Evaluating LLM Math and Coding Capabilities: From Model Selection to Quota Management

1. Why You Need Your Own Evaluation Framework

In today’s landscape of rapid LLM iteration, the gap between public leaderboards and actual user experience is widening. A model might score highly on benchmarks but stall midway through real-world, long-chain reasoning tasks. Conversely, another model might not excel in any single benchmark category but demonstrates remarkable stability in multi-turn tool calling and code review scenarios. For developers, the real value lies not in leaderboard rankings, but in a repeatable evaluation methodology tailored to specific business scenarios.

This guide focuses on two core scenarios: first, a comparative approach to evaluating advanced mathematical reasoning capabilities; second, quota consumption and cost governance in coding agent scenarios. The former addresses “which model to choose,” while the latter tackles “how to afford using them.”

2. Evaluation Dimensions for Advanced Mathematical Reasoning

2.1 Distinguish Between “Solving Problems” and “Tackling Open-Ended Questions”

When evaluating math capabilities, it is crucial to distinguish between two types of tasks. The first involves closed-set problems like competition math or textbook exercises, where a model’s performance heavily depends on the coverage of its training data. The second comprises open-ended mathematical problems, such as conjecture verification, constructive proofs, and counterexample searches. These tasks lack pre-existing answers and test a model’s ability to autonomously decompose problems, design reasoning paths, and adjust strategies after failures.

From practical observation, models that can consistently handle open-ended math problems remain exceptionally rare. Some leading models trade blows on closed-set tests, but once they enter long-chain reasoning requiring multi-step self-correction, the performance gap widens rapidly. Therefore, evaluations should prioritize designing tasks that require “process verification without reference answers” rather than merely drilling existing problem sets.

2.2 Chain-of-Thought Quality Matters More Than the Final Answer

An easily overlooked metric is the conciseness and readability of the Chain-of-Thought (CoT). A lengthy CoT does not necessarily indicate strong reasoning; it may simply mean the model is going in circles or experiencing self-doubt. A high-quality CoT should possess three characteristics:

• Traceable steps: Every deduction step logically follows from the previous conclusion or known conditions.
• No redundant backtracking: It does not repeatedly overturn confirmed intermediate conclusions.
• Fast convergence: It provides a clear answer within a reasonable number of steps, rather than expanding indefinitely.

In practical testing, you can record the number of reasoning steps, the count of invalid backtracks, and the token consumption per task. Combining these three forms an “inference efficiency” metric. This metric is particularly critical for cost-sensitive production environments.

2.3 Practical Advice for Tiered Evaluation

It is recommended to build a test set divided into three difficulty tiers:

Difficulty Tier	Task Characteristics	Evaluation Focus
Basic	Single-step calculation, formula transformation	Accuracy, format compliance
Intermediate	Multi-step deduction, requires intermediate verification	CoT completeness, error localization capability
Advanced	Open-ended problems, constructive tasks	Strategy adjustment capability, self-correction quality

Prepare 20 to 30 questions for each tier and run the same set across different models. Record the accuracy, average reasoning steps, average time consumed, and token usage. This approach yields a multidimensional profile rather than an isolated score.

3. Capability Tiering in Coding Agent Scenarios

3.1 Task Tiering is the Prerequisite for Cost Control

Runaway usage of coding agents is often caused not by expensive models, but by a lack of task tiering. Assigning low-complexity tasks like “finding bugs, reviewing code, or adding minor features” to a high-reasoning-tier model is a classic resource mismatch.

A sound approach is to categorize tasks by complexity:

• High Reasoning Tier: Architecture design, complex root cause analysis, cross-module refactoring plans.
• Standard Tier: Feature implementation, unit test writing, routine code reviews.
• Lightweight Tier: Formatting, adding comments, simple find-and-replace, log analysis.

