The blog post explores using linear programming to optimize League of Legends character builds. It frames the problem of selecting items to maximize specific stats (like attack damage or ability power) as a linear program, where item choices are variables and stat targets are constraints. The author details the process of gathering item data, formulating the linear program, and solving it using Python libraries. They showcase examples demonstrating how this approach can find optimal builds based on desired stats, including handling gold constraints and complex item interactions like Ornn upgrades. While acknowledging limitations like the exclusion of active item effects and dynamic gameplay factors, the author suggests the technique offers a powerful starting point for theorycrafting and understanding item efficiency in League of Legends.
This blog post explores the application of linear programming (LP) to optimize item builds in the video game League of Legends. The author posits that finding the mathematically optimal combination of items for a given champion in a specific game scenario is a complex problem well-suited for this optimization technique.
League of Legends involves two teams of players controlling powerful characters, called champions, who battle to destroy the opposing team's base. Each champion can purchase items that enhance their stats, such as attack damage, ability power, armor, and magic resistance. The vast number of possible item combinations makes it challenging for players to determine the most effective build, especially considering that optimal builds vary depending on the enemy team composition and the current state of the game.
The author proposes formulating the item optimization problem as a linear program. The objective function aims to maximize a chosen metric, such as damage output or survivability, represented as a linear combination of the relevant stats. This function is subject to several constraints. One key constraint is the budget limitation imposed by the in-game gold economy. Other constraints include the maximum number of each item that can be purchased (usually limited to one unique item) and the item build path dependencies, as some items require prerequisite components.
The blog post then delves into the specifics of setting up the LP problem. It details how various in-game statistics, such as attack damage, ability power, armor, magic resistance, critical strike chance, and cooldown reduction, can be incorporated into the objective function and constraints. The author explains how these stats contribute to a champion's overall effectiveness and how they can be modeled linearly, acknowledging the inherent limitations and simplifications involved. Furthermore, the post discusses incorporating situational factors into the optimization process, including adjusting the objective function based on the enemy team's composition and focusing on maximizing damage against specific types of defenses (armor or magic resistance).
The author acknowledges the inherent challenges and complexities of perfectly modeling League of Legends within the framework of linear programming. Factors such as item actives, unique item passives, and complex interactions between champions and items are difficult to represent linearly. Despite these limitations, the post suggests that LP can offer valuable insights into optimal item builds and serve as a powerful tool for understanding the underlying mathematical relationships between item stats and champion effectiveness. The author concludes by suggesting potential improvements and future directions for this approach, including exploring different objective functions, incorporating more sophisticated models of in-game mechanics, and potentially integrating the optimization process into a real-time tool to assist players during matches.
Summary of Comments ( 15 )
https://news.ycombinator.com/item?id=42796292
HN users generally praised the approach of using linear programming for League of Legends item optimization, finding it clever and interesting. Some expressed skepticism about its practical application, citing the dynamic nature of the game and the difficulty of accurately modeling all variables, like player skill and enemy team composition. A few pointed out existing tools that already offer similar functionality, like Championify and Probuilds, though the author clarified their focus on exploring the optimization technique itself rather than creating a fully realized tool. The most compelling comments revolved around the limitations of translating theoretical optimization into in-game success, highlighting the gap between mathematical models and the complex reality of gameplay. Discussion also touched upon the potential for incorporating more dynamic factors into the model, like build paths and counter-building, and the ethical considerations of using such tools.
The Hacker News post titled "Using Linear Programming to find optimal builds in League of Legend" generated several interesting comments discussing the application of linear programming to optimize in-game item builds.
Several commenters expressed enthusiasm for the approach and its potential. One user highlighted the cleverness of using linear programming for this purpose, finding it a refreshing departure from the typical machine learning approaches often discussed. They also appreciated the clear explanation provided in the blog post.
Some users delved into the specifics of the model. One pointed out the challenge of defining the objective function, questioning how "best" is defined and whether maximizing damage output is always the optimal strategy. They also raised the issue of dynamic gameplay, where the optimal build might change depending on the opposing team's composition and in-game developments. Another user elaborated on this point, mentioning the difficulty of capturing complex interactions, such as crowd control abilities and item actives, within the linear programming framework.
The discussion also touched upon the practical limitations of using such a tool in real-time gameplay. One commenter questioned the feasibility of calculating the optimal build quickly enough during a match. Another user suggested that pre-calculating optimal builds for various scenarios could be a more practical approach.
A few users shared their own experiences with similar optimization problems in other games, drawing parallels and suggesting potential improvements. One user mentioned using linear programming for optimizing builds in Path of Exile, highlighting the complexity introduced by unique item affixes. Another suggested exploring other optimization techniques, such as genetic algorithms, as alternatives to linear programming.
The limitations of modeling the game within a linear framework were also discussed. One commenter noted that certain aspects of League of Legends, such as critical hit chance and lifesteal, introduce non-linear elements that might not be accurately captured by a linear model.
Finally, there was some discussion about the blog post itself. A user praised the author for their clear explanation and for providing the source code, enabling others to experiment with the model. Another user suggested incorporating item interactions, such as combinations that grant unique bonuses, into the model.