice that the scores of each match are all reasonable, so the above scenario could certainly occur. What are the final standings for this group? By applying rule a) it is clear that Slovenia finishes the group in fourth-place since it has 0 points (in bold above). Rules b) and c) do not separate the remaining three teams. Therefore, the remaining three-way tie must be broken starting from rule d), and the

Country | Pts | W | D | L | GF | GA | GD |
---|---|---|---|---|---|---|---|

Algeria | 3 | 1 | 0 | 1 | 5 | 3 | +2 |

USA | 3 | 1 | 0 | 1 | 2 | 3 | -1 |

England | 3 | 1 | 0 | 1 | 3 |
4 | -1 |

Algeria | 3 | USA | 2 | England | 3 | |||

USA | 0 | England | 0 | Algeria | 2 |

Each team obtained three points within these matches, so the teams remain tied after applying rule d). Since Algeria's +2 goal difference (in bold) is better than USA and England's goal difference of -1, then rule d) implies that Algeria finishes first in the group. However, determining the second-place team is more subtle due to the ambiguity of the

On one hand, the complete rankings of Algeria, USA, and England have not been fully determined, so one could argue that the teams concerned still include these three teams. In this interpretation, we continue to rank all three teams, and so the relevant matches include the three matches given above. Using this interpretation, England beats out USA by rule f) since England scored 3 goals (in bold) to USA's 2 goals. That is, if one continues to break the three-way tie then the final standings are

- Algeria.
- England.
- USA.
- Slovenia.

Country | Pts | W | D | L | GF | GA | GD |
---|---|---|---|---|---|---|---|

USA | 3 |
1 | 0 | 0 | 2 |
0 | +2 |

England | 0 | 0 | 0 | 1 | 0 | 2 | -2 |

USA | 2 | |

England | 0 |

Using this interpretation, USA would finish in second-place by rule f) since it scored 2 goals (in bold) while England scored 0. Alternatively, rule d) has higher-precedence than rule f), and since USA beat England then it finishes in second-place based on its 3 points (in bold) among the two teams concerned. That is, if one breaks the two-way tie then the final standings are

- Algeria.
- USA.
- England.
- Slovenia.

Stepping back, the real problem is that rules d)-g) appear to have been written with only two- or three- or four-way ties in mind, and without consideration for partially-unbroken three-way ties. The resulting ambiguity would allow FIFA to logically justify either of the above interpretations, and this could open the door to protests and questions of impartiality. (The analogous scenario given to FIFA and CSA differed from the above scenario only in the specific countries involved. The specific countries involved were upcated to reflect the actual teams appearing in Group C.)

With respect to the previous discussion, the NFL changes the teams concerned and restarts its tiebreaker rules from the beginning whenever a tie is partially-unbroken. (This is directly opposite to how FIFA's Media Department interpreted their own tiebreaker rules.) FIFA should learn from the NFL and add a similar clarification to their tiebreaker rules. Whenever a tie is partially-unbroken, FIFA needs to specify: i) the next tiebreaker rule to apply, and ii) the teams concerned when applying this rule.

On the topic of improving the FIFA rules, one can also observe that rules d)-f) cannot be used to break a four-way tie. In particular, given a four-way tie, rules d)-f) are simply repeats of rules a)-c). Furthermore, points, goal difference, and goals scored provide are comparisons in a two-way tie. Therefore, rules d)-f) only need to be applied to three-way ties. This simplification should be used when FIFA is rewriting its rules.

In some situations, points, goal difference, and goals scored cannot be used to break ties. (For example, every match in a group could end in a 1-1 draw.) FIFA should consider adding the

Country | Pts | W | D | L | GF | GA | GD |
---|---|---|---|---|---|---|---|

Spain | 9 |
3 | 0 | 0 | 4 | 1 | +3 |

Switzerland | 3 | 1 | 0 | 2 | 2 | 3 | -1 |

Honduras | 3 | 1 | 0 | 2 | 2 | 3 | -1 |

Chile | 3 | 1 | 0 | 2 | 2 | 3 | -1 |

Spain | 2 | Spain | 1 | Spain | 1 | Switzerland | 2 | Chile | 1 | Honduras | 1 | ||||||

Chile | 1 | Switzerland | 0 | Honduras | 0 | Honduras | 1 | Switzerland | 0 | Chile | 0 |

Spain finishes first by rule a) (in bold). Since the remaining teams have the same goal difference and the same number of goals scored, then the remaining positions are determined by the matches involving these teams:

Country | Pts | W | D | L | GF | GA | GD |
---|---|---|---|---|---|---|---|

Switzerland | 3 | 1 | 0 | 1 | 2 | 2 | 0 |

Honduras | 3 | 1 | 0 | 1 | 2 | 2 | 0 |

Chile | 3 | 1 | 0 | 1 | 1 |
1 | 0 |

Switzerland | 2 | Chile | 1 | Honduras | 1 | |||

Honduras | 1 | Switzerland | 0 | Chile | 0 |

Since the teams have the same number of points, and the same goal difference, then the teams remained tied after applying rule d) and e). Chile has a lower number of goals scored than the other two teams, so it finishes in fourth-place by rule f) (in bold). Given the FIFA Media Department's earlier response, it seems most likely that they would proceed to rule g) and draw lots. One one hand, it does not seem appropriate to draw lots between all three teams, since the Chile should finish in fourth-place by rule f). On the other hand, it does not seem appropriate to draw lots between Switzerland and Honduras due to Switzerland's victory over Honduras. That is, Switzerland would beat Honduras if the situation was treated as a two-way tie.

Country | Pts | W | D | L | GF | GA | GD |
---|---|---|---|---|---|---|---|

Switzerland | 3 | 1 | 0 | 0 | 2 | 1 | +1 |

Honduras | 3 | 1 | 0 | 0 | 1 | 2 | -1 |

Switzerland | 2 | |

Honduras | 1 |

In other words, it is unsatisfying to draw lots between three teams because the three-way tie was broken, and it is unsatisfying to draw lots between two teams because the two-way tie could also be broken. Again, this problem arises because we have a partially-unbroken three-way tie, and FIFA does not explicitly address these types of situations.

- Times-Colonist's favourite stories of the year (December 20th, 2009). (The second image in the PHOTOS tab here has the Monitor section cover shot.)
- The initial article in the Times-Colonist (July 12th, 2009).
- The article was reprinted in the Vancouver Sun, National Post, and so on.
- Interview for CFAX 1070 with accompanying article (July 13th, 2009).
- Interview for A-Channel (July 14th, 2009). Congratulations to Jordan Cunningham who won an Edward R Murrow award for this interview.
- Reaction from Levent Tuncel in the Department of C&O at the University of Waterloo in response to Sarah Petrescu at the Times Colonist.

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