Diagnosing a Ratio Study with Regressivity
A reassessment of 4,500 residential parcels used a sales-comparison mass appraisal model. The ratio study of 300 qualified sales produced: median ratio 0.92, mean ratio 0.95, COD 18.5, PRD 1.08, and 12% of ratios outside the 0.90–1.10 range. The highest-value quartile had a median ratio of 0.84; the lowest-value quartile had 1.01. The assessor's contract with the state requires a median ratio between 0.90 and 1.10 and a COD no greater than 15.0. The county's overall level is within tolerance, but the state review board has flagged the COD and the value-related pattern. The assessor must decide whether to defend the roll, recalibrate, or reappraise the top quartile.
1. Interpret each statistic and explain what the pattern indicates about assessment equity.
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- Median ratio 0.92: the typical property is assessed at 92% of market value. That is inside the 0.90–1.10 tolerance but below the ideal 1.00.
- Mean ratio 0.95: the average is pulled up by higher ratios, so the mean and median differ.
- COD 18.5: this exceeds the state's 15.0 limit, meaning assessment uniformity is poor. A COD above 15 generally signals unacceptable dispersion around the median.
- PRD 1.08: above the usual 1.03 threshold, indicating regressivity-lower-value properties are assessed at higher ratios than higher-value properties.
- Quartile medians: 1.01 for the low quartile versus 0.84 for the high quartile confirm the vertical equity problem.
The overall level hides the main problem: the roll is roughly within tolerance on average but is not uniform and is regressive.
2. What statistical and modeling problems are suggested, and what are the limitations of the ratio study?
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The pattern suggests the model undervalues high-end properties and overvalues low-end properties-a slope or specification error. Possible causes include inadequate land allocation, outdated cost tables, weak neighborhood variables, or a single adjustment factor applied across the roll.
The ratio study itself has limits. Three hundred sales out of 4,500 parcels may not represent the roll. Sales screening matters: non-arm's-length transfers, new construction, foreclosures, and family sales must be excluded. Time adjustments and sample size by quartile affect the statistics. The PRD can be influenced by the mix of properties sold.
The study measures level and uniformity, not individual appraisal accuracy. It is a diagnostic tool, not a substitute for reviewing the model.
3. Recommend corrective actions and explain how to prioritize them.
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- Do not defend the roll as compliant. The COD and PRD fail the state standards.
- Recalibrate the model, starting with the high-value quartile. Review land allocations, size adjustments, and amenity variables that may be flattening the value curve.
- Rerun the ratio study by quartile and neighborhood after recalibration to confirm that the COD and PRD improve, not just the median.
- Review the highest-value 10% of parcels for obvious underassessment and correct clear errors.
- Submit a written correction plan to the state board.
Avoid a flat multiplier. It would improve the median but would not fix the COD or PRD. If time is short, reappraise the top quartile and use a supplemental roll, then fix the model for the next cycle.