Research median scoring and comparison rules

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 # Defensible median scoring and comparison rules
 Research for [Establish defensible median scoring and comparison rules](https://git.bongbetic.com/xavierk/odin/issues/7), part of [Find the way to Odin’s build-ready specification](https://git.bongbetic.com/xavierk/odin/issues/1).
 **Accessed:** 25 September 2026. **Status:** decision evidence and recommendations; no final scoring formula, calibrated reference values, benchmark runs, or implementation. The user's requirement is a **median** score.
 ## What the median should mean
 There are three separate choices:
 | Level | Meaning | Main limitation |
 |---|---|---|
 | Median of repeated measurements | Typical result for one fixed workload under stated conditions | Hides occasional long stalls; does not combine CPU, storage and browser results |
 | Median across normalized workloads | Typical relative performance across a fixed test set | Domains with many tests gain more influence; changing references can change rankings |
 | Median across domain summaries | Typical relative performance across explicitly chosen domains | Domain definitions matter; poor performance in a minority of domains can disappear from the headline |
 NIST defines the sample median as the middle observation, or the arithmetic average of the middle two for an even sample count. Its resistance to extremes is useful, but it is a measure of location, not completeness, reliability, or worst-case response. [NIST location][nist-location]
 **Recommendation for discussion:** use medians to summarize repeated valid measurements, normalize against frozen references, form predefined domain summaries, then use a median across those domains for the requested headline. Preserve each stage and its raw inputs. This proposes an aggregation structure; the domain membership, weighting, reference values, repeat counts and numeric scale remain decisions.
 Established suites demonstrate why the levels must stay explicit. SPEC CPU 2017 takes median execution times from three runs, or the slower of two, then uses a **geometric mean** across ratios. Speedometer uses inverse geometric means across test durations and arithmetic means across iterations. These are methodological precedents, not permission to substitute a geometric mean for Odin's requested median. Preserve a tool's native result under its original name; label Odin's further aggregation separately. [SPEC rules][spec-rules] [Speedometer methodology][speedometer]
 ## Normalization and category balance
 Milliseconds, operations/second and GB/s cannot share a meaningful raw median. A candidate approach is a dimensionless ratio against the **same workload's** reference: observation/reference for positive higher-is-better measures, reference/observation for positive lower-is-better measures. SPEC uses the latter for elapsed-time ratios. The metric identity must include its units, workload, size, concurrency, timing boundaries and direction. Reject invalid/nonfinite inputs under declared validity rules; a zero measured duration must not become an infinite score. [SPEC overview][spec-overview]
 **Fictional arithmetic examples throughout this report:** these numbers illustrate consequences only. They are not Odin calibration or measured hardware results. A displayed index of 100 at the reference is an arbitrary illustrative scale, not a recommendation.
 | Fictional metric | Reference | Observed | Illustrative ratio / index |
 |---|---:|---:|---:|
 | Work throughput | 25 operations/s | 50 operations/s | 2.0 / 200 |
 | Memory bandwidth | 25 GB/s | 20 GB/s | 0.8 / 80 |
 | Request latency | 4 ms | 2 ms | 2.0 / 200 |
 A median of these indices is 200, despite memory bandwidth being below reference. That is a consequence of the chosen statistic. Show domain detail and slow-tail measurements alongside it. “200 versus 100” describes this index; it does not establish that every application is twice as fast.
 Fix the order of operations. For fictional repeated times `[1, 3]` ms and a 3 ms reference, normalizing the raw median gives `3 / 2 = 1.5`; taking the median of individual ratios `[3, 1]` gives 2. Even-count averaging and reciprocal normalization do not commute. The report format must specify which result it contains. [median definition][nist-location]
 Balance domains before counting metrics. If ten CPU tests each score 160 and four other domains score 40, 80, 100 and 120, the flat fourteen-test median is 160. A median across five domain summaries is 100. Adding CPU subtests should not silently redefine the product's priorities. Similarly, adding Python/Rust/Java variants must not automatically multiply the language domain's influence. A median of domain medians is a deliberate hierarchical index, not the pooled median of all observations.
