The pool. single family residence resales in ZIP 78628, Georgetown — the pool is selected by the subject’s own ZIP, the tightest geography the feed carries that a reader can check against the address. City and MLS area are used only where no ZIP is on the record; an MLS area is not a ZIP and neither nests inside the other. Sun City and other 55-and-over communities are excluded, asking between $459,000 and $621,000 (the band actually observed runs $460,000 to $617,000), closed August 8, 2025 through August 4, 2026: 149 sales. Recent sales count more heavily, so every share quoted is a weighted share, and the two payment shares overlap — a sale can carry both a closing-cost credit and a repair credit, so they do not sum to the share that paid anything at all.

What is being estimated. Four proportions in one pool of closed sales: p₀ = Pr(C + R = 0), the share where the seller paid nothing toward the buyer’s closing costs and credited no repairs, and pᵣ = Pr(original list > list), the share that had reduced the asking price before the sale; and the same pool split the other way, pᶜ = Pr(C > 0), the share where the seller put something toward the buyer’s closing costs, and pᵣ = Pr(R > 0), the share that credited repairs. All four are properties of this pool, not forecasts for this property. pᶜ and pᵣ are not mutually exclusive — a sale carrying both is counted in each — so they do not sum to 1 − p₀ and should not be read as a partition.

Weighting, and why the interval is not built on 149. Sales are weighted by recency on a 6-month half-life, wᵢ = 2^(−aᵢ/h) with aᵢ the age of the sale in months, so the estimate is the weighted proportion p̂ = Σwᵢxᵢ / Σwᵢ. Weighting costs information: the effective sample size is nᴱ = (Σwᵢ)² / Σwᵢ² = 127.9 against 149 rows, and every interval below uses nᴱ. Using the row count instead would overstate precision by about 1.1 times.

Intervals. Wilson score intervals at 95%, which is the right choice here because a share near 0 or 1 makes the normal approximation cover badly and can put a bound outside [0, 1]: gave nothing 37.0% [29.2%, 45.7%]; had cut the price 74.5% [66.3%, 81.2%]; paid closing costs 51.2% [42.6%, 59.7%]; credited repairs 20.3% [14.2%, 28.0%]. The intervals assume the sales are independent. They are not entirely: sales cluster by subdivision, by listing agent and by month, so a cluster-robust interval would be wider. Read these as the narrowest defensible bounds, not the final word.

Measurement limits, stated rather than buried. A zero and a missing value are indistinguishable in the concession fields, so p₀ is an upper bound on how often a seller truly gave nothing. The reduction test compares the feed’s original list price with its current one, and a relisting can reset that original, so pᵣ is a lower bound on how often an asking price came down. Neither is corrected by a guess.

Interval formula. For a weighted proportion p̂ with effective size nᴱ = 127.9 and z = 1.96, the Wilson score interval is [p̂ + z²/2nᴱ ± z√(p̂(1−p̂)/nᴱ + z²/4nᴱ²)] ÷ (1 + z²/nᴱ) — the inversion of the score test, which keeps both bounds inside [0, 1].

Assumptions. The pool is treated as one population, stationary within the window once recency weighting is applied: the half-life down-weights older behaviour but does not model a change in it. Sales are treated as exchangeable within the pool whatever their price inside the band, subdivision or listing agent.

How this connects to the valuation, and how it does not. None of these shares enters the valuation. Each comparable’s net sale price is computed from its own recorded figures, Pᵢ = closeᵢ − Cᵢ − Rᵢ, with Cᵢ the buyer closing costs its seller paid and Rᵢ its repair amount, both read from that sale’s MLS concession fields. The pool says how common concessions are; it is never used to impute one to a sale. Its recency-weighted mean contribution share, s̄ = Σwᵢ(Cᵢ+Rᵢ)/Pᵢ ÷ Σwᵢ = 1.03%, feeds the offer ladder and the page’s closing-cost control, not the valuation.

What the net price cannot detect. A concession delivered outside those two fields — a credit entered in another field, or one paid outside the closing — leaves the net equal to the closed price, so in exactly those cases the net overstates what the seller achieved. An amount entered in error is carried as entered: Texas is a non-disclosure state, the settlement statement is not public, and nothing in the pipeline audits the MLS figure against it.

Pool and exclusions. Single Family Residence resales in MLS area GTW, asking price within ±15% of this property’s, at least 15 days on market, closed August 8, 2025 to August 4, 2026 with a 45-day settle window so pending sales cannot enter, and a 36-month cap on age. Sun City and other 55+ communities are excluded, as is new construction: both negotiate on terms a resale does not.

What “top N%” is measured against. Elementary: 3,911 rated Texas campuses; Middle: 1,123 rated Texas campuses; High School: 1,352 rated Texas campuses. A percentile is the share of those campuses scoring at or above this one in 2025-26. No interval is attached: the comparison is a census of rated campuses for that year, not a sample, so the only uncertainty is TEA’s own scoring, which the agency does not publish an error for.

Provenance. Read from abor_reference.tea_campus_history and tea_campus_current in ALEX’s warehouse on 2026-09-21, rating year 2025-26. The campus report (TAPR) figures in the second table are for 2024-25 — a different year from the ratings, because that is the latest TEA has published. Distance and drive time are routed by the OSRM public routing service, with a straight-line fallback; where a campus could not be located, both are left blank.

Grades and scores are the Texas Education Agency A–F accountability ratings for 2025-26, read from ALEX’s TEA tables. The domain grades are TEA’s three: Student Achievement, School Progress and Closing the Gaps. “Statewide” is the share of Texas campuses at the same level scoring at or above this one in 2025-26. Trend is the change in overall score from 2024-25 to 2025-26; the district trend compares the district’s current and prior ratings. District rank orders the district’s rated campuses at the same level by score, with their average. The campus table is TEA’s Texas Academic Performance Report (TAPR) for 2024-25, the latest year loaded, all students: enrollment, the share economically disadvantaged, students per teacher and average teacher experience, the share of STAAR tests at Meets Grade Level or above across all subjects, attendance and chronic absenteeism, and for high schools the four-year longitudinal graduation rate and the share of graduates enrolled in Texas higher education. Values TEA masks for small groups are shown as a dash. Distance and drive time are routed from the property to the campus location; where a campus could not be located, both are left blank rather than estimated.

