This thesis examines the strategies used during the Ban/Pick phase of professional League of Legends matches by using a quantitative model to study its influencing variables, including win rates of champions, team compositions, team sides, and other components. By studying patterns and relationships between them, the purpose is to gain a deep understanding of decision-making techniques in this context, with which we aim to provide professional League of Legends coaches with state-of-the-art Ban/Pick strategies.

To achieve this, we first provide an introduction to the objectives and mechanisms of League of Legends before discussing the structure and rules of the Ban/Pick phase, which is often regarded as the most important aspect of game strategy within the game. We then discuss the methods and datasets used for quantitative analysis by comparing methods using different criteria and assessing their efficiency, consistency, and robustness. Finally, we summarize the results and recommend directions for further research.

In this project we study the stability of stationary solutions of interactive particle systems with shortrange repulsion and long-range attraction. Firstly we describe the model and discuss ring steady state solutions. We give a comprehensive and detailed proof of Theorem 2.1 done in [2]. This theorem gives the conditions for the (in)stability of stationary ring solutions. Omitting details of the computations, we present Theorem 3.1 in [2] to find the conditions for (un)stable stationary solutions in the situation when the mode is sufficiently large. Having these conditions altogether we find the region of the parameters in which the stationary solutions are stable. Finally, we use a steepest descent method for the simulations of the model. Figures of equilibrium states of the particles corresponding to various families of interaction forces will be shown.