metric-design — Decomposed, Multi-Criteria Metrics for LLM Pipelines

> "It's unproductive to launch optimization runs using a poorly designed program or a bad metric." > — DSPy core team dspy.ai/learn/optimization/overview/]

> "LLM judges exhibit self-preference, recency, rubric-order, score-ID, and length biases." > — Synthesized from arxiv.org/pdf/2506.02592, arxiv.org/pdf/2509.26072]

This is a tool skill. It produces a metric function (and a calibration receipt) that other skills consume — DSPy compilers (MIPROv2 / GEPA / BootstrapFewShot), LlamaIndex FaithfulnessEvaluator/RelevancyEvaluator/RetrieverEvaluator, LangGraph eval judges, RAGAS, TruLens. The metric is the optimization target. Get it wrong and every downstream optimizer is theatre.

1. 何时激活 (When to Activate)

Activate when any of these is true:

• Optimization runs: a DSPy / OpenAI-Evals / RAGAS / TruLens job is about to consume a metric(example, pred) -> bool|float. The metric drives gradient-free search; bias propagates into the artifact.
• RAG evaluation: deciding chunk size, reranker, hybrid alpha, retriever-k. A bad metric here picks the wrong chunking strategy and you ship it.
• Agent benchmarks: tool-use, multi-step, planning. A single holistic LLM judge cannot distinguish "wrong tool" from "right tool, wrong args".
• Prompt tuning that has gone past 2 manual iterations: if you're tuning a prompt and have no quantitative metric, you are guessing. Stop the prompt edits, write the metric.
• Production regression test: every chunking / embedding / retriever / prompt PR change needs a metric gate (LlamaIndex OP-10 EvalLoop).

Do NOT activate for:

• One-off exploratory prompt tests where no decision rides on the output.
• Tasks where exact-match / unit-test / schema-validity already gives ≥95% of signal — don't over-engineer.
• Where the user explicitly refuses to commit to any evaluation criteria (then dspy-sop will refuse to compile anyway; this skill cannot help).

2. 核心心智模型 (Core Mental Model)

"The metric IS the model. Change the metric, change the behavior."

A DSPy/GEPA/MIPRO optimizer is a black-box search that maximizes metric(pred, example). Whatever the metric rewards, the compiled prompt will produce. If the metric prefers verbose, hedged answers (which an LLM judge will, by default — judges over-prefer length arxiv.org/pdf/2506.02592]), the optimizer will produce verbose, hedged answers. A bad metric beats a good optimizer every time.

Three corollaries:

1. Decompose by default. A single holistic LLM-as-judge call ("is this answer good? rate 1-5") collapses orthogonal axes (factuality, tone, length, relevance) into one noisy scalar. Decompose into N orthogonal yes/no sub-judges, then aggregate. Same number of LM calls in the limit, vastly less noise.
2. Bool during compile, float during eval. Same metric function, two return types based on the trace argument. Compile-time bool prevents the optimizer from chasing noise in the middle of the distribution; eval-time float gives gradient for reporting and debugging. dspy.ai/learn/evaluation/metrics/]
3. The metric must be calibrated against humans. ≥20 spot-checks where you (the human) rate the same examples the metric does. If metric disagrees with human on >20% of cases, fix the metric before any compile. Otherwise the optimizer just learns the metric's bias.

Why holistic judges fail (the catalog)

| Bias | What it does | Source | |---|---|---| | Length bias | Judges prefer longer answers regardless of quality | arxiv.org/pdf/2506.02592] | | Self-preference | A judge from family X prefers outputs from family X | arxiv.org/pdf/2506.02592] | | Recency / position | Last option in a pairwise rated higher | arxiv.org/pdf/2509.26072] | | Rubric-order | Criteria listed first weighted more | arxiv.org/pdf/2509.26072] | | Score-ID | "5" and "10" anchor differently across rubrics | arxiv.org/pdf/2509.26072] | | Provenance | Knowing the source model biases the rating | arxiv.org/pdf/2506.02592] |

Full catalog in references/R2-judge-bias-catalog.md.

