Quantifying AI Effectiveness: A Formulaic Model for Skills, Prompts, and Platforms

Core Formula for AI Usage Effectiveness

AI usage effectiveness can be expressed as the product of three major factors:

Professional ability – the user’s understanding of the task’s essence.

Prompt engineering skill – the proficiency in interacting with the AI.

AI platform capability – the performance and suitability of the AI tool itself.

Decomposition and Modeling of the Three Abilities

1. Professional Ability

Professional ability consists of three core dimensions: knowledge reserve, practical experience, and learning ability. These can be described with a nonlinear formula.

Knowledge reserve – the user’s mastery of domain knowledge such as mathematical theory or programming languages.

Practical experience – the ability to model and solve real‑world problems.

Learning ability – the adaptability and self‑improvement when facing new problems.

The AI usage effectiveness formula acts like a magnifying glass, amplifying your strengths while revealing weak spots.

A low learning ability can limit overall performance even when knowledge reserve and practical experience are high.

2. Prompt Engineering Skill

The BROKE framework (Background, Role, Objective, Key Results, Evolve) is used to model prompt skill.

Background : Provide context so the AI understands the task.

Role : Define the AI’s function (e.g., “math‑modeling expert”).

Objective : State clear goals and scope.

Key Results : Specify the desired output format or content.

Evolve : Iterate and refine through multiple interactions.

A good prompt is like the combination to a safe; a tiny error can lead to huge mistakes.

Prompt skill is modeled as the product of its dimensions, each scored positively.

3. AI Platform Capability

Platform capability reflects tool performance and depends on three key metrics:

Responsiveness : Speed of task processing.

Accuracy : Reliability of the output.

Scalability : Ability to handle complex tasks.

These metrics are combined non‑linearly, with higher weights for real‑time chat tasks and greater emphasis on accuracy and scalability for rigorous mathematical modeling.

From personal experience, platform ranking for modeling quality is: ChatGPT > DeepSeek > Claude > Kimi > Wenxin Yiyan.

Case Study: AI Usage Effectiveness for Math‑Modeling Learners

Different user types should focus on different dimensions:

Beginners : Strengthen basic knowledge and practical skills, learn to provide clear background information and objectives, and choose a high‑responsiveness platform.

Competition‑oriented participants : Enhance learning ability and iterative skills, and select a highly scalable platform for complex modeling.

Application‑oriented learners : Deepen domain knowledge, define clear roles, and leverage platforms with precision and multifunctionality.

Optimizing AI usage effectiveness is not to replace humans, but to enable each person to become more efficient and wiser.

By constructing and refining this formulaic model, we can better understand the sources of AI usage differences and offer precise improvement suggestions for various users.