Request a valuation

What the method is called

Comparables are chosen by Mahalanobis-metric nearest-neighbour matching with calipers, and the valuation is a kernel-weighted local linear regression — a local polynomial fit, the same family as LOESS — evaluated at this property. Both are in services/comp_match.py.

Which sales are admitted, and the boundary that is not drawn

The pool starts from this property’s own subdivision family — every spelling of it in the feed treated as one place — and widens outward only when that is too thin to support a valuation. It is not capped at the subdivision. A hard boundary sounds safer than it is: where a subdivision has produced four sales in two years, confining the model to them buys a tidy boundary at the cost of a valuation resting on four houses. Where the pool does widen, every rule that widened it is printed in this report, with how many sales each step admitted or dropped.

How far apart two houses are

Similarity is not distance on a map. Each sale is described by six measurements: living area in logs, year built, lot size in logs, distance from this property, months since it closed, and bedrooms plus half the bathrooms. The Mahalanobis distance combines all six into one number, scaled by how much each varies in this market and corrected for the fact that they move together. Bigger houses tend to be newer and to sit on different lots; a plain Euclidean distance would count that one difference three times. Geography is one of the six, not the whole of it — a near-identical house half a mile away is better evidence than a different house across the street, and the metric says so.

The kernel, and why this one

Each admitted sale is weighted by an Epanechnikov kernel of its distance: with u = d/h for bandwidth h, the weight is 1 − u², reaching zero at the bandwidth and staying there. It is the kernel that minimises asymptotic mean squared error (Epanechnikov, 1969).

This is not the tricube kernel that LOESS uses by default, and not a Gaussian one, and the difference is not cosmetic at these sample sizes. On six comparables, tricube put 41% of the weight on one sale and 1.8% on another — a six-comparable valuation actually resting on two. Epanechnikov falls away gently enough that the set keeps contributing. The decay is quadratic and bounded, not exponential: a sale past the bandwidth contributes nothing at all rather than a little, which is what makes the admitted set an honest count.

The regression itself

With the weights fixed, the model runs a weighted least squares fit of adjusted net price per SF on the logarithm of living area, and reads the answer at this property’s size. Two things follow from that. The fit is local: it is estimated for this property and discarded, and the next valuation estimates its own. And the errors it minimises are weighted, so the line is pulled toward the sales that resemble this house and is allowed to miss the ones that do not.

Two diagnostics are reported with every valuation. The bandwidth says how far the model had to reach. The effective sample size says how many comparables the weighting really amounts to: nine sales weighted 12% each is nine pieces of evidence, while nine weighted 80/20 is closer to two. Where the effective sample size is too small, or there are too few comparables, the model refuses to fit a slope at all and falls back to a kernel-weighted mean of price per SF — the Nadaraya-Watson estimator — rather than fitting a line the data cannot carry.

The fitted size slope

Price per SF is not flat across sizes: a larger house of the same kind usually fetches less per SF. Rather than assume a figure, the model fits a line through the weighted comparables’ price per SF against the logarithm of their living area and reads this property’s size off it. The slope is estimated on every report, so a market where size barely matters and one where it matters a great deal are each handled on their own terms. Where there are too few comparables, or their weights are too concentrated for a slope to be estimated honestly, the fit falls back to a weighted average of price per SF rather than fitting a line it cannot support.

Transparent, and statistically valid

Transparent because every step is written down in this report: which sales were admitted, which were set aside and why, how each was weighted, and what was adjusted. Statistically valid because it is an estimator with stated assumptions whose accuracy is measured against sales it was never shown, and reported here whether or not that flatters the figure. A number that can be checked is worth more than one that cannot.

Where the rest of it is

The full treatment — the exact kernel, the caliper widths, the effective sample size, the bandwidth, the held-out test and the interval around the figure — is set out in The statistics.

Forecast standard deviation (FSD) — defined

Formula. Each comparable in turn is hidden and its net sale price Pᵢ is predicted from the others as P̂ᵢ. FSD is the sample standard deviation of the log ratios: FSD = √( Σ (dᵢ − d̄)² / (n − 1) ), with dᵢ = ln(P̂ᵢ / Pᵢ). Here n = 5 and FSD = 0.0895.