The key is that the primary agent must be explicitly instructed to delegate lightweight tasks to lower-cost sub-agents. This requires clearly defining division of labor rules in the system prompt or configuration file, for example:

orchestration:
  primary_agent:
    role: "Task decomposition and high-complexity reasoning"
    escalate_when: "Involves cross-module dependencies or unknown root causes"
  sub_agents:
    - name: "code_scanner"
      model_tier: "lightweight"
      tasks: ["Syntax check", "Naming convention", "Simple bug localization"]
    - name: "test_writer"
      model_tier: "standard"
      tasks: ["Unit test generation", "Boundary case supplementation"]

The core philosophy of this orchestration method is: use expensive capabilities only where they are genuinely needed.

3.2 Practical Constraints of Quota Mechanisms

Most subscription-based coding tools employ multi-level rate limits: short-term limits (e.g., a few hours) overlaid with long-term limits (e.g., days or a week). A common issue in practice is that once the short-term limit is rapidly exhausted, the remaining long-term quota cannot be linearly converted into available short-term cycles, leading to the awkward situation of having weekly quota remaining but being unable to continue working immediately.

From an engineering perspective, this requires developers to establish usage monitoring habits:

1. Record a baseline: Track the percentage of quota consumed per hour under normal load.
2. Set alert thresholds: Actively downgrade task tiers or split tasks when short-term consumption exceeds 30%.
3. Off-peak scheduling: Schedule batch code reviews and full-scope scans during periods of quota abundance.

3.3 Measuring the Benefits of Sub-Agent Delegation

Assume a medium-sized refactoring task requires the primary agent operating independently to consume about 40% of the high-reasoning tier’s short-term quota. If code scanning, test generation, and similar phases are delegated to lightweight sub-agents, the primary agent’s actual consumption can drop to 15%–20%. The overall task completion time remains largely unchanged, but the quota pressure is significantly alleviated.

The prerequisite for this benefit is that the delegation instructions must be sufficiently explicit. If the prompt vaguely says “try to delegate to sub-agents,” the model will likely still handle most of the work itself. An effective approach is to write delegation rules as executable conditional statements and require the primary agent to output a task decomposition list at the beginning of each task before assigning items individually.

4. Selection Strategy for Multi-Model Collaboration

4.1 Avoid Single-Model Dependency

Any single model has capability boundaries and supply fluctuations. A more robust approach in production environments is to maintain two or three complementary model channels and route tasks accordingly. For instance, route mathematical reasoning down one channel, routine coding down another, and long-text processing down a third. This ensures that the overall workflow does not collapse when one channel hits its quota limit or experiences service volatility.

4.2 Evaluation Must Track Version Updates

Model versions update frequently, and previous evaluation conclusions cannot be directly applied. It is recommended to re-run key metrics using a fixed test set after every major version update, focusing on: whether the pass rate for advanced tasks has dropped, whether the CoT length has grown abnormally, and whether token consumption per task has increased. A version upgrade does not guarantee universal improvement; sometimes it enhances certain dimensions while degrading others. Only empirical test data can reveal the truth.

4.3 Factor Evaluation Costs into the Budget

Evaluation itself consumes quota. It is recommended to reserve 10%–15% of the total quota as an evaluation budget for regular regression testing. The return on this investment is avoiding the continuous waste of resources in the wrong direction.

5. Engineering Implementation Checklist

• Build math and coding test sets tiered by difficulty, with at least 20 questions per tier.
• Record accuracy, reasoning steps, and token consumption metrics for each model.
• Clearly define task delegation rules between primary and sub-agents in the agent configuration.
• Set up dual alert thresholds for both short-term and long-term quotas.
• Maintain at least two switchable model channels to avoid single-point dependency.
• Execute regression evaluations and compare against historical baselines after every major version update.

6. Conclusion

Comparing model capabilities should not stop at surface-level claims of “who is stronger,” but must be grounded in specific tasks, specific metrics, and specific costs. For developers, the most valuable conclusion is rarely about a model’s ranking, but rather: “Given my task distribution, which combination can deliver stable results within budget.” Establishing your own evaluation system, implementing proper task tiering, and monitoring quotas will yield more sustainable engineering benefits than chasing leaderboard rankings.