Notation and formulas. For campus j at level ℓ with TEA overall score xⱼ in 2025-26, the statewide percentile is πⱼ = 100 · #{k ∈ ℓ : xₖ < round(xⱼ)} / #{k ∈ ℓ}, and the column prints Top max(1, 100 − πⱼ)% — the share scoring at or above. Trend is Δⱼ = xⱼ,2025-26 − xⱼ,2024-25 in score points, not percent. District rank orders the district’s rated campuses at the same level by xⱼ. The overall score itself is TEA’s: by the agency’s published A–F method, the better of Student Achievement and School Progress weighted 70% and Closing the Gaps 30%.

How each school was identified. The listing names a school as text; it is matched to a TEA campus by name within the district. Raye McCoy Elementary: campus match; Charles A Forbes Middle: campus match; Georgetown High: campus match. A partial-name match is the weaker of the two and is worth confirming with the district.

Assumptions and limitations. Level ℓ is assigned from the campus name (Elementary, Primary, Intermediate; Middle, Junior High; High School), so a campus whose name carries none of those words is in no level’s denominator, and a K–8 or 6–12 campus is placed by its name, not its grades served. Percentiles are taken on rounded scores, so campuses within a point of one another can share one. A rating summarises outcomes on a campus; it is not a measure of what the school adds, which is why the student-mix column (share economically disadvantaged) sits beside it. No school figure enters the valuation: nothing here is priced, and the only place a school appears in the method is the school district used as an admissibility rule in comparable selection.

1. Leave-one-out back-test (median absolute percentage error). Each used comparable has adjusted value per SF rᵢ = (Pᵢ + Aᵢ) / sᵢ — Pᵢ its net sale price, Aᵢ ALEX’s adjustments carrying it to this property (the plain living-area line excluded), sᵢ its living area. For i = 1..n comparable i is removed and its net sale price predicted from the others: P̂ᵢ = sᵢ · (n−1)⁻¹ Σ_j≠i r_j − Aᵢ — the valuation formula run backwards, since removing i’s own adjustments carries the prediction from this property back to i. The held-out comparable is excluded from the average it is predicted from. The reported statistic is medianᵢ |P̂ᵢ − Pᵢ| / Pᵢ (9.0%), with the mean n⁻¹ Σ |P̂ᵢ − Pᵢ| / Pᵢ (8.5%) reported beside it. The adjustments are not refit: they are ALEX’s per-comparable adjustments to this property, so the test measures how well the others’ per-SF evidence reproduces each sale, not the error in the adjustment rates themselves. LOOCV is approximately unbiased for expected out-of-sample risk but has high variance: the n training sets share n−2 observations, so fold estimates are strongly positively correlated and the apparent precision is optimistic (Hastie, Tibshirani & Friedman, ESL 2nd ed., §7.10). At n = 3 this is the binding caveat and the reason the figure is presented as descriptive of this comparable set rather than as a population claim.

2. Mean absolute adjustment — a proxy for accumulated model error. n⁻¹ Σ gᵢ/Pᵢ, gross adjustment over net sale price. Every adjustment is itself an estimate carrying its own error, so total adjustment magnitude bounds how much of a final figure is model rather than observed transaction. Under the approximation that adjustment errors are independent with variance proportional to magnitude, the error contributed grows with √Σg² — which is the reason gross rather than net is the right summary: offsetting adjustments cancel in the net but not in the error they carry. It is an ordering statistic, not a calibrated error: it ranks comparables by how much work was done to them without asserting how wrong that work was.

3. Mean comparable age — exposure to temporal drift. Mean days between each comparable’s close date and the valuation date. Time adjustment removes the expected market movement, so residual risk is the variance of the index estimate over the carry interval, not the movement itself. Under the Case–Shiller error decomposition that variance grows roughly linearly in the interval, Var ≈ σ²ᵘΔt + 2σ²ᵤ, so age is a proxy for how much index uncertainty each comparable imports. Here the mean is 246 days; the relevant exposure is not the elapsed time but the month-to-month volatility of the index across it, which the market-timing section quantifies directly.

What the three are jointly evidence of. Taken together they describe the provenance of the estimate, not its accuracy: how much of the final figure is observed transaction and how much is model (mean absolute adjustment), how much temporal extrapolation was required (comparable age), and how the method performed when it could not see the answer (the back-test). Only the last is an error measure. The first two can both look excellent on a valuation that is wrong.

Why they cannot simply be combined. A reader’s instinct is to average them into a single quality number. They are not independent, and the dependence runs the wrong way. Comparables selected for similarity have small adjustments by construction — the model chose them for it — so a low mean adjustment partly reflects the selection rule rather than the market. Tight agreement among comparables adjusted by one rate table reflects the common rate table. Formally, for estimates with pairwise error correlation ρ, the variance of their mean is (σ²/n)[1 + (n−1)ρ]: at ρ near 1 the effective sample size approaches 1 regardless of n, and observed spread understates true uncertainty by an unknown factor. Nothing here estimates ρ — three observations cannot.

The failure mode this section exists to expose. Comparables that are genuinely alike, adjusted by a shared and slightly wrong rate table, will produce close agreement, small adjustments, and a low back-test error — while every one of them is biased in the same direction. Correlated error is invisible to all three measures simultaneously.

What none of these three is. None is a confidence interval, and none should be read as one. Coverage statements live in Cross Validation, where they are derived from the held-out error distribution rather than from agreement among comparables — agreement among correlated estimates being precisely the thing that can be high while the answer is wrong.

The three, evaluated on this property. Back-test over n = 3 held-out comparables: MdAPE 8.99%, MAPE 8.46%, worst 10.74%. Mean gross adjustment n⁻¹ Σ gᵢ/Pᵢ = 34.09%, with gᵢ = Σₖ |aᵢₖ| the sum of the absolute values of every engine line k on comparable i; the largest single line in the set is $114,876. Mean age n⁻¹ Σ (t₀ − tᵢ) = 246 days, t₀ the report date and tᵢ each close date.

