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INTERNATIONAL MATHEMATICAL MODELLING CHALLENGE For five consecutive days in March, we participated in the International Mathematical Modelling Challenge (IMMC). This competition is open to all Australian high school students; winners of this competition are then judged internationally. Contestants are given a detailed scenario and have to produce a 20-page report involving comprehensive analysis using mathematical models of their own creation. In 2021, the scenario involved determining the GOAT (Greatest Of All Time) in two sports. In the end, we were awarded National Finalists with Honourable Mention, placing us sixth overall in Australia. We were also the youngest placing team with all teams placed higher than us containing Year 11 and 12 students. There were no other placing teams with Year 9 students. You can see the full results at www.immchallenge.org.au/results. Unfortunately some of our names are rendered incorrectly.
For the scenario, there were four parts: 1. Who is the GOAT (greatest of all time) of female tennis players in 2018 based on Grand Slam Results? • We had to create a mathematical model using a variety of aspects that would contribute to the system we used for scoring. We considered the important components of a tennis game carefully before deciding upon three main areas: achievements, stability and resilience. We used statistics to support each of these, hoping to produce a result that would be a combination of these aspects. Through trial and error, we repeatedly evaluated the value assigned to each variable. In the end, we were able to arrive at a ranking system which we used to determine the GOAT.
• To present our results in a format that showed comparison between players, we used the concept of the ‘perfect player’. This ‘perfect player’ was not one of the candidates for the GOAT, rather, a hypothetical player who would achieve a perfect score of 100. Based on this, we scaled our variables and found the percentage for each player being considered. The closest to the ‘perfect player’ that we had was Simona Halep with a score of 41.98% followed by Angelique Kerber (39.32%) and Caroline Wozniacki (37.80%). Naomi Osaka (37.63%) and Serena Williams (36.64%) were 4th and 5th respectively. This shows that humans still have room to improve our physical capabilities, but also how difficult it is to develop as a tennis player as it involves a large range of skills and techniques. 2. Extend the model to another individual sport • When looking for another individual sport, we aimed to find a sport that was not as well known, yet involved different and interesting characteristics to explore. • We chose snooker and implemented a model similar to the one we had for tennis. However, this scenario involved looking at the actual greatest of all time (rather than the greatest of 2018), meaning we had a lot more data and variables to work with. • We used the same general concepts (ie. ‘perfect player’); however, our variables were focusing on what we considered to be important in snooker: consistency, comparison and achievements. This required a lot of extra research on the sport itself and how they were generally scored in a game.
Julia Fang, Lydia Kim, Anastasia Prokhorov and Amy Feng participated in the International Mathematical Modelling Challenge and were awarded National Finalists with Honourable Mention, and secured sixth overall in Australia.
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• According to our model, we found that the player closest to the ‘perfect player’ in snooker was Ronnie O’Sullivan, landing with an overall 13.64%. This was followed by Judd Trump (13.49%), Ding Junhui (11.36%) and Neil Robertson (11.01%). Although players showed skills in particular areas, it is evident
