Analisis Konvergensi Barisan Rata-Rata Performa Pemain League Of Legends Menggunakan Konsep Limit Pada Analisis Real : Convergence Analysis of the Sequence of Average Player Performance in League of Legends Using the Limit Concept in Real Analysis - Siagian, Sebastian Hansen; M. Alfin Syahrin; Simbolon, Fernandus Hotlan; Sukma Indra Bayu (PUSDATIN Institut Agama Islam Sultan Muhammad Syafiuddin Sambas, 2025)
League of Legends (LoL) is a competitive online game characterized by dynamic player performance that fluctuates over time. This study aims to analyze the convergence behavior of the average performance sequence of LoL players using the concept of limits within Real Analysis. Data were collected from a third-party performance tracking platform (OP.GG) through purposive sampling, comprising cumulative win rates of multiple players over up to 100 matches each. Each player’s progress was represented as a real-number sequence illustrating win rate evolution relative to the number of matches, while the aggregate average formed a cross-player sequence. The analysis involved sequence visualization, limit testing, and determining the supremum and infimum to assess performance stability. The results indicate that most individual sequences tend to converge toward specific limit values, reflecting performance stabilization after a certain number of matches. The aggregated average sequence also exhibits convergence, with decreasing variance as the number of matches increases. Thus, the application of limit and convergence concepts to LoL performance data demonstrates a mathematical phenomenon of stabilization and highlights the practical relevance of Real Analysis to empirical data in the field of esports.