A definitional caveat on measure 2. gᵢ counts every engine line, including the dollar living-area line that the per-square-foot valuation leaves out of Aᵢ. On a comparable of different size it therefore overstates the adjustment the valuation actually carries: it measures how different the comparable is from this house, which is related to, but not the same as, how much of the valuation is model.

In plain terms. Each comparable is moved by the difference in lot size times one land rate per square foot, taken from the county’s own figures for this parcel.

Model. Land is priced at a constant rate per square foot of lot. For comparable i the land line is aᵢ^lot = (L − ℓᵢ) · λ, with L this property’s MLS lot size (23,087 sf), ℓᵢ the comparable’s MLS lot size, and λ = land value ÷ (acres × 43,560) from this property’s own county record: λ = $124,254 ÷ 23,086.8 sf = $5.3820/sf. The comparable’s own county rate is used only when this parcel has none; where neither exists the line is zero and flagged (GEN-020) rather than estimated. No cap is applied. A line of 10% or more of the comparable’s net sale price, |aᵢ^lot|/Pᵢ ≥ 0.10, raises a variance notice (GEN-005) and changes no arithmetic. The table’s “Difference” is ℓᵢ − L and “Share of net” is |aᵢ^lot|/Pᵢ. The line is part of Aᵢ and passes through the per-square-foot step like every other non-size adjustment.

Assumptions. (i) Linearity. Every square foot of lot is worth the same, the 5,000th and the 50,000th alike. The marginal value of land ordinarily falls as lots get larger, so an average rate applied to a large difference tends to overstate it, and the bias is largest where the line is largest. (ii) The county’s land value is a market value. It is a mass-appraisal figure set by schedule for taxation; how closely it tracks what buyers pay for land is not tested here. (iii) One rate for the set. This parcel’s rate is applied to every comparable, which suits a set drawn from one subdivision and suits it less as the set spreads out.

What it cannot detect. Usable land is not lot area: slope, flood plain, easements, shape, frontage and view are not in ℓᵢ and are not priced by this line, so two lots of equal size can differ materially in value. The MLS lot size sets the difference and the county record sets the rate; for this parcel the two records of its size differ by 0.0%. No interval is attached to λ: the county publishes none, and none is invented.

Values are the Williamson CAD certified market roll for parcel R045978 (SERENADA WEST SEC 4, BLOCK D, LOT 29, ACRES 0.530): land plus improvement equals the total. They are the county’s mass-appraisal figures for taxation, not an opinion of this property’s market value. The roll’s total is not used as a value anywhere in this report. Its land component is used, and only for one purpose: the land section prices lot-size differences at this parcel’s own county land rate, and says so there. Nothing else in the valuation reads from the roll.

“Of the change, X% is land.” Those two shares are of the ABSOLUTE component movements, not of the net change: |Δland| ÷ (|Δland| + |Δimprovement|) and the same for improvement. Here land moved +$12,997 and improvement −$638, which is why the shares can read as 95/5 while the net change is smaller than the land movement alone. No exclusions are applied to the peer groups: splits, new construction and parcels that changed use are all in them, which is part of why a county median can fall while a settled neighbourhood rises.

No interval is attached to any peer median. Each is the median of a complete enumeration of that group’s parcels carrying both rolls — every parcel in the neighbourhood, the ZIP, the city or the county, not a sample of them — so a sampling interval would be answering a question nobody asked. The uncertainty that does exist is in the appraisal itself: the county’s mass-appraisal model, its choice of neighbourhood codes, and any parcel whose use or boundaries changed between rolls. None of that has a published error, and none is invented here.

Peer medians are the median percentage change in total market value between the 2025 and 2026 rolls across every parcel in each group carrying both years. “A larger change than N%” is the share of the neighborhood’s parcels whose change was below this parcel’s (10th–90th percentile −3.2% to +4.8%). Unit values compare land per acre and improvement per square foot with the neighborhood median among parcels carrying those measures. Taxing units: Williamson CAD (CAD); Williamson CO (GWI); Wmsn CO FM/RD (RFM); Georgetown ISD (SGT); Wmsn ESD #8 (F08).

Annual taxes are as reported on the listing; the effective rate divides them by the county market value, before any exemption the owner holds, so a buyer’s bill can differ.

Notation and formulas. Let M_t, L_t and I_t be the roll’s market, land and improvement values in year t, with M_t = L_t + I_t. The change is Δ%M = 100(M_t/M_t−1 − 1), and the same for each component. Land’s share of the 2026 total is L/M = 28.1%. The effective rate is τ = annual tax ÷ M₂₀₂₆ = 1.51%. For peer group G the figure is median_k∈G 100(M_k,t/M_k,t−1 − 1) over parcels carrying both rolls, and the rank is the share of neighbourhood parcels whose change was smaller than this parcel’s.

Assumptions and limitations. The roll’s market value is the district’s mass-appraisal estimate as of January 1 of the roll year, produced by schedule across every parcel; its accuracy for a single parcel is not published (districts are tested in aggregate, by ratio studies, not parcel by parcel). It is not the taxable value: a homestead’s appraised value may rise by no more than 10% a year under the Texas Tax Code, and exemptions reduce the taxable value further, so a bill does not follow the market-value change one for one. The annual tax is the listing’s figure — the current owner’s bill under the current owner’s exemptions — and a buyer’s bill is computed on the buyer’s own. Peer comparisons are produced only for Williamson CAD parcels with both rolls on file.

What no figure in this section carries. No standard error is computed for any monthly index level, and therefore none for the factor applied to a comparable. The repeat-sales regression would support one — the residual variance of the log price differences is estimable — but it is not computed in this pipeline, and an interval that has not been computed is not printed. What the section does state instead is the evidence behind each month: the number of repeat-sale pairs, and the shrinkage weight applied when a month is thin. A month resting on a handful of pairs is pulled toward the metropolitan path for exactly the reason an interval would be wide there.

