Introduction
I’ve always been a big sports fan. One of the things that always interested me, and many similar to me are the various rivalries that exist between sports teams. These competitions between teams create excitement, suspense, and really gets the fans involved with the players on the team. For example, I personally used to be a huge FC Barcelona fan and one of my favourite past times back in the day used to be watching their El Clasico games against Real Madrid (their biggest rivals!)
Although we can all agree rivalries have done a lot to promote the attraction of sports, have you ever wondered how these teams that have rivalries become like that? Sometimes it makes no sense, one team can be far superior in terms of performance to another yet they are still seen as rivals. The reason for these rivalries can be answered by analyzed further using our knowledge of graph theory
The Problem and Motivation
One problem that this information tackles is the lack of understanding of what determines teams to be rivals. As we mentioned in the previous paragraph, it definitely isn’t based on a level of skillset as there are a ton of counter examples to that! Where extremely strong teams are rivals against much weaker ones. So what really determines what teams have a rivalry? Another major issue this one tackles, is as you’ll see later in this article, this fails the theory of structural balance. So how exactly does it break this and how can this be explained?
The main reason we are interested in it is because it helps us realize why we support the teams we do and how their competitors were decided. After all, according to an online study found that 83% of people believe rivalries make sports more exciting while 59% believe it lets them release their frustrations. Given it’s such a huge and integral part of each and every sports fans journey, learning how rivalries are decided sounds like it’s something we should research as well! It’s failure to upkeep the theory of structural balance is also very interesting as you would expect the graph to resolve back to a balanced state however this is not the case.
Analysis
Let’s begin by analyzing how rival teams are decided. While there are some exceptions, majority rivalries exist based on geographical proximity to each other. This shouldn’t be hard to understand why, and a perfect example would be to examine the English Premier League. Manchester United and Manchester City are perfect examples of this, as they both located in the same city have been rivals since 1881. Fans in the same geographical proximity are more likely to form rivalries amongst each other as the amount of interaction between the two places is also higher. Let’s consider a game happening between Man City and Man United, both fanbases would be entitled to watch this (skyrocketing ticket sales) and while it being the hot commodity of conversation it pretty much boils down to people becoming fans so they don’t become a social outcast.
Now we also mentioned earlier how this fails against the Structural Balance Property. This property if you recall,
basically states that for every triangle formed in a graph, it is only balanced if all 3 nodes have a positive edge amongst each other, or if theres 2 negative and 1 positive edge. It might be surprising why the graph of rivalries wouldn’t be satisfied here, but let’s look into one possible counter example. It’s safe to assume that if two teams are rivals, they have a negative relationship amongst them when graphing out all the teams in the league. Let’s consider the huge rivalry that exists between Arsenal and Spurs (North London Derby). These two teams have a huge rivalry so we would denote a huge negative value in between these.
Now, let’s add in a third team. Another team that’s a rival to both of these ones, is Chelsea! Their rivalry has never reached that of Spurs and Arsenal but they are one of the commonly known competitors to both of these teams. So let’s make a graph representing this as well (this one given from the article cited below):
As you can see here, this clearly fails the structural balance theorem. We have 3 edges, all with a negative edge. From what we learned in lecture, we should have a situation of
The enemy of my enemy is my friend
However that is not the case. The main reason this never reverts back to a balanced state, is as we mentioned before rivalries are always good for everyone. It makes the fans more invested, engaged and triggers their inner competitive nature. It also results in much more popularity towards sports and thus more sales so it’s a win win for everybody. For this reason, it’s better to keep as many rivalries as possible and since fans are often associated with a singular team, they won’t support another even if it means their teams competition going down.
Sports is a very unique case, because fans would rather see their own team succeed than their opposition fall. Because of this nature, the “enemy of my enemy is my friend” as we discussed in lecture doesn’t apply here, and thus the graph remains in an unbalanced state. This is probably for the best of everyone but it was really cool to see how despite breaking one of the theorems we learned about, it maintains an unbalanced state and typically doesn’t revert back to a balanced one, and theres not a lot of examples you can think of like this one!
Conclusion
Thus we have seen why and how rivalries exist, as well as how their unique nature exists in graph theory. They exhibit a never ending unbalanced graph behaviour which is really atypical with most graphs, making this a really unique and cool case!
Citations:
(PDF) The long shadow of rivalry: Rivalry Motivates Performance today … (n.d.). Retrieved October 22, 2022, from https://www.researchgate.net/publication/323464237_The_Long_Shadow_of_Rivalry_Rivalry_Motivates_Performance_Today_and_Tomorrow
Melore, C. (2022, January 31). Best rivalries in sports: Survey reveals top clashes across leagues — and fan bases. Study Finds. Retrieved October 21, 2022, from https://studyfinds.org/best-rivalries-sports-fans/
Networks. Positive/Negative Relationships, Strong/Weak Ties, and Rivalry in the English Premier League : Networks Course blog for INFO 2040/CS 2850/Econ 2040/SOC 2090. (n.d.). Retrieved October 21, 2022, from https://blogs.cornell.edu/info2040/2021/09/15/positive-negative-relationships-strong-weak-ties-and-rivalry-in-the-english-premier-league/#respond
Uoftlibraries. (n.d.). University of Toronto Libraries. my.access – University of Toronto Libraries. Retrieved October 21, 2022, from https://www-jstor-org.myaccess.library.utoronto.ca/stable/20788803?read-now%3D1%23page_scan_tab_contents=&seq=8#metadata_info_tab_contents