How to read it. Lower is better. It is the same measure automated valuation vendors (Zillow, HouseCanary, Cotality) publish for their own estimates, so it can be compared with theirs — with the caution that theirs is measured on thousands of sales and this one on 5.

Overall error score (RMSLE) — defined

In plain terms. One number that sums up how wrong the predictions were across all the hidden comparables, counting a 10% miss high and a 10% miss low as equally bad. Lower is better; 0 would be perfect. This property scores 0.0803.

Formula. Root mean squared logarithmic error, RMSLE = √( (1/n) Σ (ln(1 + P̂ᵢ) − ln(1 + Pᵢ))² ), over the same 5 held-out predictions. Because it works on logarithms, it measures proportional error, and because it squares each miss, one large miss raises it more than several small ones.

How to read it. RMSLE has no upper bound and no threshold: it starts at 0, which would be perfect prediction, and rises without limit, so lower is always better. Because it is measured in logarithms, its value reads roughly as a proportion — 0.10 corresponds to predictions typically about 10% off, and 1.0 would mean being wrong by a factor of about 2.7. House-price models in practice fall between about 0.05 and 0.25; this property scores 0.0803. It is most useful for comparing one method against another on the same sales, rather than read on its own.

Median error (MdAPE) — defined

Formula. MdAPE = medianᵢ |P̂ᵢ − Pᵢ| / Pᵢ, over the same n = 5 held-out predictions, expressed as a percentage: 3.44%. The mean of the same errors (MAPE) is 6.59% and the largest single one is 15.35%.

Why it is here, beside RMSLE. The two answer different questions and are reported together deliberately. RMSLE squares each miss, so it is carried by the worst comparable; MdAPE is a median, so it is carried by none of them. A set with four close comparables and one poor one shows a low MdAPE and a raised RMSLE, and that gap is itself the finding — it says the method works on this property except on one sale, which is worth knowing before the gap is averaged away. Where the two agree, the error is spread evenly through the set.

What it does not say. With n = 5, the median is one of 5 numbers, not an estimate of a population median: change one comparable and it can move to the next order statistic. It is the typical miss on this set, not the typical miss of the method.

Within 5% and within 10% (PPE5, PPE10) — defined

Formula. PPEᵙ = (1/n) Σᵢ 1[ |P̂ᵢ − Pᵢ| / Pᵢ ≤ k ] — the share of held-out predictions inside a tolerance of k. Here PPE5 = 3/5 = 60% and PPE10 = 4/5 = 80%. These are the industry’s own yardstick: PPE10 is what vendors quote as “within 10%”.

The interval, and why it is not optional. A share measured on 5 trials can only take the values 0%, 20%, 40%, 60%, 80%, 100% — it moves in steps of 20 points, so the figure alone would claim a precision the sample cannot carry. Each is therefore reported with a Wilson score interval at 95%: ( p̂ + z²/2n ± z√( p̂(1−p̂)/n + z²/4n² ) ) / (1 + z²/n) with z = 1.96. Wilson rather than the textbook p̂ ± z√(p̂(1−p̂)/n) because that interval collapses to zero width at p̂ = 0 or 1 — a run of 5 hits would report certainty — and its coverage is poor at small n (Brown, Cai & DasGupta, 2001). Wilson stays inside [0, 1] and keeps its nominal coverage here. PPE5 is 23% to 88%, PPE10 38% to 96%. The width of those ranges, not the shares inside them, is the honest summary of what 5 held-out sales can establish.

What is not claimed. The tolerances are fixed at 5% and 10% before the errors are seen, never chosen to flatter the result. And a share is a blunt instrument by construction: a miss of 5.1% and a miss of 50% both count as outside, which is why MdAPE and the error band are reported beside these and not instead of them.

Cross validation — the error measured on this property

Which figure these measures belong to. Every error, band and interval here is computed on ALEX’s valuation of $413,161 — the same net sale price shown at the head of the report, on the same basis: what the seller keeps after paying the buyer’s closing costs and any repair credit. It is not the grossed-up contract price quoted against the outside estimates in Benchmarks. If an agent has changed an adjustment, the figure at the head of the report moves; these measures do not move with it, because they measure how ALEX’s method performed on this property, not how a revised figure would perform. A changed valuation carries no measured band until the change is tested the same way.