Specification. Bailey, Muth & Nourse (1963), A Regression Method for Real Estate Price Index Construction, JASA 58(304), 933–942. For a dwelling transacting at periods s and t with s < t, the model is ln(Pᵗ/Pₛ) = βᵗ − βₛ + εₛᵗ. Let X be the N × T design matrix with xᵢₛ = −1, xᵢᵗ = +1 and zero elsewhere. Then β̂ = (X′X)⁻¹X′y with yᵢ = ln(Pᵗ/Pₛ). The base period is normalised to β₀ = 0 and its column deleted; retaining it makes X′X singular, since the indicators sum to zero by construction. The index is Iₜ = 100·exp(β̂ₜ).

Identification. The estimator is consistent for the market factor under the assumption that E[ε | X] = 0 — that idiosyncratic price changes are mean-independent of when a property happened to transact. Dwelling fixed effects difference out exactly because the same unit appears with opposite signs on both sides, which is what removes omitted-variable bias from unobserved quality and is the method’s central advantage over a hedonic index.

Error structure. Case & Shiller (1987, New England Economic Review; 1989, AER 79(1), 125–137) decompose εₛᵗ = (Hᵗ − Hₛ) + (uᵗ − uₛ), where H is a Gaussian random walk in the property’s own value and u is i.i.d. transaction noise. The implied variance Var(ε) = σ²ᵘ(t−s) + 2σ²ᵤ grows linearly in the holding interval, motivating their three-stage weighted least squares: OLS, regress squared residuals on the interval, then GLS with weights 1/√(â + b̂(t−s)). This index does not apply that weighting. It instead excludes holds under 180 days and annualised changes beyond ±60% outright — a trimming rather than a down-weighting strategy, which is more conservative, discards information the WLS would retain, and is stated rather than left implicit.

Shrinkage. County-month estimates are shrunk toward the metropolitan estimate in log space, ln Iᶜₜ = w ln Iᶜₜᶜ + (1−w) ln Iᵐₜ with w = n/(n+k), k = 20. This is the James–Stein / empirical-Bayes posterior mean under a normal-normal hierarchy where k is the ratio of within-month sampling variance to between-county prior variance; here it is fixed rather than estimated. The effect is that thin months borrow strength in proportion to how little evidence they carry of their own — September 2026, with 38 pairs, sits at w = 0.655.

Known limitations. (i) Sample selection. The index is estimated only on dwellings that transacted at least twice, which is not a random sample of the stock; properties that turn over frequently differ systematically, and no Heckman-type correction is applied. (ii) Revision. Estimates for recent periods move as later transactions arrive, so the most recent months are the least stable — a property shared with all repeat-sales indices including S&P CoreLogic Case–Shiller. (iii) Renovation. The dwelling-constant assumption fails where a property was materially improved between sales; the ±60% annualised filter removes the extreme cases and cannot remove the moderate ones. (iv) Aggregation. A single county index assumes a common market factor across submarkets within it.

Empirical note on smoothing. A trailing three-month average of the log index was tested against the raw monthly series by ten-fold cross-validation on 20,631 Williamson County pairs (September 2026), scoring out-of-sample RMSE of predicted log price change. It was worse in 10 of 10 folds (mean difference +0.00171, 95% CI [+0.00139, +0.00202], t = +10.70); a five-month window was worse again (t = +22.77). Monotonicity in the smoothing window is the signature of signal removal rather than noise suppression, consistent with the shrinkage above already performing the variance reduction a second pass would duplicate.

From the index to a comparable’s line. For a comparable that closed in month m, the factor is fᵢ = I_m* / I_m and the line is Pᵢ(fᵢ − 1), with m* the month shown as “Index now”; the index’s latest month is September 2026, level 167.172 against January 2016 = 100, estimated from 19,824 repeat-sale pairs for Williamson County. The line enters Aᵢ like any other, so it passes through the per-square-foot step and the held-out test unchanged.

Assumptions specific to its use here. The factor multiplies the whole net price, so land and structure are assumed to appreciate at one rate, and the county rate is assumed to hold for this subdivision and price band. A sale is carried to m*, not to the report date; movement after the latest index month is not in the figure. And because every comparable is carried by the same index, an error in its recent level is common to the whole set: it moves the valuation and does not appear in the held-out error.

Converting a net price to a contract price

Why there are two, and where each is used. This valuation is a net sale price. Two places in the report need a contract price instead, and they do not use the same conversion, so both are stated here rather than left to be discovered.

One: the neighbourhood ratio, used for comparison. ρ̂ = median(net / close) over closed sales in Serenada West (the subject's subdivision) in the last 24 months, n = 16, with a minimum of 15 sales before the level is used at all. Here ρ̂ = 0.9940, an implied seller contribution of 0.60% of the contract price. It grosses our net figure up for the Benchmarks comparison and sets the “how far above the evidence the asking price sits” percentage. It is a median of ratios, unweighted, with no interval reported: at n = 16 a median carries real sampling error, and none is claimed for it.

Two: the pool share, used for the offer ladder. ŝ = Σwᵢ(Cᵢ+Rᵢ)/Pᵢ ÷ Σwᵢ, a recency-weighted MEAN of the actual contribution share over the negotiation pool, with its own drawer in the recommendation section. The two differ in estimator (median of a ratio against a weighted mean of a share), in pool (a subdivision over 24 months against an MLS-area price band over 36), and in what they measure (net divided by close, which includes anything that separated the two, against closing costs and repairs specifically).

What that means for a reader. The two conversions do not have to agree, and on this property they do not: they differ by -0.43 percentage points of the contract price (0.60% against 1.03%). Neither is used to alter the valuation itself, which is and remains a net sale price. Where a contract price appears, the conversion behind it is named in that section.

The headline figure uses a third. The contract price at the head of the report is C = (V̂ + R)/(1 − c), rounded to $500, with c the closing-cost share and R the repair credit set in the page’s closing-cost control, which starts from the negotiation pool and which the agent can change. It is not ρ̂. Grossing by ρ̂ for the Benchmarks comparison gives G = V̂/ρ̂ = $467,979 ÷ 0.9940 = $470,822.

