Composite

The composite is the harmonic mean of per-trait scores on a score card. It returns a single number that emphasizes the weakest trait: a low trait score pulls the composite down more than a high trait score pulls it up.

§1Definition

Given per-trait scores s₁, s₂, …, s_n on a score card, the composite is:

composite = n / (1/s₁ + 1/s₂ + … + 1/s_n)

The harmonic mean is always less than or equal to the arithmetic mean. The two means are equal only when all per-trait scores are equal; as the spread between traits widens, the harmonic mean falls further below the arithmetic mean.

§2Mechanism

§2.1Why the harmonic mean

The harmonic mean makes the composite sensitive to the lowest inputs. A single low trait score therefore has a larger downward effect than a high trait score has an upward effect. The composite behaves as a bottleneck summary: improving the weakest trait raises the composite more than improving an already-high trait.

surprise

density

absurdity

Composite

Figure 1. Three traits with arithmetic mean 62 produce a composite of 52. The low absurdity score pulls the harmonic mean below the arithmetic mean. The composite bar is rendered in a neutral accent because the composite carries no tier.

§2.2Composite confidence

The composite’s confidence is the minimum per-trait confidence on the score card. A composite score inherits the reliability of its least reliable input, so a single low-confidence trait makes the whole composite low-confidence.

§2.3Composite headroom

The composite’s headroom is the maximum per-trait headroom on the score card. Because the harmonic mean is bottleneck-sensitive (§2.1), the trait with the largest headroom is the one whose improvement would move the composite most. Composite headroom therefore points at the trait to work on first.

§3Interpretation

The composite is useful as a single decision signal — comparing two pieces of content, routing content above a threshold, tracking a portfolio over time. It is not a substitute for per-trait scores when the decision requires knowing which trait is weak. Per-trait scores carry diagnostic information that the composite collapses.

The composite does not carry a tier label, a set of breaks, or a tier color. The following section is an index of what the composite intentionally does not include, with the reason in each case.

§4What the composite does not carry

Does the composite have a tier label?

No. Tier labels are derived from breaks, and breaks are computed from per-trait training distributions. The composite has no training distribution of its own, so no defensible tier boundaries exist for it. Labeling the composite would require either choosing arbitrary thresholds or combining per-trait labels in a way that can contradict individual trait labels.

Does the composite have breaks?

No, for the same reason. Breaks are a property of a trait’s training distributions. A harmonic mean over traits has no analogous distribution to derive breaks from.

Why is the composite bar rendered without tier coloring?

Tier coloring communicates tier assignment. Because the composite has no tier, coloring its bar by score would create the impression that it does. A neutral accent is used instead, distinct from the tier palette.

Why does the composite report headroom if it has no breaks?

Composite headroom is the maximum per-trait headroom (§2.3), which is defined relative to the trait’s breaks, not the composite’s. The composite is forwarding a per-trait signal, not introducing one of its own.

§5Related concepts

Traits — the inputs summarized by the composite.
Confidence — composite confidence is the minimum per-trait confidence.
Headroom — composite headroom is the maximum per-trait headroom and identifies the bottleneck trait.
Score card — where the composite and per-trait scores are rendered together.

Score cardThe full output where every concept appears together→