The Rugby World Cup, which is due to start on September 20 in Japan is the showpiece event for rugby union and the third-largest sporting event in the world. Such an event is a fantastic opportunity to enhance the reputation of the sport globally.

But incidents such as The disgrace of Gijon in the 1982 FIFA World Cup, in which West Germany and Austria appeared to play out a 1-0 scoreline to allow both sides to progress at the expense of a popular Algeria team, can cause great damage to the reputation of a sport.

Similarly eight badminton players were disqualified at the 2012 Olympics after two women's doubles matches were spoiled when both sets of players deliberately tried to lose and come second in their group, believing this to provide a more favourable draw in the knockout stages. The matches were played out to a chorus of boos from the crowd. The Badminton World Federation accused the players of "conducting oneself in a manner that is clearly abusive or detrimental to the sport".

In both of these cases, athletes were accused of a lack of sporting integrity, since while settling on a result or deliberately losing could have been advantageous, they would have all still progressed in their tournaments had they simply tried their best to win.

Rugby fans could see an even more farcical scenario in the 2019 World Cup, in which deliberately conceding a try would not merely gain a potentially easier draw for a team, but may even be necessary in order for a team to progress out of the pool stage.

The rules

Before outlining a potential scenario, let us first look at the tournament rules, as taken from the RWC website. In the pool stage, all teams play each other once, with the following system used to award match points at the end of pool phase matches:

Our scenario is based on a situation in which either two or three teams are tied on match points at the end of the pool phase. Ranking is then decided by the following criteria, again as taken from the RWC website.

The winner of the match in which the two tied teams have played each other shall be the higher ranked.

The team which has the best difference between points scored for and points scored against in all its pool matches shall be the higher ranked.

The top two ranked teams in a pool progress to the quarter finals. The problem

We will look at Pool A, containing Ireland, Scotland, Japan, Samoa and Russia. The final game in this pool will be Japan vs Scotland on Sunday October 13. To keep things simple we will say that Ireland win every match by 20 points (note these points refer to the score within a game itself rather than the match points awarded afterwards) and Russia lose every game by 20 points, with no bonus points awarded for scoring four tries in any of these matches.

In the other games, suppose we have historical repeats of Scotland 17-16 Samoa and Japan 10-13 Samoa. In the final game, with five minutes to go, suppose Japan repeat their heroics of RWC 2015 against South Africa and find themselves 24-10 up against Scotland. As it stands, the pool looks as follows:

Japan are set to fail to qualify since they are tied with Samoa on match points but finish below them due to their loss to Samoa, as per the first criterion (above). Now suppose Japan decide to deliberately concede a converted try in the last five minutes to take the score to Japan 24-17 Scotland. Importantly, Scotland are now looking at a loss by 7 points or less. The table now looks as follows:

Scotland now join Japan and Samoa on 13 match points. Since each of the three has one win and one loss against each other, the first criterion (above) cannot be used to separate the teams. We move onto the second criterion, which allows Japan to overtake Samoa due to their superior points difference of +4 over +2.

The solution

The scenario outlined above is unlikely but historical results do show it to be a possibility, however remote, that could seriously damage the reputation of the Rugby World Cup. All of the following minor rule changes would prevent the above scenario from being a possibility:

Scrapping the bonus match point for a loss of 7 points or less.

Keeping the losing bonus point but taking it away from the winning team, so that a win of 7 points or less would only gain 3 match points. Using points difference as the main tie-breaking criterion.

All three propositions have their drawbacks. Scrapping the losing bonus point would lead to more games in which the losing side has nothing to play for at the end of the game. Having some wins seen as better than others potentially goes against sporting ideals and reverting to points difference could mean that pools are decided by whichever team is able to humiliate the weakest team in the pool the most.

But all three must be considered better than the possibility of a team having to deliberately allow their opponents to score.

Author: Laurence Shaw - Lecturer in Mathematics, Nottingham Trent University