Assumptions and limits of ρ̂. The sample is every closed sale with a positive close and net price whose subdivision name begins with Serenada West, with no filter on property type, condition, price band or arm’s-length status beyond what the warehouse table already applies; a neighbouring subdivision whose name shares the prefix is included. A median of ratios is not the ratio of medians and ignores how large the contributions were: where most sales carry none, ρ̂ can be exactly 1 while a minority carried large ones. A sale whose concession was never recorded in the MLS fields enters at a ratio of 1.

How the comparables were chosen

Why this matters for everything above. The held-out error, the bands and the confidence score all rest on the comparables actually chosen. If the selection rule were unstated, a reader could not judge whether the held-out comparables and the subject are alike enough for the error measured on them to say anything about the subject. The rule is therefore stated in full, in the order it runs.

The method, named. Selection is Mahalanobis-metric nearest-neighbour matching with calipers (Rubin 1980, Biometrics 36:293; Rosenbaum & Rubin 1985, The American Statistician 39:33; Abadie & Imbens 2006, Econometrica 74:235), run inside an ordered set of geographic strata. The strata decide where this market is; the metric decides which sales inside it are comparable. This replaced a cascade of several hundred criteria sets that stopped at the first rung holding six candidates and then ranked them on a weighted score of stated conventions. Two differences matter: the cascade treated any two sales clearing the same rung as equally comparable, and when a rung ran short it widened the living-area band to as much as ±45% — producing candidates this valuation’s own ±25% standard then discarded. Selection now cannot hand the estimator a sale the estimator must refuse.

Step 1 — what is removed before anything else. Sales that are not arm’s length (REO, short sale, auction, HUD, corporate-owned, probate, and overbid sales whose remarks name any of those), sales in fair or poor condition, sales in a FEMA flood zone, sales more than ±20% from this property’s asking price, and the subject’s own earlier sale — that last only when at least three other comparables remain, since below that the set is too thin to refuse the help.

Step 2 — admissibility. These are the differences a distance must never be allowed to trade away. Each is categorical: a two-storey house is not a one-storey house that happens to be far away, and no dollar adjustment converts one into the other. Each rule below is applied in order, to what the rule above it left. The first two are hard: they are never relaxed, even when relaxing them is the only way to field a comparable, because a valuation with no comparable is a problem an agent can see and a valuation built on the wrong product is one nobody sees. The rest are relaxed only if applying them would leave nothing at all, and any such relaxation is named in the table.

Step 3 — the market area, tightest first. The remaining sales are placed in nested strata: the same street in this subdivision, then the same phase or section, then the subdivision — taken as every subdivision sharing its name in this city, so a “Serenada West” sits with “Serenada” and “Serenada Estates”, because the distinction between them is a platting artefact and not a market boundary — then half a mile, one, two, three and five miles, then the postal code. The shared name must be distinctive on its own: a first word under five letters keeps its second, so “Sun City” never collapses to “Sun” and sweep in Sunrise. The search stops at the tightest stratum holding at least five eligible sales — eligible, not merely present, and five because that is the number the estimator is built on. A subdivision holding five admissible sales is not abandoned for a one-mile ring holding six: that trades the definition of the market for one more observation, which is the wrong trade. That distinction is the second fix: the old rule stopped at the first rung holding six candidates, and the valuation then discarded those outside its size standard and finished on three. The rung looked full and the report was thin.

Step 4 — the hard calipers. A sale is eligible only if its living area is within ±25% of this property’s — the same appraisal size standard the valuation itself applies, so the two can never disagree — and only if it closed within the time window. The window opens at 13 months, which guarantees a full seasonal cycle, and widens to 24 only when 13 cannot fill the stratum. Time widens before geography: a sale two streets away eighteen months ago is better evidence than a sale two miles away last month, because the repeat-sales index can carry a date and nothing can carry a different market. This report used a 13-month window.

Step 5 — the distance itself. Each eligible sale is placed in a 6-dimensional space — living area (logarithm), year built, lot size (logarithm), distance from this property, in miles, months between the sale and today, and bedrooms plus half the bathrooms — and its distance from this property is measured as d² = (xᵢ − x₀)′ Σ⁻¹ (xᵢ − x₀), where Σ is the covariance of those covariates across every admissible sale in the market area. Estimating Σ on the market rather than on the handful of sales in hand is what makes the distance mean something: two hundred square feet is a large difference in a tract of identical houses and nothing in a custom one. Each variance is ridged before inversion (Ledoit & Wolf 2004, in its simplest diagonal form); where the market area holds fewer than five sales per covariate the off-diagonal terms are dropped and the measure becomes standardised Euclidean distance, which is the same statistic under independence. The basis line records which was used.
Mahalanobis distance on 6 covariates (metric from 201 sales in the market area), within Serenada, across its sections, in Georgetown; 5 of the 21 sales there clear the size and time standards, 5 of those are inside the distance caliper, 13 months of sales considered

The caliper, and the factor of two in it. A sale is admitted when d² ≤ 2χ²_p,0.5, the median contour of the reference distribution. The factor of two is not a tuning choice: the subject is one draw and the comparable another, so their difference has covariance 2Σ and d² is distributed as 2χ²_p, not χ²_p. Calipering at the plain χ² median — the error this model carried until it was measured — admits only the nearest sixth of an honest pool. For this report the caliper is d² ≤ 10.70. The caliper excludes only while exclusion still leaves five comparables. Below that the nearest sales fill the set and each one past the caliper is named, because a sixth constraint that silently cuts a valuation to three is not a better valuation.
2 of these comparables lie past the usual distance for a match; this market area holds nothing closer

This property, in numbers. 201 closed sales survived step 1, 40 of them admissible under step 2, 5 eligible inside the chosen stratum after the size and time calipers, 5 inside the distance caliper, and n = 3 used.

What is deliberately NOT a selection rule. The old cascade filtered on price per square foot — within 15% at its tightest rung, and 0.125 of its ranking score. That is the very quantity the valuation goes on to average, so choosing comparables for already agreeing on it narrows the measured dispersion by assuming the answer. It has been removed. Nothing in selection now looks at the comparable’s price except the ±20% asking-price screen in step 1 and the sale-to-list test in step 2, and that test compares each sale with its own list price, never with this property’s. Outliers are handled after adjustment, where they can be seen and named.