3. SOP (Standard Operating Procedure)

0. Confirm activation criteria (§1)
1. DECOMPOSE: list orthogonal criteria
2. CHOICE: bool vs float per criterion
3. WRITE: implement sub-judges + aggregator
4. BIAS-TEST: probe for length, position, self-preference
5. CALIBRATE: ≥20 human spot-checks; agreement ≥80%
6. SHIP: hand metric to optimizer / eval loop

Stage 1 — Decompose

Write down the criteria the user actually cares about. For an open-ended Q&A:

• Factual? (yes/no) — answer makes no unsupported claims
• On-topic? (yes/no) — addresses the question
• Concise? (length penalty, scalar) — token count vs budget
• Non-hedging? (yes/no) — no "as an AI language model..." or "it depends" cop-outs
• Cites source? (yes/no) — if grounded retrieval is required

For RAG specifically, copy LlamaIndex's triad: Faithfulness (answer entailed by context), Relevancy (answer addresses query), Retriever quality (MRR / hit-rate on labeled QA pairs). See references/R1-source-evidence.md.

Output of this stage: a checklist of 3–6 sub-criteria, each with type (bool / scalar) and aggregation rule (AND for hard gates, weighted sum for soft).

Stage 2 — Bool vs Float Choice (per criterion)

Per dspy.ai/learn/evaluation/metrics/]:

| Criterion shape | Return | Why | |---|---|---| | Hard requirement (factual, schema-valid, no PII) | bool | Optimizer should reject anything that fails, not partially credit | | Soft preference (concise, fluent, on-tone) | float ∈ [0,1] | Optimizer benefits from gradient | | Length | explicit scalar penalty, not LLM-rated | LLM judges over-prefer length; bake the penalty in deterministically |

Universal rule (DSPy OP-030): wrap the whole metric so it returns bool when trace is not None (compile mode) and float otherwise (eval mode). Same function, two semantics.

Stage 3 — Write the Judge

python
import dspy

class Assess(dspy.Signature):
    """Assess a single binary criterion. Reply yes/no."""
    text_to_assess = dspy.InputField()
    assessment_question = dspy.InputField()
    assessment_answer: bool = dspy.OutputField()

def metric(example, pred, trace=None):
    # Hard gates (bool sub-judges)
    factual = dspy.Predict(Assess)(text_to_assess=pred.answer,
        assessment_question="Is every factual claim supported by the context?").assessment_answer
    on_topic = dspy.Predict(Assess)(text_to_assess=pred.answer,
        assessment_question=f"Does this address the question: '{example.question}'?").assessment_answer
    non_hedging = dspy.Predict(Assess)(text_to_assess=pred.answer,
        assessment_question="Does this answer commit to a position (no 'it depends' / 'as an AI' hedging)?").assessment_answer

    # Length penalty (deterministic — DO NOT delegate to judge)
    over_budget = len(pred.answer.split()) > 150
    length_score = 1.0 if not over_budget else max(0.0, 1.0 - (len(pred.answer.split()) - 150) / 150)

    if trace is not None:  # compile mode → strict bool
        return factual and on_topic and non_hedging and not over_budget

    # eval mode → float for reporting
    return (factual + on_topic + non_hedging) / 3.0 * length_score

Rules:

• One yes/no question per sub-judge. Combining ("is it factual AND concise?") re-introduces holistic confusion.
• Length is a deterministic scalar, never an LLM call. Judges have systematic length bias arxiv.org/pdf/2506.02592].
• Use a cheaper / different model family for the judge than the task model (mitigates self-preference). E.g. task = GPT-4o, judge = Claude-Haiku.

Stage 4 — Bias Test

Before calibration, run these probes on a 20-example dev set:

1. Length probe: take 10 good answers, append a redundant paragraph. Does the metric score them higher? If yes, your length penalty is too weak.
2. Self-preference probe: generate the same answer from 2 model families. Does the judge prefer its own family by >10pp? If yes, swap judge family.
3. Position probe (pairwise only): swap A/B order. Does winner flip >10% of the time? If yes, randomize order or average both orderings.
4. Rubric-order probe: list sub-judges in 2 different orders. Does aggregated score shift >5pp? If yes, randomize sub-judge order per call.

Document failures in references/R2-judge-bias-catalog.md for this project.

