Researchers have introduced an innovative concept in the mathematics that forecasts the outcomes of various competitions, encompassing sports, games, and social hierarchies in both humans and animals.
Researchers have introduced an innovative concept in the mathematics that forecasts the outcomes of various competitions, encompassing sports, games, and social hierarchies in both humans and animals.
This new idea, termed “depth of competition,” can be applied across many significant and profitable areas. For example, it may assist in predicting the victors of sports matches, anticipating consumer choices, ranking universities, and assessing hiring methodologies.
Furthermore, this concept establishes a unified framework to analyze and draw conclusions from a broad range of competitive scenarios. Provided that researchers have access to sufficient data, whether it originates from board games or fights among baboons, their model has the capability to determine the depth of any competition featuring a winner and a loser.
“Our model doesn’t differentiate between a sports dataset and an animal dataset,” explained Max Jerdee, a doctoral student in physics at the University of Michigan and a co-author of the study. “Our goal is to create a universal method for assessing inequality across diverse contexts.”
Within this framework, a competition with greater inequality is deemed to be deeper. In such deeper competitions, participants exhibit more variation in skill and status. Surprisingly, this indicates that human games and sports are situated towards the lower end of this depth spectrum.
However, this characteristic is intentional, noted Mark Newman, a professor of physics and complex systems at U-M.
“Taking basketball as an example, it might not seem shallow,” Newman remarked. “There is a vast range of skills, and players compete at various levels. Yet, people often don’t engage at all levels because pitting an average high school player against an NBA pro serves little purpose.”
Jerdee highlighted that even among NBA teams, those with poorer records have an increased opportunity to draft promising young players, enhancing their chances of improvement.
“Referring to something as shallow might carry negative implications, but it can also imply higher competitiveness, unpredictability, or excitement,” Jerdee noted. “All these attributes essentially reflect the same concept.”
While humans have established norms and frameworks to encourage parity and thrilling competitions, many animals lack this structure.
For example, in chicken flocks, known for the phrase “pecking order,” there’s a distinct hierarchy where dominant birds easily assert their superiority over weaker ones, facing minimal risk in these power displays.
According to Jerdee and Newman’s evaluation, basketball possesses a depth of fewer than 1 layer, while the pecking order of chickens reaches nearly 20 layers. The social dominance structures among hyenas are even more rigorous, boasting a depth of over 100 layers.
Competitive dynamics in human settings, such as university rankings and social hierarchies among high school peers, find themselves positioned between sports and animal competitions concerning depth.
Besides measuring competition depth, the new model can also forecast potential “winners” in various contests. This technique could prove beneficial for evaluating university rankings, predicting consumer preferences, or estimating outcomes of sports events—even between competitors who have never previously faced each other.
To showcase this predictive power, the researchers demonstrated that the University of Michigan’s 2022 football team would have had an 89% probability of defeating the University of Wisconsin had they faced each other.