How this was tested, in one sentence: we covered up one of the five sales, worked out what this method would have said that house was worth using only the other four, then uncovered it and measured how close we got — and did that five times, once for each sale.

Five tests is a small number from which a spread can be quoted. These figures are real and specific to this house, but thin: one unusual comparable moves them materially. Treat them as the shape of the uncertainty, not a precise measurement of it.

What happened when each sale was hidden and predicted from the others: how far off that prediction was, as a share of what the sale actually netted. Past 10% is red.

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 Sierra Vista (the subject's subdivision) in the last 24 months, n = 34, with a minimum of 15 sales before the level is used at all. Here ρ̂ = 0.9979, an implied seller contribution of 0.21% 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 = 34 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 -1.16 percentage points of the contract price (0.21% against 1.37%). 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 = $413,161 ÷ 0.9979 = $414,051.

Assumptions and limits of ρ̂. The sample is every closed sale with a positive close and net price whose subdivision name begins with Sierra Vista, 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 SF 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 226 sales in the market area), within Sierra Vista; 5 of the 8 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. 226 closed sales survived step 1, 72 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 = 5 used.

What is deliberately NOT a selection rule. The old cascade filtered on price per SF — 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, two further rules. (1) Same neighbourhood. When at least three of the selected comparables share this property’s subdivision family, only those are kept. Family, not the recorded plat name: matching on the exact name made this rule fight the selection ladder above it, throwing out the sibling sections that ladder had just brought in. (2) 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 = 5.

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 five 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 four sales chosen to be like it. Removing the price-per-SF 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. 71 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 — 15 on the same street, 10 in the same phase, 5 in the subdivision, nothing beyond it — and the total is then capped at 100. The bonus covers exactly the rungs that are the same market rather than merely nearby. Labels: high at 70 or above, medium at 50 or above, low below 50 — this property scores 71, high.

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 3.44%, FSD 8.95%, RMSLE 0.0803, 68% interval ±7.63%, from five held-out comparables. Specific to this house, and thin: five 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 and the weighted fit is re-run on the rest, re-centred on i so the kernel weights are distances from i rather than from this property. Writing r̂_−i for that fit read at i’s own size, its net sale price is predicted as P̂_−i = sᵢ · r̂_−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.

What the test can and cannot see. An earlier version of this report derived a closed-form identity here — eᵢ = n sᵢ(r̄ − rᵢ)/((n−1)Pᵢ) — which is exact for an equal-weighted mean and is not exact for the estimator this report now uses. Under kernel weighting the held-out fit is re-centred on the comparable being predicted, so its weights change with i and the error is no longer a fixed rescaling of r̄ − rᵢ. It is stated here rather than quietly deleted because the identity was wrong for one version of this page and a reader may have taken it.

The qualitative conclusion survives the change, and it is the one that matters: the test measures how much the comparables disagree after adjustment, and it cannot measure whether their common level is right. An error shared by every rᵢ — a mispriced submarket, a rate table set wrongly for all of them, a time index that is off — moves every prediction and every actual together and very nearly cancels from every eᵢ. No held-out test on a set can detect an error common to the whole set. That is what the population figures below are for.

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 = 5 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 = 5. 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 five 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 6.59% against 3.44% indicates one residual pulling the mean away from the median.

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: 4 of 5 within 10%, 5 of 5 within 20%. Reported as counts, not percentages: the estimator takes only 6 values at n = 5, and a Wilson score interval on 4/5 spans roughly [0.38, 0.96].

Bias check. Mean signed error n⁻¹ Σ eᵢ = +0.92%, median signed error −2.31% (positive means the held-out prediction was above the actual net); 2 of 5 predictions were high. At n = 5 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 five 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.

Statistical appendix — model, estimator and error measures

The models used, named

Every method below is a published one, named so it can be looked up and argued with. Nothing in this report is a proprietary formula whose behaviour cannot be checked.