After selection, one further rule. Size. The set used is K = {i : |sᵢ/S − 1| ≤ 0.25} if |K| ≥ 3, and otherwise every comparable with a known living area and net price; here none was set aside. The final set is n = 3.

Where the agent stands in this. The comparables on this page are the model’s own. An agent may replace or remove any of them, and the report then records that it was an agent’s set. A comparable an agent adds by hand carries no computed distance and is given full weight in the estimator, deliberately: the agent has asserted it is comparable, and that assertion is the best evidence available about it.

The limit this creates, stated plainly. Selection is not random. The three sales are the closest matches the rule could find, which is what makes them useful evidence and also what makes the leave-one-out error an optimistic estimate of the error on an arbitrary house: a held-out comparable is being predicted by two sales chosen to be like it. Removing the price-per-foot filter narrows this bias but does not end it: sales alike in size, age, lot and location are alike in price, so selection still favours agreement. The population figures in this section, measured on a blind holdout of sales the model never saw, are the pessimistic bound on the same question. Both are printed for that reason.

The evidence-quality score

What it scores. 65 of 100 scores the EVIDENCE behind this valuation, not the property and not the probability that the figure is right. It is an index built from four factors, each worth up to 25 points with a floor of 12, because even a weak signal carries some information:

Factor 1, how tight the market area had to be. The model walks a ladder of geographic strata from tightest to widest — the same street, then the phase, the subdivision, then half a mile out to five, then the postal code — and stops at the tightest one holding enough eligible sales. The score is that stop’s position on the ladder, linearly: the tightest rung earns 25, the widest 12. The stratum used is named in the selection drawer.

Factor 2, the back-test error. One point deducted per percentage point of leave-one-out error, flooring at 12 once the error reaches 13%. The factor is a restatement of measured performance, not a second opinion about it — measured by the valuation engine on its own proposed set, which is not necessarily the table above (see the cautions below).

Factor 3, how recent the comparables are. One point deducted per 15 days of average age across the set, flooring at 12 once the average passes 195 days.

Factor 4, how much adjustment was needed. One point deducted per percentage point of average absolute adjustment as a share of each comparable’s net price, flooring at 12 at 13%. A set that needed little adjustment scores higher than one rebuilt line by line.

When a factor cannot be measured. It is omitted rather than filled in, and the remaining factors are averaged and scaled to the same 100-point frame; the valuation records which factors were measured. A score built from two real factors is reported as such rather than padded to four with invented inputs.

The tightness bonus and the cap. A set drawn from the top of the ladder earns up to 15 additional points, tapering to zero across the tightest rungs; the total is then capped at 100. Labels: high at 70 or above, medium at 50 or above, low below 50 — this property scores 65, medium.

Formally. With τ the stopping stratum’s position on a ladder of T strata (0 the tightest), ē the engine’s mean held-out error in percent, ā the mean comparable age in days and ḡ = n⁻¹ Σ 100|Σₖ aᵢₖ|/Pᵢ: f₁ = round(25 − 13τ/(T−1)); f₂ = max(12, 25 − round(ē)); f₃ = max(12, 25 − ⌊ā/15⌋); f₄ = max(12, 25 − round(ḡ)). Over the m factors that could be measured, Q = min(100, round(4Σf/m) + B), with B = round(15(1 − π/0.03)) for π = τ/(T−1) < 0.03 and 0 otherwise.

Two cautions the formula makes visible. Factor 4 takes the absolute value of the net adjustment, |Σₖ aᵢₖ|, so offsetting lines cancel and a heavily adjusted comparable can score as lightly adjusted — the opposite choice from the gross measure in the provenance section, and the weaker one. And the score is computed by the valuation engine on its own proposed set and its own held-out test, before this report applies the same-subdivision rule, the ±25% size standard and the per-square-foot average: ē therefore need not equal the median error in the table above, and the score is not recomputed when the agent edits the set.

What it is not. The deductions above are conventions chosen so the score moves in the right direction and can be read off the inputs; they are not fitted coefficients, the score has no sampling distribution, and no interval is attached to it. It is not a probability and must not be read as one. The only uncertainty this report claims is the held-out error and the bands built from it, immediately above.

How the population figures were produced. They come from the training run’s own artifact, not from this page: a single temporal split, train on everything closing on or before 2026-03-08 and test on the 6 months after it, so no sale in the test set was seen in any form during fitting. 19,486 test sales out of the full table. Leases are removed, and the metrics are reported segmented by property type and price band as well as overall, because a single blended figure hides exactly the segments that matter. No interval is attached to these population figures in the artifact, and none is invented here.

What they do and do not describe. They describe the ALEX statistical model across a metro-wide holdout. They are not the accuracy of the comparable-sales figure on this page, which is measured by leaving each comparable out, immediately above; the two are different estimators on different samples and are reported separately for that reason.

Part one — what a valuation should be measured against

This section is reserved. The standard is being supplied separately and will be placed here in full. It is deliberately empty rather than filled with a plausible-looking threshold: a benchmark that this report happened to pass would be indistinguishable, to a reader, from one it had actually been measured against. Until the paper is here, no accuracy standard is being claimed or implied anywhere in this report.

What is known today, pending that standard. Three sets of numbers exist and none of them is a standard — they are measurements, and they are not measuring the same thing:

1. This property. Median error 8.99%, FSD 10.74%, RMSLE 0.0882, 68% interval ±9.62%, from three held-out comparables. Specific to this house, and thin: three observations describe this comparable set accurately and generalise weakly.

2. This model, across its blind holdout. MdAPE 7.77%, MAPE 11.22%, RMSLE 0.1605 over 19,486 sales the model never saw during training. This is the right basis for any general claim about the method, and it is deliberately not what the tiles above report — those answer “how accurate is this valuation”, which is a different question.

3. What the vendors publish for themselves. HouseCanary: national MdAPE 2.8% over 1,994,203 transactions internally, 2.9% on a blind third-party test. Zillow: median error 1.79% on-market and 7.20% off-market. Two cautions before either is treated as a bar to clear. Both are national aggregates dominated by dense, homogeneous tract housing where an automated model does best, and neither is conditioned on the kind of property this is. And the on-market figure is not independent of the asking price — both vendors consume list price, which is the whole point made in the Benchmarks section.