Stage 5 — Human Calibration

• Sample 20 (or 30 if open-ended) examples spanning the task distribution.
• A human rates each on the same sub-criteria.
• Compute per-sub-judge agreement (Cohen's κ or simple accuracy).
• Threshold: ≥80% agreement on each sub-judge, ≥80% on aggregate.
• If below: fix the metric, do not compile. Common fixes: rephrase the assessment question, switch judge model, narrow the question scope.

This is non-negotiable. Per DSPy Case C: "Never compile against a metric you haven't human-validated on ≥ 20 spot-checks." Garbage metric → garbage compiled program.

Stage 6 — Ship

Hand off:

• The metric function (callable).
• A calibration receipt: {n_spot_checks, per_judge_agreement, bias_probe_results, judge_model_id, task_model_id, date}. Stored next to the compiled artifact. Required for any later audit.
• Recommended optimizer pairing: if sub-judges produce textual feedback (not just bool), pipe into dspy.GEPA for sample efficiency; otherwise MIPROv2.

4. 操作模型 (Operations)

OP-M01 — DecomposeMultiCriteria

• Trigger: Open-ended generation; multiple correctness axes (factuality + tone + length + relevance).
• Action: List 3–6 orthogonal yes/no sub-criteria. One dspy.Predict(Assess) call per criterion. Aggregate with AND (hard) + weighted sum (soft).
• Output: Multi-judge metric callable; one criterion per call.
• Evidence: dspy.ai/learn/evaluation/metrics/]; DSPy Case C; LlamaIndex Faithfulness+Relevancy+Retriever triad.

OP-M02 — BoolDuringCompileFloatDuringEval

• Trigger: Writing any metric used for both compile (teleprompt.compile) and dspy.Evaluate.
• Action: Inside the metric, if trace is not None: return bool_aggregate; else: return float_aggregate.
• Output: One metric function, two modes; optimizer avoids chasing float noise.
• Evidence: dspy.ai/learn/evaluation/metrics/]; dspy.ai/cheatsheet/]; DSPy OP-030.

OP-M03 — ExplicitLengthPenalty

• Trigger: Any LLM-as-judge metric (always).
• Action: Add a deterministic scalar length_score = clip(1 - max(0, len - budget) / budget, 0, 1) multiplied into the final float. Do NOT delegate length judgment to the LLM.
• Output: Length-controlled metric immune to the judge's length bias.
• Evidence: arxiv.org/pdf/2506.02592]; DSPy SOP step "Add length penalty as separate scalar".

OP-M04 — CrossFamilyJudge

• Trigger: Judge model is in same family as task model (e.g., both GPT-4).
• Action: Swap judge to a different family (Claude, Llama, Gemini, Mistral). Document choice.
• Output: Self-preference mitigated.
• Evidence: arxiv.org/pdf/2506.02592].

OP-M05 — HumanSpotCheck20

• Trigger: Before any compile / production rollout of a new or modified metric.
• Action: 20 (open-ended: 30) human ratings on the same sub-criteria. Compute agreement. Reject if <80% per-sub or aggregate.
• Output: Calibration receipt; metric is human-validated.
• Evidence: DSPy Case C step 4; dspy.ai/learn/evaluation/metrics/].

OP-M06 — RAGFaithfulnessRelevancyContext

• Trigger: RAG pipeline; tuning chunk size / reranker / retriever-k / hybrid alpha.
• Action: Instantiate three evaluators: FaithfulnessEvaluator (answer entailed by retrieved context), RelevancyEvaluator (answer addresses query), RetrieverEvaluator(["mrr","hit_rate"]) (does retrieval pull the gold passage). Gate every PR.
• Output: 3-axis RAG quality vector; never a single number.
• Evidence: LlamaIndex OP-10 EvalLoop; developers.llamaindex.ai/python/framework-api-reference/evaluation/].

OP-M07 — BiasProbeSuite

• Trigger: Before calibration.
• Action: Run length-probe, self-preference probe, position probe, rubric-order probe (§3 Stage 4) on 20 examples. Log deltas.
• Output: Bias-probe report; rejected if length probe ≥+5pp on padded answers or position flips >10%.
• Evidence: arxiv.org/pdf/2509.26072]; arxiv.org/pdf/2506.02592].