Two of these are ours to defend rather than merely to cite: the distance caliper is set at twice the chi-square median, because the subject and the comparable are two draws and their difference carries twice the covariance; and the kernel bandwidth is the caliper itself rather than a bandwidth read off the sample, so it is fixed before any sale is seen. Both choices are argued where they are used.

Notation. Subject living area S. For each comparable i = 1..n used in the valuation: net sale price Pᵢ (closing price less seller-paid buyer closing costs less seller repair credits), living area sᵢ, and Aᵢ, the sum of its adjustments to the subject across every factor except the dollar living-area line (time carry, lot, age, finish and quality-of-space lines included; agent entries replace the engine’s line where made).

Model. Each comparable is assumed to share, after adjustment, a common value per SF with the subject: (Pᵢ + Aᵢ) / sᵢ = r + εᵢ, where r is the subject’s value per SF and εᵢ is comparable-specific error, taken as exchangeable with mean zero. The indication for the subject is vᵢ = S·(Pᵢ + Aᵢ)/sᵢ. Size enters through the ratio, not through a dollar line, so a size difference is priced once.

Estimator. The valuation is the sample mean V̂ = (1/n) Σᵢ vᵢ — the ordinary least-squares estimate of S·r under equal error variances. The median of the vᵢ is reported beside it: the mean has a breakdown point of zero (one mispriced comparable moves it by 1/n of its error), the median a breakdown point of 50%. Eligibility is the appraisal size standard |sᵢ/S − 1| ≤ 0.25, waived if it would leave fewer than three sales. The headline converts V̂ to a contract price C = (V̂ + R)/(1 − c), with c the seller contribution as a share of price and R the repair credit, rounded to $500.

Out-of-sample design (leave-one-out). For each i, comparable i is withheld and the weighted fit is re-run on the remaining n − 1, re-centred on i so the kernel weights are distances from i rather than from this property. Reading that fit at i’s own size gives r̂₋ᵢ, and its net price is predicted as P̂ᵢ = sᵢ·r̂₋ᵢ − Aᵢ; Aᵢ carries the prediction from the subject back to comparable i. The percentage error is eᵢ = (P̂ᵢ − Pᵢ)/Pᵢ. The adjustments are ALEX’s and are not refit, so the design measures the weighting step and the dispersion of the adjusted values, not the error in the adjustment model itself. A local estimator validated at the wrong centre is not the estimator being validated, which is why the re-centring is done.

Error measures, defined. Median absolute percentage error MdAPE = medianᵢ |eᵢ| = 3.44%; mean absolute percentage error MAPE = (1/n)Σ|eᵢ| = 6.59%. Confidence interval (empirical): the q-quantile of |eᵢ| by linear interpolation between order statistics, Q(q) = x⃝ₖ⃝ + (h − ⌊h⌋)(x⃝ₖ₊₁⃝ − x⃝ₖ⃝), h = q(n−1), k = ⌊h⌋ (Hyndman–Fan type 7); the 68% band is V̂(1 ± Q(0.68)) = ±7.63%, the 95% band ±14.14%. Forecast standard deviation: FSD = sd(ln(P̂ᵢ/Pᵢ)) with the n−1 divisor = 0.0895; under log-normal error about 68% of outcomes fall within ±FSD in log terms, the convention Zillow and HouseCanary use. RMSLE: √((1/n)Σ(ln(1+P̂ᵢ) − ln(1+Pᵢ))²) = 0.0803, symmetric in proportional over- and under-prediction. Share within 10%: 4 of 5, Wilson 95% score interval [38%, 96%].

Inference at small n, stated plainly. With n = 5 held-out errors, each quantile is an interpolation between two order statistics and the sampling error of every measure is of the same order as the measure. A parametric check: the standard error of the mean indication is SE = sd(vᵢ)/√n, and a 95% interval on it uses Student’s t with n−1 degrees of freedom (t₀.₉₇₅,₂ = 4.303 at n = 3), which is why three sales support a point estimate but not a narrow interval. The measures assume exchangeable, independent comparables; they cannot detect an error common to every comparable (a mispriced submarket, a shared time-index bias), which moves the valuation and the band together. Additional sales within the size standard are the only remedy that narrows them.

