International Mathematical Modelling Challenge

12 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.

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. • 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. • 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

Overall, our team worked very well together, and were able to harness the different strengths of our team in order to allocate members the roles that they would be able to do the best in.

that it is difficult to become a ‘perfect player’. This is because a perfect player has reached the score of 100% for every variable, which is quite impossible due to human errors.

3. Describe the changes necessary for the model in order to find the

GOAT in terms of team sports

• In summary, we considered the fact that each player has their own role, and makes their own contributions alongside collaborating with the rest of the team. Therefore, we established that GOAT in terms of team sports must be evaluated in relation to the individual players of the team.

• We explained our considerations of a player’s physiological, tactical, technical, and psychological capabilities • Physiological: Strength, power, agility, coordination, etc. • Tactical: Team’s ability to work together, communicate • Technical: Recovery, speed, control, offence/defence

• Psychological: concentration, motivation, sportsmanship • This shows that a lot of knowledge and everyday observations in the sport field are required to fully understand the concepts lying underneath. Mathematics modelling isn’t only about calculations, but about understanding the topic of interest and how things work in real life.

4. Letter to the director of a sports magazine explaining our findings

• We wrote a letter summarising our key findings and a brief description of our model addressed to the director of a sports magazine, who was said to be a fan of our chosen sport (snooker). While working, everyone had a specific role that they played in order to equally distribute the workload and increase efficiency. Amy was responsible for the collection and analysis of data from many different sources for both sports, as well as compiling the data using spreadsheets and a Python program. Anastasia wrote up many mathematical concepts using sophisticated, concise and understandable language. She also did a lot of writing and editing towards creating the final report. Lydia helped with the general research and was in charge of researching snooker in order for the team to achieve a thorough understanding and henceforth create a thoughtful solution. Julia evaluated the important variables to be considered for each sport and created the formulas by adjusting the weighting given to each variable. (Based on her own experience, Julia also provided the rest of the team with valuable insight about tennis.) Overall, our team worked very well together, and were able to harness the different strengths of our team in order to allocate members the roles that they would be able to do the best in.

By participating in this competition, our team members each gained valuable experience working together as a team, providing us an opportunity to exchange and bounce off each other’s ideas and opinions. We found that through this experience, we gained the ability to learn and develop skills such as problem solving, time management, researching and organisation. As this competition is an annual occurrence, we look forward to participating in it in following years, with more experience and knowledge gained.

Julia Fang, Lydia Kim, Anastasia

Prokhorov, Year 9 and Amy Feng, Year 10

SAVE THE DATE 2022 DRAMA PRODUCTIONS

Staff and students from the Drama Faculty are working hard to deliver an amazing line-up of performances in 2022.

We are looking forward to welcoming audiences back to the Audrey Keown Theatre next year—we hope to see

you there!

MIDDLE YEARS PRODUCTION

Wendy & Peter Pan 5 & 6 April, 6.30 pm

PLC SYDNEY MUSICAL

Oliver

27 April, 6.30 pm: Junior School Preview Night 28 & 29 April, 7.30 pm 30 April, 6.30 pm CARLTON CUP

Theatresports

16 March, 7.00pm

Keep an eye on Notices next year for ticket sale information or follow us on Instagram.

@plcsydneyperformingarts