Bayesian Skill Determination via Factor Graph Message Passing
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Solution Overview
Problem
Existing methods for determining relative skills of players in multi-player games, such as computer games, face challenges in accuracy and computational complexity, especially when dealing with multiple players or teams, and are not well-suited for game modes beyond two-player matches.
Innovation Solution
A method using Bayesian statistical techniques and factor graphs with message passing to update player skill statistics, allowing for efficient computation of relative skills in games involving multiple players or teams by forming a factor graph with nodes representing player skills and game outcomes, and applying message passing techniques to update these statistics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional Bayesian statistical techniques are used to determine relative skills of multiple players, then accuracy of skill indication is improved, but computational complexity increases significantly
Solution Approach 1:
The patent segments the computational problem by representing player skills as independent Gaussian distributions rather than solving a single complex system. Each player's skill is modeled separately with mean and variance parameters, allowing the overall problem to be divided into manageable individual player assessments that can be updated independently based on game outcomes.
Solution Approach 2:
The patent transforms the complex skill assessment problem into a parameter-based system using Gaussian distributions characterized by mean and variance. By changing the representation from raw skill values to statistical parameters, the system enables efficient computation through closed-form Bayesian update equations that operate directly on these parameters rather than requiring complex numerical methods.
2Measurement precision
If traditional methods are used to rank players in multi-player games, then comprehensive skill assessment is achieved, but processing time increases
Solution Approach 1:
The patent applies preliminary action by pre-defining the Gaussian distribution parameters (mean and variance) for each player before game outcomes are processed. This allows the system to prepare the computational framework in advance, so that when game results arrive, only simple parameter updates are needed rather than performing complex calculations from scratch.
Solution Approach 2:
The patent implements feedback through iterative Bayesian updates where each game outcome provides feedback that refines the skill estimates. The system continuously updates the mean and variance parameters based on new game results, with each update building on previous information. This feedback mechanism allows progressive refinement of skill assessments without requiring reprocessing of all historical data.
3Adaptability or versatility
If existing ranking systems are extended to multi-player games, then versatility is improved, but computational complexity increases
Solution Approach 1:
The patent achieves universality by creating a unified Gaussian-based Bayesian framework that handles both two-player and multi-player games through the same mathematical principles. The system uses identical mean and variance parameter updates regardless of the number of players involved, making it universally applicable across different game modes without requiring separate algorithms.
Solution Approach 2:
The patent transitions from traditional ranking approaches to a statistical dimension by introducing probability distributions. Instead of deterministic skill values, the system operates in the dimension of probability spaces characterized by mean and variance, allowing it to naturally accommodate varying numbers of players through the same probabilistic framework.
Data Source
AI summary
There is a desire to provide a way to determine relative skills of players of games such as computer games, chess, tennis and any other suitable type of game. Our earlier Bayesian Scoring system is implemented in Xbox Live (trade mark) and is currently commercially available under the trade name TrueSkill (trade mark). Here we build on our earlier work and use a new method of computation to enable processing times to be significantly reduced. Message passing techniques are adapted to enable computation of updated skill beliefs to be obtained quickly even in the case of multiple teams of multiple players.