The estimator, written out. Each comparable i contributes an adjusted net price per SF yᵢ = (Pᵢ + Aᵢ)/sᵢ, where Pᵢ is its net sale price, Aᵢ the sum of its adjustments other than living area, and sᵢ its floor area. The valuation is that quantity read off at this property’s own coordinates: V̂ = S · β̂₀, where (β̂₀, β̂₁) minimise Σᵢ wᵢ (yᵢ − β₀ − β₁[ln sᵢ − ln S])². This is kernel-weighted local linear regression (Cleveland & Devlin 1988, JASA 83:596; Fan & Gijbels 1996; in housing, Meese & Wallace 1991 and Pace 1993). The weights are wᵢ = 1 − (dᵢ/h)² for dᵢ ≤ h — the Epanechnikov kernel, which minimises the asymptotic mean squared error of this estimator — with dᵢ the matching distance defined in the selection drawer and h the selection caliper itself, fixed before any sale was seen rather than read off the sample (h = 6.683).

What it replaced, and why. Until this version the same indications were combined by a trimmed mean: from five comparables up, the highest and the lowest were discarded on rank alone and the rest averaged with equal weight. It answered a real worry — that one unusual sale should not carry the figure — with the bluntest available instrument. It threw away evidence, it did so on rank rather than on distance, and it gave a sale two doors down exactly the weight of one across the subdivision. Nothing is discarded here. An unusual sale is handled by weighing it less, which is the same remedy applied continuously instead of at a cliff.

The fit on this property. S = 2,104 sf, n = 5, β̂₀ = $196.37 per SF, so V̂ = $413,161. The size slope is β̂₁ = -96.4 dollars per SF per log-foot, so a comparable 10% larger than this property indicates about $9 less per SF before any other difference. The weights sum to one and their effective count is n_eff = (Σwᵢ)²/Σwᵢ² = 4.7 of 5 (Kish). That number, not n, is how many comparables are really speaking; it is printed because a weighted estimator can otherwise claim a sample it does not have. A slope is fitted only when n ≥ 5 and n_eff ≥ 4.

What each comparable actually carried. Distance is the matching distance dᵢ from the selection drawer; the weight is wᵢ/Σw. These are ALEX’s own figures, before any change an agent makes on this page; edit a comparable and the weights recompute in front of you.

Where this number is computed. Twice, deliberately: once on the server in services/comp_match.py and once in the browser, because this page recomputes the valuation the moment an agent edits an adjustment, removes a comparable or adds one. The two implementations are checked against each other on identical inputs and agree to floating-point precision; if they ever disagree, the figure on this page is wrong and should not be used.

Assumptions of the model, each stated so it can be checked. (i) Size. The per-SF step carries value in proportion to living area, and price per square foot ordinarily falls as size rises, so proportionality alone overstates this property where it is larger than its comparables and understates it where it is smaller. The local slope β̂₁ estimates that departure from the comparables in hand and corrects for it; where n_eff < 4 no slope is fitted, proportionality stands unaided, and the ±25% band bounds the resulting bias without removing it. (ii) Additive adjustments. Each non-size difference is a dollar amount independent of the others and of size. (iii) Unequal, declared weights. The εᵢ are assumed independent but NOT identically distributed: a comparable further from this property in the matching metric is taken to be noisier evidence and is weighted down by the kernel accordingly. This replaces the exchangeability the equal-weighted average required. What it assumes instead is that matching distance is a good proxy for that noise — monotone and correctly scaled. Each comparable’s weight is printed, so a reader can judge that assumption rather than take it. (iv) The net price is right. Pᵢ uses the seller-paid closing costs and repair amount as recorded in the MLS concession fields; a concession recorded nowhere, or recorded wrongly, is carried as recorded. (v) One time path. Each comparable is adjusted to the latest index month by the repeat-sales factor, applied to land and structure alike.

What the model cannot detect. Any feature of this house that none of the adjustment lines measures (condition not captured in the listing, layout, noise, a view the data do not record) is outside Aᵢ, and if the comparables share it, it is also invisible to every error measure in this drawer.