OP-M08 — TextualFeedbackForGEPA

• Trigger: Sub-judge can articulate why it failed (e.g., "answer was verbose", "missed cited source").
• Action: Return dspy.Prediction(score=float, feedback=str) from the metric. Pair with dspy.GEPA optimizer (not MIPROv2).
• Output: Sample-efficient, reflection-evolved prompts.
• Evidence: dspy.ai/api/optimizers/GEPA/overview/]; arxiv.org/abs/2507.19457]; DSPy OP-004.

OP-M09 — RandomizeJudgeOrder

• Trigger: Pairwise judge or rubric with N>3 criteria.
• Action: Per-call: randomize A/B order in pairwise; randomize sub-judge ordering. Or run both and average.
• Output: Position and rubric-order bias mitigated.
• Evidence: arxiv.org/pdf/2509.26072].

OP-M10 — CalibrationReceipt

• Trigger: Ship a compiled artifact.
• Action: Save JSON next to artifact: {metric_version, n_spot_checks, per_judge_agreement, bias_probe_results, judge_model_id, task_model_id, date, criteria_list}.
• Output: Audit-ready provenance for the metric used to compile.
• Evidence: General audit best-practice; DSPy save(save_program=True) analog.

5. 困境决策案例 (Dilemma Cases)

Dilemma 1 — MIPRO inherited the judge's verbosity bias

困境: Team compiled an open-ended customer-support response program with MIPROv2(metric=llm_judge, auto="medium"). Auto-eval score climbed from 0.62 to 0.84. Production rolled out. Users complained answers were too long. Auditor traced it: the LLM judge gave +0.18 to answers >120 words across the eval set, including some objectively wrong ones. The optimizer faithfully chased that signal.

约束: Re-compile costs ~$30. Cannot re-label dataset. Cannot change judge model (vendor approval cycle).

决策步骤:

1. Diagnose: Confirm length bias on a held-out set: bin answers by length, plot judge-score vs length. Look for monotonic positive slope. (It was there: +0.21 per 50 words.)
2. Patch the metric, not the artifact: Add explicit length penalty (OP-M03) and decompose the holistic judge into factual / on-topic / non-hedging sub-judges (OP-M01). Length is now deterministic, not judge-rated.
3. Re-calibrate on 30 human spot-checks (OP-M05). Agreement: was 64%, now 87%.
4. Re-compile: Same MIPROv2, new metric. Score on new metric: starts at 0.55 (because old prompts over-verbose under new metric), recovers to 0.79 after compile.
5. Production A/B: New artifact has 38% shorter answers, equal factuality, +12% user thumbs-up.

结果: The "score regression" (0.84 → 0.79) was misleading — the old metric was the bug. Real quality improved because the metric finally matched the user.

可提取的操作: OP-M01 DecomposeMultiCriteria, OP-M03 ExplicitLengthPenalty, OP-M05 HumanSpotCheck20. Lesson: when a compiled program is "good on metric, bad in production", the metric is wrong. Don't tune harder — fix the metric.

Dilemma 2 — RAG faithfulness = 100% but answers are wrong

困境: RAG pipeline reports Faithfulness = 1.0 across 200 eval QA pairs. Users complain answers don't address their questions. Team is confused: "but we're 100% faithful…"

约束: Cannot change evaluator vendor. Existing eval suite has only FaithfulnessEvaluator.

决策步骤:

1. Realize the missing axis: FaithfulnessEvaluator only asks "is the answer entailed by retrieved context?" An answer of "The context discusses Q3 financials" is faithful to the context but does not answer "What was Q3 revenue?".
2. Add RelevancyEvaluator (does the answer address the question?) and RetrieverEvaluator(["mrr", "hit_rate"]) (is the gold passage even retrieved?). LlamaIndex OP-10]. This is OP-M06.
3. Re-evaluate: Faithfulness still 1.00. Relevancy: 0.41. MRR: 0.62. Now the picture is clear — retrieval pulls some relevant passages, but the synthesizer hedges with topic-level statements rather than answering the question.
4. Fix the synthesizer prompt, gated on the 3-axis metric. Add a sub-judge: "Does the answer give a direct response to the question (not just describe the context)?" — bool, AND-gated.
5. Result: Faithfulness 0.97, Relevancy 0.79, MRR 0.74. Users stop complaining.