What a standard would need to specify to be usable here, and what the forthcoming paper will presumably settle: which statistic is the criterion (MdAPE, FSD, coverage, or a hit rate); whether it is a point threshold or a distribution; whether it applies per property or per portfolio; how it is conditioned on price band, property type and evidence depth; and whether an interval must be calibrated — that is, whether a stated 68% interval must actually contain the outcome 68% of the time, which is a materially stricter requirement than a median error threshold and the one most AVM disclosures avoid.

Where this report already exceeds common practice, whatever the standard turns out to be: the comparables are named, every adjustment is itemised with its reason, the estimator and its weights are stated, and the held-out test results are printed so every summary statistic can be recomputed by hand. A standard can be applied to a number; it can only be verified against a number whose derivation is visible.

Part two — how this valuation was measured

Why hold anything out at all. Scoring a method on the same sales it was given measures how well it can interpolate data it has already seen, which is not the quantity anyone cares about. The quantity of interest is expected loss on an observation drawn from the same population and not used in fitting: Err = E_(X,Y)[L(Y, f̂(X))]. Resubstitution error is downward-biased for it by construction.

Design: leave-one-out cross-validation. The adjustments Aᵢ are ALEX’s per-comparable adjustments to this property (repeat-sales time carry included, the plain living-area line excluded), giving each comparable an adjusted value per SF rᵢ = (Pᵢ + Aᵢ) / sᵢ. For i = 1,…,n comparable i is removed, the others’ average r̄_−i = (n−1)⁻¹ Σ_j≠i r_j is taken, and its net sale price is predicted as P̂_−i = sᵢ · r̄_−i − Aᵢ — the valuation run backwards, subtracting i’s own adjustments to carry the prediction from this property back to i — giving CV = n⁻¹ Σᵢ L(Pᵢ, P̂_−i). The headline statistic is the median of the absolute percentage errors; the mean is reported beside it. Critically, the held-out comparable is excluded from the average it is predicted from; leaving its own rᵢ in that average would leak the answer into the prediction.

An exact identity for this estimator. Because r̄_−i = (n r̄ − rᵢ)/(n − 1) and Pᵢ = sᵢ rᵢ − Aᵢ, the held-out error is P̂_−i − Pᵢ = sᵢ(r̄_−i − rᵢ) = sᵢ · n/(n−1) · (r̄ − rᵢ), so eᵢ = n sᵢ(r̄ − rᵢ) / ((n−1) Pᵢ). The leave-one-out test on this estimator is therefore a deterministic rescaling of how far each adjusted value per SF sits from their mean. It measures how much the comparables disagree after adjustment; it cannot measure whether their common level is right, because any error shared by every rᵢ cancels from every eᵢ.

Properties, and the one that governs here. LOOCV is approximately unbiased for Err — it trains on n−1 of n points, so the pessimistic bias of k-fold at small k is largely absent. It pays for this in variance: the n training sets are nearly identical, sharing n−2 observations, so the fold-level estimates are strongly positively correlated and Var(CV) does not contract at the 1/n rate an independent average would. At n = 3 this is the binding constraint on everything below (Hastie, Tibshirani & Friedman, ESL 2nd ed., §7.10–7.12; Efron & Tibshirani, An Introduction to the Bootstrap, 1993, ch. 17).

Forecast standard deviation. FSD = sd{ln(ŷᵢ/yᵢ)}, computed on the held-out pairs. The log ratio is scale-invariant, so the statistic is comparable across price points and across vendors without normalisation. Under an approximately log-normal error, exp(±FSD) bounds a one-standard-deviation multiplicative interval; the log-normality is an approximation and is not tested at n = 3. This is the AVM industry's disclosure convention, which is what makes the comparison against the vendors’ published figures like-for-like in definition — though not in sample, since theirs are national aggregates over millions of transactions and this is three comparables for one house.

Interval construction, and why not a normal-theory interval. The 68% and 95% figures are empirical quantiles of the absolute percentage error distribution {|ŷᵢ−yᵢ|/yᵢ}, not μ̂ ± zσ̂. A normal-theory interval would import a distributional assumption the sample cannot support and would be symmetric in levels, which a multiplicative error process is not. The trade-off is explicit: a quantile at the 95th percentile of a handful of observations is an extrapolation of the fitted distribution, not an observed exceedance rate, and is labelled as such wherever it is quoted. Coverage validity requires exchangeability between the held-out comparables and the subject — the assumption underpinning conformal prediction (Vovk, Gammerman & Shafer, Algorithmic Learning in a Random World, 2005) — which close, same-era selection supports without guaranteeing. It is worth noting that conformal width calibration was measured for this pipeline and rejected: a six-month-forward holdout violates exchangeability outright, and coverage did not improve.

RMSLE. RMSLE = [n⁻¹ Σ (ln(1+ŷᵢ) − ln(1+yᵢ))²]^1/2. Squaring in log space penalises proportional rather than absolute error and bounds the leverage of a single large residual relative to RMSE. It is asymmetric in levels: under-prediction is penalised more heavily than over-prediction of the same absolute size, since |ln(1−δ)| > ln(1+δ). The 1+ offset is vestigial at these magnitudes. RMSLE is a relative statistic with no absolute interpretation — it exists to rank methods, and quoting it alone says nothing.

MdAPE and MAPE. MAPE = n⁻¹ Σ |ŷᵢ−yᵢ|/yᵢ; MdAPE is the median of the same summands. MAPE is undefined at y = 0 and structurally asymmetric: unbounded above for over-prediction, bounded by 1 for under-prediction, so it systematically favours methods that under-forecast. The median is reported alongside because it has a 50% breakdown point against the mean's 1/n. Here 8.46% against 8.99% indicates no single dominating residual.

Hit rates. PPE_k = n⁻¹ Σ 1{|ŷᵢ−yᵢ|/yᵢ ≤ k} at k = 0.10 and 0.20 — the empirical CDF of absolute percentage error at two points. On this property: 2 of 3 within 10%, 3 of 3 within 20%. Reported as counts, not percentages: the estimator takes only 4 values at n = 3, and a Wilson score interval on 2/3 spans roughly [0.21, 0.94].