Range — the lowest and the highest, and the weighting inside it

How the two ends are built. Each comparable’s net sale price Pᵢ plus its adjustments to this property Aᵢ, divided by its own living area sᵢ, is its adjusted value per SF; multiplied by this property’s 2,104 SF it is that comparable’s indication Iᵢ = (Pᵢ + Aᵢ) / sᵢ × S. The cell reports minᵢ Iᵢ and maxᵢ Iᵢ, each adjusted to the same basis as the figure above by (v + R) / (1 − c) — R the repair credit, c the closing-cost share — and rounded to $500. The plain living-area dollar line is left out of Aᵢ, because the per-SF step already carries size; adjustments for the quality of the space, such as second-floor area, stay in.

The ends are NOT weighted. The valuation is. This is the distinction to hold on to. The two ends are what single comparables say, each on its own, and no weighting is applied to them — a comparable carrying 6% of the weight still sets the low end if it is the lowest. Weighting them would narrow the range toward the answer and hide exactly the disagreement this cell exists to show. What the weighting does is decide where the valuation sits between those ends.

The weighting, in full. Every comparable that survives selection is used — nothing is discarded — and each is weighted by how near it is to this property in the matching metric described in the selection drawer. The weight is wᵢ = 1 − (dᵢ/h)², the Epanechnikov kernel, where dᵢ is that comparable’s distance from this property and h is the bandwidth, here 6.683. Three properties of that formula matter:

(i) It is a curve, not a cliff. A comparable does not count fully and then stop counting. Weight falls away smoothly with distance, so a sale that is slightly further off is worth slightly less, not nothing.

(ii) The bandwidth is fixed before the sales are seen. h is the selection caliper itself, not a number read off this set. A bandwidth chosen from the data can be tuned, knowingly or not, until the answer looks right; this one cannot, because it was settled before any comparable was chosen.

(iii) Epanechnikov is the minimum-variance kernel (Epanechnikov 1969), meaning that among all kernel shapes it gives the smallest expected squared error for this estimator. It is also gentler than the tricube shape used in classical LOESS, which matters at these sample sizes: on an earlier build tricube put 41% of the weight on one sale and 1.8% on another, which is a six-comparable valuation resting on two.

How much is really speaking. Because the weights are unequal, the count of comparables overstates the evidence. The honest count is Kish’s effective sample size, n_eff = (Σwᵢ)² / Σwᵢ², which here is 4.7 of 5. That figure, not 5, is what the error measures should be read against. Each comparable’s own weight is printed in the statistical appendix, so the weighting can be checked rather than taken on trust.

The weighted interval, for contrast. The range in the cell is the spread of the raw evidence. The weighted fit also produces an interval of its own around the valuation: $387,838 to $438,490 at one standard error, and $346,051 to $480,277 at roughly 95%. These are narrower than the raw range because they describe uncertainty about the fitted value, not the disagreement among the comparables. Both are printed because they answer different questions, and quoting either as though it were the other would overstate what is known.

What it is and is not. Two readings of the same 5 indications the valuation is fitted through. The low end is the least any one comparable supports for this house and the high end the most. Neither is a confidence interval and neither carries a probability. With 5 comparables both ends are extremes of a very small sample and will move as evidence is added — an extreme is the least stable statistic a small sample has. For a statement carrying a probability, use the error band in the Confidence card.

Why per SF and not per house. The comparables are different sizes. Their adjusted totals would answer “what did those houses sell for”, which is not a value for this property. Dividing by each comparable’s size and re-multiplying by this property’s answers the question actually asked, and it is why the plain living-area dollar line is kept out of Aᵢ — otherwise size would be counted twice.

It moves when the agent works. Every figure here is recomputed in the page from the comparables as they currently stand, including the agent’s adjustments, additions and removals. The server’s own first pass is not what you are reading once an agent has touched a line.

Asking price

What this is. The current asking price as the MLS carries it. It is a datum, not an estimate: it has no error, because it is not measuring anything. It is what the seller is asking.

Why it is not evidence of value. An asking price is one party’s opening position. Across the comparable pool the median sale closed at 98.9% of the asking price, and 64% of those sellers had already reduced before they sold — which is why this report values the property from closed sales and reports the asking price beside that valuation rather than inside it.