结果: A single metric (faithfulness) created a blind spot. Decomposition exposed the actual failure (synthesizer hedging) which no single number could surface.

可提取的操作: OP-M01, OP-M06 RAGFaithfulnessRelevancyContext. Lesson: a single RAG metric, however precise, is structurally incomplete. Triad is the minimum.

Dilemma 3 — Vendor metric ships in 11 installs but covers one axis

困境: A vendor-tied cekura-metric-design skill (11 installs) wraps a single proprietary judge. Convenient, but: (a) cannot inspect the rubric, (b) cannot swap judge family, (c) cannot add length penalty, (d) calibration receipt does not include bias probes. Optimizer is chasing the vendor judge's blind spots.

决策步骤:

1. Diagnose dependency: Identify which axes the vendor judge covers (often: a holistic "quality" score). Identify what is missing (length, hedging, position bias mitigation).
2. Wrap, don't replace: Use the vendor score as one sub-judge in a composed metric (OP-M01). Add length penalty (OP-M03), non-hedging sub-judge, cross-family fact-check (OP-M04).
3. Calibrate the composed metric (OP-M05), not the vendor's alone.
4. If vendor score correlates <0.7 with human aggregate after composition: drop the vendor; you are paying for noise.

结果: Vendor metrics buy convenience but lose audit and bias control. Open, decomposed metrics dominate for any pipeline that will be optimized against.

可提取的操作: OP-M01, OP-M03, OP-M04, OP-M10. Lesson: a vendor-tied holistic metric is a managed optimizer target you cannot inspect. Decompose around it.

6. 反模式与边界 (Anti-Patterns & Boundaries)

Anti-patterns

| # | Anti-pattern | Why it's wrong | Fix | |---|---|---|---| | AP-1 | Single holistic LLM-as-judge ("rate 1-5") as optimizer metric | Conflates orthogonal axes; inherits all judge biases; optimizer chases noise | Decompose into yes/no sub-judges (OP-M01) | | AP-2 | No length penalty in a generation metric | Judges over-prefer length; optimizer learns to be verbose | Deterministic length term (OP-M03) | | AP-3 | Same family for judge and task model | Self-preference bias inflates score 5–15pp | Cross-family judge (OP-M04) | | AP-4 | Skipping human calibration | Optimizer learns the metric's bias, not the task | ≥20 spot-checks (OP-M05) | | AP-5 | Throwing optimizers at a stalled compile | If metric is bad, no optimizer can save it | Return to metric design | | AP-6 | Single-axis RAG metric (faithfulness only) | Misses query-relevance and retrieval-quality | Triad (OP-M06) | | AP-7 | LLM-rated length ("is this concise?" as a judge call) | Inherits length bias; deterministic is free | Length is len(tokens), not a judge call | | AP-8 | Hand-edited metric mid-experiment without re-calibration | Past compile artifacts now have invalid calibration receipts | Bump metric version; re-calibrate | | AP-9 | Float metric in compile mode | Optimizer chases sub-percent noise; overfit | bool in compile, float in eval (OP-M02) | | AP-10 | Compiling without a metric at all | Without a metric DSPy degenerates to verbose prompting | Refuse the compile (DSPy OP-024) |

Boundaries (when this skill cannot help)

• No willingness to define success criteria: if the user cannot articulate any criterion for "good", no metric exists. Route to scientific-critical-thinking for problem definition first.
• Tasks where exact-match dominates (classification, structured extraction, code-passes-tests): use the obvious metric; this skill's decomposition machinery is overkill. Don't gold-plate.
• Pure preference-pair tasks (RLHF data): preference judges have their own bias profile (Bradley-Terry-style); see simpo / trl-fine-tuning skills, not this one.
• Aesthetic / subjective tasks with no human ground truth (poetry, art): metric design here is essentially arbitrary. Be explicit that you are encoding one aesthetic, not measuring quality.

