Knowledge Retrieval Efficiency Estimator
Estimates the overall Knowledge Retrieval Efficiency (KRE) score by combining F1 score (harmonic mean of precision and recall) with a time-penalty factor and an index-size scaling factor.
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Formulas
1. F-beta Score
Fβ = (1 + β²) · P · R / (β² · P + R)
2. Time-Penalty Factor
Tfactor = min(1, Qbaseline / Qactual)
3. Index-Size Scaling Factor
Sfactor = 1 / (1 + log10(N) / 10)
4. Knowledge Retrieval Efficiency
KRE = Fβ × Tfactor × Sfactor
Assumptions & References
- Precision and Recall are computed over a representative query set using standard IR definitions (Manning et al., Introduction to Information Retrieval, 2008).
- The F-beta score generalises the F1 score; β = 1 weights precision and recall equally (van Rijsbergen, 1979).
- The time-penalty factor is capped at 1: a system faster than the baseline receives no bonus, preventing time from inflating the score.
- The index-size scaling factor uses a logarithmic model reflecting that retrieval difficulty grows sub-linearly with index size (Zipf/power-law document distributions).
- KRE = 0 when either precision or recall is 0, or when query time is infinitely slow.
- Ratings: ≥ 85% Excellent, ≥ 70% Good, ≥ 50% Fair, ≥ 30% Poor, < 30% Very Poor.
- All inputs are assumed to be measured under consistent, reproducible conditions.