 Exclude health counters, memory-test pass/fail, driver availability and installed RAM capacity from throughput arithmetic. Multiple correlated outputs from one workload—throughput, IOPS, average latency and several percentiles—also need an explicit selection rule before any becomes an independent scored contribution.
 ## Calibration is a substantive decision
 SPEC establishes per-workload reference times on a named machine and publishes the calculation rules. Its documentation explains that reference changes preserve relative overall rankings for its geometric-mean calculation. **That invariance does not generally hold for a median across normalized metrics.** [SPEC reference explanation][spec-overview]
 For three fictional higher-is-better workloads, let machine A produce `[1, 10, 10]` and B produce `[2, 2, 20]` in each workload's own units:
 | Fictional reference vector | A's normalized results → median | B's normalized results → median | Ordering |
 |---|---|---|---|
 | `[1, 1, 1]` | `[1, 10, 10]` → 10 | `[2, 2, 20]` → 2 | A higher |
 | `[1, 10, 10]` | `[1, 1, 1]` → 1 | `[2, 0.2, 2]` → 2 | B higher |
 The measurements did not change. Changing the reference altered the relative scales and which observations occupied the middle. Retain the requested median, make the reference rationale public, and version reference changes rather than treating them as cosmetic rescaling.
 | Reference option | What it supports | Decision cost |
 |---|---|---|
 | Named reference configuration | Auditable, fixed anchor with documented per-test measurements | One machine's balance influences the median; configurations and repeatability need validation |
 | Frozen reference cohort | Per-test references from a documented collection of machines | Cohort selection, sampling bias and revision policy become part of the score |
 | User's own baseline | Local before/after comparisons | A score relative to oneself cannot rank different machines |
 Recommend evaluating a frozen, locally distributable calibration manifest. Include reference measurements and provenance, reference conditions, workload and artifact digests, units/directions, aggregation order, required domains and calibration identity. Store it with results so calculation remains reproducible offline. Raw observations must survive changes; a recalculated score should identify its new calibration and preserve the original.
 An arbitrary scale factor is acceptable if described as an index. A claim such as “100 is the median Linux machine,” a percentile rank, or a universal poor/good threshold requires representative population evidence that does not exist yet. Separately normalizing each architecture to its own average would also prevent interpreting those numbers as one common cross-architecture scale.
 ## Repetitions, warmup and uncertainty
 Google Benchmark documents warmup, repetitions, median, standard deviation and coefficient of variation; it distinguishes user-visible wall time from CPU consumption. NIST recommends examining ordered observations for changing location/spread and says potential outliers should not simply be deleted when their cause is unknown. These support retaining all repeated observations and their conditions. [Google Benchmark][google-guide] [NIST run sequence][nist-runseq] [NIST outliers][nist-outliers]
 Recommended measurement rules:
 - Define warmup separately for each workload and retain its duration. Warm caches/JIT throughput, cold launch time and sustained thermal performance are different questions. Do not discard a slow first run from a declared cold-start test.
 - Fix repetition and stopping rules before observing scores. A quick run may estimate a median without enough evidence for a useful confidence interval; it should not claim the precision of the standard profile. Calibrate the minimum repeats against the 10–20 minute budget.
 - Retain run order, warmup, elapsed time, temperatures/power context, competing activity and invalidation reasons. A drifting sequence is not interchangeable independent noise. Repetitions within one process or thermal episode are not automatically independent runs.
 - Exclude observations only for declared validity failures such as incorrect output, changed workload, cancellation or protocol failure. Preserve them with reasons. A slow but valid run can represent the usability problem Odin is meant to reveal.