Days on market. 6 days as counted from the listing contract date. The feed’s own days-on-market field resets when a price changes, so it understates time on market for any property that has been reduced; this report does not use it.

Confidence — the error band, FSD and RMSLE

How it is measured. Leave-one-out cross-validation on this property’s own comparable set: each of the 5 comparables is removed in turn and the fit is re-run without it — re-centred on that sale, with the kernel weights recomputed as distances from it — then read at its own size and adjusted back to a net sale price, less its own adjustments, and compared with what it actually sold for. Every number below comes from those 5 held-out errors — none of it is a published benchmark or a figure carried over from another property.

Confidence level and band. At the 68% level, ±7.63% ($381,627 to $444,695). At the 95% level, ±14.14% ($354,756 to $471,566). These are empirical quantiles of the held-out absolute percentage errors — the 68th and 95th percentile of what the errors actually were — not a normal interval around the estimate. At 5 observations the 95% figure rests on the largest error or two and should be read as indicative; the 68% figure is the more stable of the two.

FSD and RMSLE on this property. FSD 0.0895 — on the vendor convention of 1 − FSD that reads 0.9105, and in dollars ±$36,988. RMSLE 0.0803, over the same 5 held-out pairs. Both are defined under their own cards at the head of this report. FSD is reported beside, never instead of, the error band above: it assumes a log-normal shape that 5 points cannot confirm.

Error distribution. Median absolute percentage error 3.44%; mean 6.59%; worst single error 15.35%. 4 of 5 held-out valuations landed within 10% (Wilson 95% interval 38%–96%), 5 of 5 within 20%. The mean sitting above the median is the ordinary sign of a right-skewed error distribution: most valuations are close, a few are not.

What this does not claim. The errors are measured on the same comparables that built the valuation, in the same submarket, over the same period. They describe how well this method reproduces these sales; they are not a guarantee about the sale price of this house, and they cannot detect an error shared by every comparable in the set — a mispriced submarket moves the valuation and the error band together. With 5 observations, treat every figure in this drawer as an estimate with its own uncertainty.

Evidence — the comparable set

What is being counted. 5 closed sales used as comparables. Every valuation figure in this report is built from these 5; no other sale, model output or vendor estimate enters the number.

How they are combined. Each comparable’s net sale price is adjusted for every difference from this property except size; the adjusted net is divided by that comparable’s living area to give its adjusted value per SF, and that is multiplied by this property’s 2,104 SF. The valuation is the average of those indications, with the median reported beside it. Only comparables whose living area is within ±25% of this property’s are used — the appraisal size standard — unless that would leave fewer than three.

Why 5 is a small number, stated plainly. With 5 observations the average has real sampling uncertainty — each comparable moves it by a full 1/5 of its own error — the median and maximum beside it are read from the same small sample, and where cross-validation was possible every accuracy figure above rests on 5 held-out points. The defensible reading is that this is the best available evidence for this property, not that it is precise.

Selection. All within Sierra Vista

What the chart shows

Each estimate as a bar on one money scale, with its published range shown behind it where the vendor publishes one. ALEX’s valuation is the crimson bar — the same figure as the head of this report. The gold bar is that same valuation grossed to a contract price, which is the basis the outside estimates quote on and the only basis on which they can honestly be compared with ours.

The outside estimates below were not used to produce our number. Each “vs ALEX” percentage compares that vendor with $414,051 — our net figure grossed to a contract price by the neighbourhood ratio described in the drawer below — not with the figure at the head of this report, because the vendors publish contract-price estimates and a net price is not the same quantity. They are here so you can see what else is being said about this house. Each is a contract price, and each is compared with the ALEX figure above.

How close any model can get

There is a floor, around ±5%. No model can reliably predict a single sale much closer, because sales themselves disagree — the same house listed twice in one month will not fetch the same price. Different buyers, different negotiation, different day. That scatter is how houses are sold, not a flaw in any model, and more data will not remove it. Treat any accuracy claim much tighter than ±5% on one property with suspicion.

What we will and will not claim about that floor. The ±5% figure above is a judgement about transaction noise, not a published result we can cite, and this report does not rest on it: nothing here is measured against 5% or against any industry target. What is measurable is on this page — the held-out error on this property and the population figures in Cross Validation — and that is the only standard this valuation asks to be judged against.

