Efficiency
Total operational amplification versus the AA 7:2:1 baseline. How much operating activity you generate per unit of fresh input.
The Efficiency formula
E = (R + W + O) / (4I)
Where R = cache_read, W = cache_write, O = output, and I = input. The numerator is total non-input operating activity: reused context plus new context plus generated output. The denominator is 4 times fresh input.
Efficiency can be decomposed as E = (L + V + W/I) / 4 — the average of Leverage, Velocity, and Commitment (cache_write per input). It is the only public metric that includes cache_write, restoring the commitment dimension that Yield and Leverage omit.
What Efficiency measures
Efficiency measures operational amplification — how much operating activity an operator generates per unit of fresh input. It rewards cache reads, cache writes, and output equally per token. This makes it closer to compounding intensity or system utilization than to ordinary economic efficiency.
The name “Efficiency” is established in the production system. The definition makes clear what it actually measures: operational amplification versus the AA baseline, not monetary efficiency or proven quality. An operator with high Efficiency is generating a lot of operating activity per unit of input — but that activity could be cache reads, cache writes, or output, and the formula does not distinguish between them.
The 4.0 baseline
The 4.0 divisor comes from the Artificial Analysis pricing baseline, which models a 7:2:1 cache-read:cache-write:input ratio for the “average AI user.” The derivation:
4.0 = (7 + 1) / 2 At the AA baseline pillars: I = 1, O = 0.5, R = 3.5, W ~ 0 (R + W + O) / I = (3.5 + 0 + 0.5) / 1 = 4.0 Efficiency = 4.0 / 4.0 = 1.00 (by construction)
The two 4.0s are the same number by design — that is the calibration. An Efficiency of 1.00 means the operator matches the modeled average user. Above 1.00 means more amplification than the baseline; below 1.00 means less. The baseline comes from published model pricing data, not from SigRank's own sample.
The Commitment identity
Because Efficiency = (L + V + W/I) / 4, the commitment ratio (cache_write per input) is algebraically recoverable from public metrics:
W/I = 4E - L - V
If Efficiency, Leverage, and Velocity are public, then Commitment is already public — even though it is not displayed directly. This is not a problem; it is a consequence of the algebraic architecture. The metric stack is internally consistent by construction.
FAQ
- What is Efficiency in SigRank?
- Efficiency = (cache_read + cache_write + output) / (4 * input). It measures total operational amplification — how much operating activity an operator generates per unit of fresh input. The 4.0 divisor calibrates the AA baseline to 1.00.
- Why is it called Efficiency and not Amplification?
- The name is established in the production system. The formula rewards cache reads, cache writes, and output equally per token, which makes it mathematically closer to operational amplification than ordinary economic efficiency. The definition makes clear what it measures.
- What does the 4.0 baseline mean?
- The 4.0 divisor comes from the Artificial Analysis 7:2:1 baseline. The derivation: 4.0 = (7+1)/2. At the AA baseline pillars, Efficiency = 4.0/4.0 = 1.00 by construction. Every operator is measured against this reference point.
- How does Efficiency relate to the other cascade metrics?
- Efficiency = (Leverage + Velocity + W/I) / 4. It is the only public metric that includes cache_write (Commitment). If Efficiency, Leverage, and Velocity are public, then W/I = 4E - L - V is algebraically recoverable.
Related: Yield (Y) · Leverage · Velocity · Methodology