 - Show central spread such as MAD or IQR, plus tails where the workload supplies enough events. NIST defines MAD and IQR as distinct measures of spread; neither is itself a confidence interval. A median across repeated p99 values must not be labelled the p99 of all requests. [NIST scale][nist-scale]
 NIST documents median confidence intervals based on order statistics/binomial probabilities, interpolated methods and bootstrap alternatives. Choose and validate a median-appropriate method; do not apply a mean's standard-error formula to a median. Confidence also depends on sample count and assumptions about the measurements. For an aggregate, account for shared run-level variation and state whether uncertainty in the calibration reference is included. The spread **between different domain scores** is not sampling uncertainty about the headline. [NIST median intervals][nist-median-ci]
 Keep a graph of results in time order. Google documents CPU selection, boost, scheduler contention, SMT, caches and NUMA as variance sources. Its suggestions for controlled laboratory microbenchmarks include changing system settings; Odin's installed-system baseline should record existing conditions and label any tuned experiment separately. The existing [CPU/memory report][odin-cpu] and [portability/UI report][odin-portability] explain TUI interference and qualification needs. Stable repeated numbers alone do not prove that a workload represents real usability. [Google variance][google-variance]
 ## Comparability must be attached to every score
 SPEC requires performance-relevant observation conditions and valid workload outputs; its CPU suite intentionally measures processor, memory subsystem **and compilers**. Even a fixed-toolchain comparison describes a defined software/hardware configuration. [SPEC rules][spec-rules] [SPEC overview][spec-overview]
 Recommend two explicit comparison purposes:
 - **Installed-system usability:** the chosen installed browser, shell, runtimes, drivers and kernel are part of what is measured. Version/configuration changes may explain a score change without any hardware change.
 - **Controlled reference workload:** fixed workload assets, runtime/compiler contracts, flags, input data and execution modes improve comparison across machines. Architecture-specific artifacts must implement equivalent declared work and validate outputs; different ISA policies need disclosure.
 Neither mode needs to masquerade as a pure hardware measurement. Keep their result identities distinct. Kernel/libc/distro differences can be the subject of a comparison, but they must be visible and the workload contract must remain equivalent.
 A comparison identity should include suite/scoring/calibration versions, workload set, run profile, tool/artifact versions, options and data digests, timing/aggregation rules, browser mode, hardware/virtualization context and validity/coverage. Require a documented equivalence decision before combining scores across changed tools or workloads. SPEC warns that scores across different suite generations generally cannot be converted. [SPEC overview][spec-overview]
 Speedometer 3.1 instructs users to use a clean browser profile, close competing programs/tabs, keep its page focused, avoid device interaction, use AC power and allow cooling when needed. Its official UI computes a 95% interval around its **arithmetic mean**; that interval cannot be attached to Odin's median unchanged. Preserve native browser score/uncertainty and label any median of complete runs separately. Headed and headless measurements need separate identities until an equivalence study justifies any shared interpretation; background versus foreground execution is also material. [instructions][speedometer-instructions] [3.1 result code][speedometer-main]
 VM results characterize the guest allocation and virtualization environment. Keep native, virtualized and emulated cohorts identifiable; VM compatibility success does not establish native performance. Storage cache mode, queue depth, engine, filesystem and durability policy similarly belong to the workload identity. A fallback such as buffered I/O cannot silently replace a direct-I/O measurement with the same scoring identity. [CPU/memory report][odin-cpu] [storage report][odin-storage] [portability report][odin-portability]
 ## Missing tests and eligibility
 For fictional domain indices `[40, 80, 100, 120, 160]`, the complete median is 100. Omitting 40 produces 110; omitting both 40 and 80 produces 120. Available-only aggregation can reward absent or deliberately skipped weak components.
 **Recommendation:** define a versioned required set for the full score. Permit a clearly named partial median and domain results when the full set is unavailable, with the exact subset identified. Compare partial scores only over the same compatible subset; a pairwise intersection comparison must recompute **both** results and label that narrower scope. An optional pack must not silently change the headline's membership.