Why these are benchmarks and not evidence

The vendor models are proprietary. Zillow, HouseCanary and Cotality — the company that acquired CoreLogic — publish neither their methods, their parameters nor their data, and their accuracy figures are self-scored on samples they choose. Nobody outside those companies can reproduce a number, test an interval, or prove any of it wrong — which is the minimum before a figure counts as a defensible statistic. Good commercial products; not evidence in the sense this report uses the word.

This does not make the vendor numbers useless. We use them as benchmarks. We do not include them in our valuation model.

How the comparison in the table is computed

What each number in the table above is, and the arithmetic that produced it.

Notation. V̂ the net valuation, ρ̂ the neighbourhood median of net ÷ close (Sierra Vista, n = 34, ρ̂ = 0.9979), 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 = $414,051; HouseCanary +3.2%; Zillow −54.9%; the county roll −6.5%. Against the asking price, 100(G − list)/list = −1.4%.

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 (8.95%) 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 SF — 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 90% confidence reported for this property corresponds to an FSD of 0.10. 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 8.95% 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 five 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.

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 $357,000 and $483,000 (the band actually observed runs $359,000 to $482,500), closed August 18, 2025 through August 14, 2026: 170 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 170. 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 = 147.8 against 170 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 32.0% [25.1%, 39.9%]; had cut the price 63.6% [55.5%, 70.9%]; paid closing costs 54.4% [46.4%, 62.2%]; credited repairs 24.5% [18.3%, 32.0%]. 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 = 147.8 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 = 1.37%, 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 7 days on market, closed August 18, 2025 to August 14, 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.

Market timing: adjusting a past sale to today

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

How the land adjustment is computed

Model. Land is priced at a constant rate per SF of lot. For comparable i the land line is aᵢ^lot = (L − ℓᵢ) · λ, with L this property’s MLS lot size (17,437 SF), ℓᵢ the comparable’s MLS lot size, and λ = land value ÷ (acres × 43,560) from this property’s own county record. 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 and limits

Assumptions. (i) Linearity. Every SF 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. No interval is attached to λ: the county publishes none, and none is invented.

How to read the columns

The columns run in the order the arithmetic runs. The closed price, less what the seller paid toward the buyer’s closing costs, less any repair credit, is the net sale price. The market trend then adjusts that sale from its closing date to today on the repeat-sales index — shown in dollars and as a share of the net — giving the time-adjusted net sale price. Divided by that house’s own living area, it becomes the time-adjusted net sale price per square foot in the final column. A sale that closed last month barely moves; one that closed a year ago moves by whatever this market did in that year.

Each sale in detail, with its adjustments

Where the values come from

What the roll is. Values are the Williamson CAD certified market roll for parcel R098324 (SIERRA VISTA SEC 2, BLOCK O, LOT 10): 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.

Splitting the change between land and building

“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 −$2,500 and improvement +$4,103, 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.

Comparing this parcel with its peers

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.

How the peer figures are built. 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 −5.5% to +2.7%). Unit values compare land per acre and improvement per SF with the neighborhood median among parcels carrying those measures. Taxing units: Williamson CAD (CAD); City of Georgetown (CGT); Williamson CO (GWI); Wmsn CO FM/RD (RFM); Georgetown ISD (SGT).

The tax figures

The effective rate. 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.

The annual tax figure on the header, in full. The county market value of $387,192 for 2026, as assessed by WCAD, multiplied by the combined rate of 1.82%, gives $7,037. The combined rate is the sum of every jurisdiction levying on this parcel — county, city, school district and any special district — which is why it is quoted as one number and not attributed to any one of them. Two things move a real bill away from it: an exemption the current owner holds, which is not carried to a buyer automatically and in some cases not at all, and a reassessment, since the market value shown is the roll for 2026 and the roll is set once a year. The figure is what the parcel would be taxed at on today’s roll with no exemption, which is the only version of it that is comparable between properties.

The arithmetic

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 = 21.3%. The effective rate is τ = annual tax ÷ M₂₀₂₆ = 1.82%. 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.