The use of head-to-head records for breaking ties in round-robin soccer contests

ABSTRACT

Head-to-head records are often used in round-robin contests for breaking ties between athletes or teams that are equal on points or wins. In this paper, I argue, on the one hand, that tie-breaking systems of round-robin soccer contests should give more importance to overall goal difference than to head-to-head records. On the other hand, I also argue that even the mere inclusion of head-to-head records in the tie-breaking criteria of a round-robin soccer contest is problematic.

KEYWORDS:

• Betterness
• ranking systems
• tie-breaking systems
• goal difference
• head-to-head records
• round-robin contests
• soccer

Acknowledgement

I would like to thank two anonymous reviewers for some very useful comments, without which this article would have been of much lower quality.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. On unique and shared rankings, see Berker (2014).

2. Despite that, to the best of my knowledge, there is no other philosophical study of the use of head-to-head records for breaking ties in round-robin contests, albeit Berker’s (2014) paper on the use of head-to-head records for breaking ties in round-robin soccer contests contains some philosophical elements. It should also be noted that Hager and Torres’s (2007) philosophical paper on how points should be awarded to teams in round-robin contests (and other non-knockout contests in which teams try to gain points or wins from matches) contains a very short discussion of the use of head-to-head records for breaking ties.

3. The tie-breaking criteria of some round-robin soccer contests also include head-to-head matches won and/or head-to-head away goals scored.

4. Berker (2014) gives a more comprehensive description of the tie-breaking criteria in the group stages of the 2012 UEFA European Championship and the 2014 FIFA World Cup. See also FIFA (2013, 2016); UEFA (2009, 2013).

5. For the sake of simplicity and clarity, I concentrate on tie-breaking only in round-robin soccer contests, but my arguments could be applied to round-robin contests in many other time-based sports in which two teams face each other in a match (i.e. sports in which a match between two teams continues for a specified time). In some of those sports (e.g. in American football and basketball), some goals are worth more points than others, which means that in those sports overall points differential (i.e. the difference between points scored and conceded in all matches) is the equivalent to overall goal difference. My arguments could even be applied to round-robin contests in many score-based sports in which two athletes or teams face each other in a match (i.e. sports in which a match between two athletes or teams continues until one of the athletes or teams has won a certain amount of sets or scored a certain amount of points), and in which goals do not exist. Tennis and volleyball are good examples of such sports. In tennis and volleyball, the overall sets differential (i.e. the difference between sets won and lost in all matches) could be considered the rough equivalent to overall goal difference. The terms ‘time-based sport’ and ‘score-based sport’ come from Dixon (2003, 93).

6. Berker (2014) and Rubinstein (1980) do not make a distinction between individual contests and meta-contests. As a result of this, their definitions of ARR are conceptually less sophisticated than my definition. The term ‘autonomous relative ranking’ comes from Berker (see Berker 2014, 207).

7. Poland’s matches against Greece and Russia ended 1–1.

8. In case of a higher-scoring draw between Poland and the Czech Republic, the rankings would naturally have been the same as in case of a 0–0 draw, because the tie-breaking system that was in use gave more importance to head-to-head goal difference than it gave to goals scored in all matches.

9. If the ranking system of a round-robin soccer contest is such that the relative ranking of Team A and Team B in the round-robin contest may depend on the official result of a match that does not have anything to do with the betterness of Team A and Team B in the round-robin contest, the probability that their official final rankings in the round-robin contest will not reflect accurately their betterness in the round-robin contest must, ceteris paribus, be higher than it would be if the ranking system of the round-robin contest was such that the relative ranking of Team A and Team B in the round-robin contest could not depend on the official result of a match that does not have anything to do with the betterness of Team A and Team B in the round-robin contest.

10. If the tie-breaking criteria of a round-robin soccer contest include these two tie-breaking criteria, that round-robin contest also non-primarily tests each team’s ability to avoid red and yellow cards and each team’s ability to promote its corner kick difference (which is a function of a team’s ability to gain and prevent corner kicks).

11. Related to these considerations and questions, see Hager and Torres (2007, 30–31).