 Keep distinct outcomes: completed-valid, completed-with-limitations, unsupported, missing dependency, permission denied, unsafe to run, cancelled, timed out, and failed validation. The eventual validity contract decides whether a limited result remains score-eligible. Never impute missing results as zero, a reference score, or a healthy pass. A required workload failing verification makes the full score ineligible, while preserving completed measurements and the associated finding. Good numbers from other domains should not cancel that failure.
 The user accepted reporting unavailable tests across Linux targets. That does not resolve which domains are mandatory, whether every machine should still display a partial number, or how partial results should look. Those are explicit product decisions.
 ## Presentation, recommendations and open decisions
 Recommend a headline containing the median, score identity, full/partial state, and eligible-domain coverage. The next view should show domain values, raw units, repeat count/spread, tail latency, invalidations and reference details. Show health findings beside performance: a fast drive with serious SMART evidence still needs attention. Missing telemetry must stay unknown. The storage and CPU reports establish why speed cannot determine drive replacement or certify memory health. [storage][odin-storage] [CPU/memory][odin-cpu]
 Optimization advice should cite the observation and matching rule: for example, measured foreground stalls plus pressure evidence can support investigating memory contention. A low normalized score alone does not identify its cause. Keep severity of health evidence, completeness of coverage, measurement uncertainty and performance position as separate concepts; avoid one synthetic “confidence/health” percentage that mixes them.
 Before implementation, decide:
 1. The headline's median level, domain membership and balancing rules; whether responsiveness contributes or remains an accompanying measurement.
 2. The reference configuration/cohort, scale and calibration-release policy; collect actual calibration data before inventing thresholds.
 3. Required versus optional coverage, partial-score display and exact comparison eligibility.
 4. Installed-system versus controlled-workload defaults, architecture/ISA policies, browser modes and VM cohorts.
 5. Repetition/warmup/stopping rules, outlier validity rules, median interval method and honest quick/standard/extended precision claims.
 6. Evidence requirements for optimization rules and separation of urgent health findings from the score.
 **Evidence limits:** no calibration population, repeatability measurements, TUI-overhead budget or headed/headless equivalence study was produced. Examples are arithmetic demonstrations only. Context7 successfully resolved Google Benchmark; two BrowserBench/Speedometer searches returned unrelated packages, so its official repository and deployed 3.1 documentation were inspected directly. NIST and SPEC sources were inspected directly as statistical and benchmark-methodology references. This report neither adopts SPEC's workloads nor claims that their aggregation rules are Odin's final design.
 [nist-location]: https://www.itl.nist.gov/div898/handbook/eda/section3/eda351.htm
 [nist-scale]: https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm
 [nist-outliers]: https://www.itl.nist.gov/div898/handbook/eda/section3/eda35h.htm
 [nist-runseq]: https://www.itl.nist.gov/div898/handbook/eda/section3/eda33p.htm
 [nist-median-ci]: https://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/mediancl.htm
 [spec-rules]: https://www.spec.org/cpu2017/Docs/runrules.html
 [spec-overview]: https://www.spec.org/cpu2017/Docs/overview.html
 [google-guide]: https://github.com/google/benchmark/blob/main/docs/user_guide.md
 [google-variance]: https://github.com/google/benchmark/blob/main/docs/reducing_variance.md
 [speedometer]: https://github.com/WebKit/Speedometer/blob/main/README.md
 [speedometer-instructions]: https://browserbench.org/Speedometer3.1/instructions.html
 [speedometer-main]: https://browserbench.org/Speedometer3.1/resources/main.mjs
 [odin-cpu]: https://git.bongbetic.com/xavierk/odin/src/commit/90213d7f62cbd118f08ea8ff2f8042e94aa038a7/docs/research/cpu-memory.md
 [odin-storage]: https://git.bongbetic.com/xavierk/odin/src/commit/6e5af87a64faedd4a8ad31ba10d9be4b499e8349/docs/research/storage-health.md
 [odin-portability]: https://git.bongbetic.com/xavierk/odin/src/commit/20681cd4f184a9fc0164dd638a252de44ef230f5/docs/research/portability-ui.md