Equivalent Defects Curve

“Type” vs. Equivalent Defects

Most coffee grading practices can be represented on a continuous Type scale that increases non-linearly with the number of equivalent defects. This relationship, illustrated in the graph Type vs. Equivalent Defects (Exponential Rule), shows that the scale grows rapidly for coffees with very few defects and more slowly for coffees with higher defect counts.

For example, moving from 4 to 8 defects in a high-quality coffee can result in a noticeable shift in Type. However, at the lower-quality end, a much larger increase, such as from 160 to 260 defects, is required to produce a similar Type change. This diminishing sensitivity at higher defect counts follows an exponential pattern, meaning that the perceived difference between two samples depends heavily on where they are positioned along the curve.

This exponential approach allows a single formula to unify different grading systems, interpolate between official Type boundaries, and extend the scale beyond traditional limits (e.g., above Type 8) while preserving consistent proportionality between defect counts and Type values.

Define a continuous Type from the number of equivalent defects d as:

Type = ln(d) / b
where b ≈ 0.709

This formula aligns the curve with recognized grading standards and allows any defect count to be mapped to a precise Type value. It provides a consistent, method-agnostic backbone: official Type bands (e.g., Types 2–8) become defined ranges on the same curve, while values beyond these bands (Types above 8) can be extrapolated naturally. This approach ensures proportionality across the scale, meaning a given change in Type always reflects the same relative change in defect count, regardless of the coffee’s initial defect count.

Why Differences Cannot Be Judged as a Constant

Since Type scales exponentially with defects, a fixed defect error has different impacts across quality levels. The same absolute error (e.g., 20 defects) may push a sample across a Type boundary at high quality but barely move the needle in low quality. Therefore, differences must be measured on the curve, not by a constant error in counts.

Type-Based Concordance Between Human and Model

To compare human and model assessments, compute the absolute Type difference:

|ΔType| = |ln(d_model) − ln(d_human)| / b

With b ≈ 0.709, this is equivalent to:

|ΔType| = abs(log(d1) - log(d2)) / 0.709

The acceptance threshold can be defined as a fraction of a Type. On the log scale, this corresponds to:

1 Type → 0.709
1/2 Type → 0.354
1/3 Type → 0.236
1/4 Type → 0.177
1/6 Type → 0.118

Consider model and human assessments to be in agreement if the absolute log difference is below the chosen threshold. For example, using 1/4 of a Type, agreement occurs when:

abs(log(d_model) - log(d_human)) < 0.177

This flexible approach allows the tolerance to be adjusted according to the desired grading precision, ranging from broader agreement (1 Type) to very strict concordance (1/6 of a Type).