7. 跨框架对照 (Cross-Framework Mapping)

| Concept | DSPy | LlamaIndex | RAGAS | TruLens | This skill | |---|---|---|---|---|---| | Metric type | def metric(ex, pred, trace=None) -> float\|bool | EvaluationResult from BaseEvaluator | Metric class (Faithfulness, AnswerRelevancy, etc.) | Feedback function | metric function + calibration receipt | | Multi-criteria | sub-judges via dspy.Predict(Assess) | stack of FaithfulnessEvaluator + RelevancyEvaluator + RetrieverEvaluator | metric ensemble | Feedback per criterion | OP-M01 DecomposeMultiCriteria | | Mode switch (compile vs eval) | trace is not None returns bool | N/A (eval only) | N/A | N/A | OP-M02 | | Faithfulness | sub-judge "every claim supported?" | FaithfulnessEvaluator (entailment-based) | Faithfulness metric (claim-by-claim NLI) | groundedness feedback | sub-judge or pre-built | | Relevancy | sub-judge "addresses question?" | RelevancyEvaluator | AnswerRelevancy (embedding-based) | answer-relevance feedback | sub-judge | | Retrieval quality | LlamaIndex RetrieverEvaluator MRR/hit-rate | RetrieverEvaluator(["mrr","hit_rate"]) | ContextPrecision, ContextRecall | context-relevance feedback | pre-built (use LlamaIndex / RAGAS) | | Length penalty | manual scalar in metric | manual | manual | manual | OP-M03 (deterministic) | | Textual feedback | dspy.Prediction(score, feedback) → GEPA | N/A | rationale strings | feedback rationale | OP-M08 | | Cross-family judge | swap judge_lm in metric | swap service_context.llm of evaluator | swap evaluator LLM | swap feedback LLM | OP-M04 (always) |

Combination patterns:

• DSPy + LlamaIndex: use LlamaIndex FaithfulnessEvaluator + RelevancyEvaluator as the sub-judges inside a DSPy metric; aggregate to bool/float per OP-M02. (JetBlue/Databricks pattern.)
• DSPy + RAGAS: use Faithfulness / AnswerRelevancy / ContextPrecision as sub-scalars; pass into a DSPy metric for compile.
• TruLens for production monitoring: same sub-judges, different runtime (live, sampled). Calibration receipts should match.

Opinionated default: build the metric in pure Python with dspy.Predict(Assess) calls (transparent, version-controllable) and import LlamaIndex evaluators only for the RAG triad where the LlamaIndex evaluators are battle-tested. Avoid vendor SDKs whose rubrics you cannot inspect.

Appendix — Quickstart Skeleton

python
import dspy

class Assess(dspy.Signature):
    """One yes/no assessment."""
    text = dspy.InputField()
    question = dspy.InputField()
    answer: bool = dspy.OutputField()

# Use a DIFFERENT family from the task model
judge_lm = dspy.LM("anthropic/claude-haiku-4")  # task model is openai/gpt-4o

def make_metric(budget_words=150):
    def metric(example, pred, trace=None):
        with dspy.context(lm=judge_lm):
            factual = dspy.Predict(Assess)(text=pred.answer,
                question="Is every claim supported by the provided context?").answer
            on_topic = dspy.Predict(Assess)(text=pred.answer,
                question=f"Does this directly address: {example.question}?").answer
            non_hedging = dspy.Predict(Assess)(text=pred.answer,
                question="Does this commit to a position (no 'as an AI', no 'it depends')?").answer
        n_words = len(pred.answer.split())
        length_score = 1.0 if n_words <= budget_words else max(0.0, 1 - (n_words - budget_words)/budget_words)
        if trace is not None:
            return bool(factual and on_topic and non_hedging and n_words <= budget_words)
        return (int(factual) + int(on_topic) + int(non_hedging)) / 3.0 * length_score
    return metric

Then: bias-probe → human-calibrate → save receipt → ship.

References

• references/R1-source-evidence.md — DSPy / LlamaIndex / LangGraph source quotes
• references/R2-judge-bias-catalog.md — Judge bias taxonomy + mitigations
• intermediate/operation_candidates.json — Operation registry

Citations: dspy.ai/learn/evaluation/metrics/], dspy.ai/learn/optimization/overview/], dspy.ai/cheatsheet/], dspy.ai/api/optimizers/GEPA/overview/], arxiv.org/abs/2507.19457], arxiv.org/pdf/2506.02592], arxiv.org/pdf/2509.26072], developers.llamaindex.ai/python/framework-api-reference/evaluation/], cookbook.openai.com/examples/evaluation/evaluate_rag_with_llamaindex].