Bias check. Mean signed error n⁻¹ Σ eᵢ = +1.29%, median signed error +5.63% (positive means the held-out prediction was above the actual net); 2 of 3 predictions were high. At n = 3 a sign is informative only when every error shares it, and even then it describes this set, not the method.

What is not claimed, stated plainly. No standard error is attached to any statistic here. The sampling distribution of a standard deviation at this sample size is severely right-skewed, and a nonparametric bootstrap resamples the same few points — it would produce an interval, and that interval would be an artefact of the resampling rather than evidence about the population. No hypothesis is tested and no p-value is reported, because there is no null here worth rejecting at this sample size. These figures are offered as descriptive statistics of this comparable set, which is what they are and the most that three observations can support. The corresponding population-level figures — MdAPE 7.77%, RMSLE 0.1605 over a blind holdout of 19,486 sales — exist and are the right basis for any claim about the method in general; they are not what this page reports, because the numbers asked for are the ones specific to this property.

How the comparison in the table is computed

Notation. V̂ the net valuation, ρ̂ the neighbourhood median of net ÷ close (Serenada West, n = 16, ρ̂ = 0.9940), G = V̂/ρ̂ the ALEX figure grossed to a contract price, and x an outside figure. The “vs ALEX” column is 100(x − G)/G. Here G = $470,822; HouseCanary +17.4%; Zillow +11.9%; the county roll −6.2%. Against the asking price, 100(G − list)/list = −12.8%.

Assumptions and limits of the comparison. Each percentage is a difference between two estimates, not between an estimate and the truth: it says the two disagree, not which is nearer the eventual price. Its uncertainty is at least that of either side — a gap smaller than a vendor’s own FSD or this report’s (10.74%) is within that estimate’s typical error. G carries the error in ρ̂, a median with no interval, on top of the error in V̂. Vendor figures are as retrieved with this valuation run and change without notice; the roll is a January 1 mass appraisal. No outside figure enters the valuation.

Why an undisclosed model is not a defensible statistic. A figure is defensible when someone else can reproduce it: the estimator is specified, the data are identified, and the validation protocol is stated. Both vendors publish outputs and accuracy summaries; neither publishes the estimator, the trained parameters, or the data. Their accuracy figures are therefore self-reported and self-scored on samples they select. This is normal commercial practice and not a criticism of their competence — it is a statement about what an outside reader can check, which is: the claim, but not the calculation.

Zillow, in its own words. The Zestimate is described as combining “public records, MLS data and user-submitted home details into Zillow’s proprietary home valuation model,” offered as “a transparent, free starting point,” and explicitly “not an appraisal and can’t be used in place of an appraisal.” Published accuracy: nationwide median error 1.79% on-market and 7.20% off-market — meaning half of on-market Zestimates fall within 1.79% of the eventual sale price. Zillow states directly that on-market estimates are more accurate “because more up-to-date information is available, including listing details and recent market activity.” No specification, feature list, or training data is published.¹

HouseCanary, from its published technical brief. Considerably more is disclosed. The algorithm runs in three stages: (1) query and clean data; (2) build localised price indices; (3) train machine-learning models on time-adjusted historical prices. Models are fitted at census-tract level, borrowing from neighbouring tracts where a tract is too thin to model alone, with neighbours used for training but excluded from accuracy testing. Two index models are built — median price and median price per square foot — at census-block level, and all historical sales and list prices are carried to current values through them. The response variable is each price expressed as a percent deviation from its block’s current median for that property type; several ML models per tract are then fitted to explain that deviation and combined into one estimate. Inputs include 3,100+ county assessors, 2,700+ county recorders over 20 years, MLS characteristics, listed prices and contract prices, mortgage balances and distress measures. In non-disclosure states such as Texas, MLS contract prices substitute for recorded sale prices where an arm’s-length sale can be jointly verified — directly relevant here.²

HouseCanary’s FSD, and an important caveat they state themselves. FSD is trained on the census-tract empirical error distribution and depends both on that spread and on how much the component models disagree for the individual property. The confidence score is simply 1 − FSD, which is why the 97% confidence reported for this property corresponds to an FSD of 0.03. The interval is constructed for approximately 68% coverage: P(1 ± FSD). And in their own words: “We assume symmetry but not normality... using 2*FSD to estimate a new interval is not guaranteed to yield an approximate 95% coverage probability.” Anyone doubling their FSD to get a 95% band is doing something the vendor explicitly warns against.

What HouseCanary validates, and how. Monthly internal testing on a rolling six-month window, plus quarterly blind third-party testing. As of July 2019: national MdAPE 2.8% over 1,994,203 transactions internally, and 2.9% on the third-party blind sample for Q1 2019. They report hit rate, MdAPE, median signed error (as a bias check), within-5/10/20%, and the share of sales falling inside their own 68% interval — a coverage check, which is the right diagnostic and more than most vendors publish. Results are available by state and MSA on request, which is the boundary of the disclosure: the validation design is public, the validation data are not.

The comparison this page makes, and its limit. FSD is a shared convention, so this report’s 10.74% and theirs are the same quantity — the standard deviation of log(estimate ÷ outcome). But they are computed on different samples by different methods: theirs across millions of national transactions, this one across three comparables for this house. A national median error says what happens to a typical home; it does not say what happens to this particular property and its own comparables. Reading a vendor figure as a promise about this house would be a category error, and reading ours as vendor-grade inaccuracy would be the same error in reverse.

What this report exposes by contrast. The estimator is stated, the comparables are named with MLS numbers, every adjustment is itemised with its reason, the index method is a published 1963 regression with its exclusions listed, and the held-out test results are printed so every summary statistic can be recomputed by hand. Whether the answer is right is a separate question; whether it can be checked is not.

¹ zillow.com/z/zestimate — quotations from Zillow’s published “What is a Zestimate?” page. · ² HouseCanary Valuation Technical Brief, © 2019 HouseCanary Inc., read in full. Figures are as of that publication and may have moved since. · ³ cotality.com (formerly CoreLogic) — no valuation estimate was obtained; the contract is pending renewal.