Modelling Week - 2024, What makes a good rating system?

This week I have the honour of leading a team of pupils on the following topic: 

In football there used to be 2, now 3 points for a win. In chess, the ELO rating is used today and previously the Harkness system. Other challenges arise in indirect-competitive competitions such as climbing. In online games, millions of players are drawn against each other every day and fair and interesting pairings have to be created. In Rainbow Six Siege and Counter-Strike: Global Offensive, players criticised that the rating systems did not differentiate well enough between individual performance and team performance. A good rating system has to fulfil a lot! In this project, we are investigating the questions of why rating systems have been changed and how one can mathematically define what makes a good rating system. We are modelling different ratings and visualising our models stochastically using simulations on a PC. 

the calibrated rating model, works like a charm! Thanks team

An example of what we have modelled and simulated: