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What the method is called

Comparables are chosen by Mahalanobis-metric nearest-neighbor matching with calipers (a caliper is a maximum allowed difference), and the valuation is a kernel-weighted local linear regression — a local polynomial fit, the same family as LOESS — evaluated at this property. Both run inside ALEX’s valuation engine.

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

The search starts as close to this property as the market allows. It tries the same street within its subdivision, then the same phase or section, then the subdivision family (every section and spelling of its name in this city, treated as one place). Only when the tighter area holds too few usable sales does it widen, to rings of half a mile out to five miles, and then to the ZIP code. 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, where the market area holds enough sales to measure it, corrected for the fact that they move together. Bigger houses tend to be newer and to sit on different lots; a plain straight-line (Euclidean) distance would count what is largely one difference several times over. 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. (A bandwidth is the distance at which a sale stops counting.) Among non-negative kernels it is the one that minimizes 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 matters at these sample sizes. In testing 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 minimizes 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 size slope: measured on the wider market, read at these comparables

Price per SF is not flat across sizes: a larger house of the same kind usually fetches less per SF. The model allows for this with a size slope, the change in price per SF for each unit change in the logarithm of living area, and each comparable is carried to this property’s size along it. A regression on the comparables alone has to estimate two things from five or six sales: the level, this property’s price per SF at its own size, and the slope. Five or six sales determine a level well and a slope badly. In ALEX’s backtest of October 7, 2026, slopes fitted on the comparables alone had a median standard error of $74 per SF per log-unit of living area against a median slope of −$125, so the uncertainty was more than half the estimate; and where the house being valued was larger or smaller than every comparable, that poorly determined slope was extrapolated beyond the evidence.

The slope is therefore estimated on a wider set of sales and held fixed, while the level is still read from the comparables with their kernel weights. This is the mixed, or semiparametric, form of geographically weighted regression: a coefficient that the local sample cannot pin down is estimated over a wider area, and the coefficients the local sample can carry stay local (Fotheringham, Brunsdon & Charlton, Geographically Weighted Regression, Wiley, 2002). The wider set is the first of the following that holds at least 25 usable sales: this property’s subdivision family in its city (every section and spelling of the subdivision’s name, together with the exact subdivision); otherwise every sale within 2 miles; otherwise the whole market area searched for this valuation. A sale is usable if it closed within the last 24 months, its living area is within 40% of this property’s, and its year built and lot size are recorded. The slope is the partial ordinary-least-squares coefficient of net price per SF on log living area, with year built, log lot size, bedrooms plus half the bathrooms, and months since sale held constant, so that it measures size rather than the newer construction or larger lots that tend to come with it. Where no set qualifies, the slope is fitted on the comparables themselves, as before; where even that is not supported (fewer than five comparables, or an effective sample size below four), the fit is the kernel-weighted mean of price per SF.

On this property. This valuation’s fit was fixed before the market slope was introduced on October 7, 2026; its size slope, -92.2, was fitted on the five comparables themselves and is kept as fitted.

What it changed, measured. The test used 264 Williamson and Travis County single-family sales that closed between April 7 and October 6, 2026. Each was valued as of its own closing date, from earlier sales only. The market slope, together with the hold described next, lowered the median absolute percentage error from 7.06% to 6.10%. That is a paired difference of −0.96 points, 95% bootstrap interval −1.74 to −0.11 (ALEX backtest, October 7, 2026). The combination was chosen from about eighteen variants evaluated on the same sales, so the improvement is probably somewhat overstated. The regression’s controls are not the engine’s dollar adjustments, so an effect that moves with size, such as room count or lot, can be counted in both places; the backtest measures the method with that overlap in it rather than assuming it away.

Holding the valuation inside the evidence

Each comparable, adjusted for every difference but size and restated at this property’s size at its own price per SF, indicates a value for this house; the Traditional Arithmetic Model’s minimum and maximum are the lowest and highest of those indications. The statistical model then carries each indication along the size slope and takes the kernel-weighted average. When this house is larger or smaller than every comparable, the carry moves every indication in the same direction, and the weighted average can land above the highest indication or below the lowest. A valuation there is one that no comparable supports on its own. The committed valuation is therefore held inside the range of the indications: if the weighted average lies outside it, the valuation is set to the nearer end, and this report states the figure it replaced. The same rule is applied on the server, on this page whenever an agent edits a comparable, and in the executive summary.

The rule has a measured cost. In the same backtest, the market slope without the hold placed 10.2% of valuations outside their comparables’ indications and had the smaller errors in the tail: its mean absolute percentage error was 1.44 points below the previous method (95% interval 0.64 to 2.34), against 1.09 points with the hold (0.38 to 1.87). The hold gives up part of that gain so that every valuation stays within its evidence.

On this property. The hold does not bind: the weighted average, $417,312, lies within the indications, $407,593 to $484,299.

Transparent, and testable

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. Testable because it is an estimator with stated assumptions whose accuracy is measured by predicting each comparable from the others, 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 error band built from it — is set out in The statistics.

The VA appraisal and the Notice of Value

The VA assigns the appraiser; neither the lender nor the agents choose one. The appraiser’s opinion of value is issued as a Notice of Value, which states the “reasonable value” on which the VA guaranty is based. The appraiser also checks the house against the VA’s Minimum Property Requirements, so a condition item can become a repair that must be completed before closing.

If the appraisal may come in low: the Tidewater notice

When the lender names a point of contact, a VA appraiser who expects the value to come in below the contract price must notify that contact before completing the appraisal. The point of contact then has 2 working days to submit additional closed sales, and the appraisal includes a “Tidewater” addendum stating that the process was used (VA Circular 26-03-11). The closed sales in this report are the evidence Diane would submit at that point.

The VA funding fee

On a purchase with 0% down, the fee is 2.15% of the loan on a first use of the benefit and 3.3% on any later use: $9,028 or $13,857 on this $419,900 loan. The fee may be financed into the loan or paid at closing. It is not charged to a veteran who receives, or is eligible for, VA compensation for a service-connected disability; to a surviving spouse who receives Dependency and Indemnity Compensation; or to an active-duty service member who has been awarded the Purple Heart on or before the closing date. No fee was entered on the request sheet, so the loan figures above do not include one. Source: va.gov, VA funding fee and closing costs.

Seller concessions

The VA limits seller concessions to 4% of the property’s reasonable value, the figure on the Notice of Value. That value is not known until the appraisal is issued, so this report states the rule rather than a dollar limit.

USDA and FHA: county limits and the most you could pay

All loan types

Conventional. A loan that no government agency insures or guarantees. A conforming conventional loan is one Fannie Mae or Freddie Mac may buy. For 2026 the one-unit limit is $832,750 outside the high-cost areas the Federal Housing Finance Agency designates, and up to $1,249,125 inside them; FHFA publishes each county’s limit. With less than 20% down, the lender may require private mortgage insurance (PMI). You may ask the servicer to cancel PMI once the balance is scheduled to reach 80% of the home’s original value, and the servicer must end it when the balance is scheduled to reach 78%, provided you are current on the payments. Sources: FHFA, 2026 conforming loan limit values (news release, 11/25/2025); Consumer Financial Protection Bureau (Homeowners Protection Act).

FHA. A loan insured by the Federal Housing Administration. The minimum down payment is 3.5% with a credit score of 580 or higher, and 10% with a score from 500 to 579. The borrower pays an upfront mortgage insurance premium of 1.75% of the base loan and an annual premium paid monthly. The loan amount is limited by county: the 2026 one-unit limits range from $541,287 to $1,249,125. The seller may pay up to 6% of the price toward your costs. An FHA-approved appraiser checks the house against HUD’s property requirements. Sources: HUD Mortgagee Letter 2010-29, carried into Handbook 4000.1; HUD Mortgagee Letter 2023-05 (Handbook 4000.1, Appendix 1.0); HUD Mortgagee Letter 2025-23 and HUD's CY2026 FHA forward mortgage limit file.

VA. A loan guaranteed by the Department of Veterans Affairs for an eligible veteran, service member or surviving spouse. With full entitlement there is no VA loan limit, provided the borrower qualifies for the loan and the appraisal supports the price, and in most cases no down payment is required. With no down payment the funding fee is 2.15% of the loan on a first use and 3.3% on later uses; veterans receiving VA disability compensation and certain others are exempt. Seller concessions are capped at 4% of the value on the VA’s Notice of Value, issued by an appraiser the VA assigns. Sources: va.gov, VA funding fee and closing costs; va.gov, VA home loan limits.

USDA. A loan guaranteed by USDA Rural Development under its Single Family Housing Guaranteed Loan Program. USDA defines the eligible areas and sets household income limits; the lender checks both against USDA’s published eligibility maps and limits. No down payment is required. USDA charges an upfront guarantee fee and an annual fee; the county’s income limits, the fees and the estimator above give the figures and their sources.

Jumbo. A conventional loan larger than the county’s conforming limit ($832,750 for one unit outside high-cost areas in 2026). Fannie Mae and Freddie Mac cannot buy it, so each lender sets its own down payment, credit and cash-reserve requirements, and its interest rate can differ from that of a conforming loan.

Cash. No loan: no lender appraisal, no mortgage insurance and no loan fees, and the contract has no financing contingency. You may still order an appraisal and inspections at your own expense.

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. FSD is the measure automated valuation model (AVM) providers commonly publish with their estimates, so it can be compared with theirs in definition — 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 far off the predictions were across all the held-out comparables, treating a miss of a given proportion the same whether it was high or low. 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. 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. PPE_k = (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 and band here is computed for ALEX’s valuation of $417,312 — 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: each of the five sales was set aside in turn, its net sale price was predicted by this same method from the other four alone, and the prediction was compared with what that sale actually netted — five tests, one for each sale. This is called leave-one-out cross-validation.

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 neighborhood 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 three ways:

• Estimator: a median of a ratio, against a weighted mean of a share.
• Pool: a subdivision, or its city, over 24 months, against resales in this property’s ZIP code asking within 15% of its price, over 12 months.
• 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 -1.15 percentage points of the contract price (0.21% against 1.36%). 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 page’s closing-cost control uses a third. Where this page converts the valuation to a contract price from its closing-cost control, it uses C = (V̂ + R)/(1 − c), rounded to $500, with c the closing-cost share and R the repair credit set in that 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 = $417,312 ÷ 0.9979 = $418,211.

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 neighboring 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-neighbor 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 an earlier cascade of fixed search criteria 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 (bank-owned (REO), short sale, auction, HUD, corporate-owned and probate sales, identified from the MLS listing conditions and the listing remarks), sales in fair or poor condition, sales in a FEMA flood zone, sales whose net sale price is more than ±20% from this property’s asking price (where it has one), and this property’s own earlier sale. That earlier sale can be readmitted only when fewer than three other comparables are available, and then only if it was arm’s length, closed at least 12 months ago and can be carried to today on the price index.

Step 2 — admissibility. These are the differences a distance must never be allowed to trade away. Each is categorical: a two-story house is not a one-story 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. First the same street in this subdivision, then the same phase or section, then the subdivision. The subdivision is taken as every subdivision sharing its name in this city. So a “Serenada West” sits with “Serenada” and “Serenada Estates”: the distinction between them is a platting artifact, not a market boundary. After the subdivision come 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 sweeps 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. Counting eligible sales rather than candidates also corrects an old fault: the earlier 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 inflated slightly (5%) before inversion, a simple form of the shrinkage idea in Ledoit & Wolf (2004), so the inversion stays stable; where the market area holds fewer than five sales per covariate the off-diagonal terms are dropped and the measure becomes standardized Euclidean distance, which is the same statistic when the covariates are uncorrelated. The basis line records which was used.
Mahalanobis distance on 6 covariates (metric from 228 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. 228 closed sales survived step 1, 71 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 and gave it weight in 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 neighborhood. 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 that holds fewer than five, the band is widened to ±30% and then ±35% only as far as needed, and if fewer than three remain even then, every comparable with a known living area and net price is used; 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 favors agreement. The population figures in this section, measured on a blind holdout of sales the model never saw, are the more conservative answer to 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 − τ/3)) for τ < 3 (the same street, the same phase, the subdivision) 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 uncertainty this report measures is the held-out error and the bands built from it, 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 2026-03-30 and test on the 6 months after it, so no sale in the test set was seen in any form during fitting. The test set holds 19,621 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, 68th-percentile miss ±7.63%, from five held-out comparables. Specific to this house, and thin: five observations describe this comparable set accurately and generalize weakly.

2. This model, across its blind holdout. MdAPE 8.19%, MAPE 11.45%, RMSLE 0.1652 over 19,621 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. As self-reported by each vendor (figures they revise from time to time, not independently verified here): HouseCanary, national MdAPE 2.8% over 1,994,203 transactions internally and 2.9% on a blind third-party test; Zillow, median error 1.79% for homes on the market and 7.20% off the 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 use the list price as an input, which is the point made in the Benchmarks section.

What a standard would need to specify to be usable here. The forthcoming paper will presumably settle five questions:

• 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;
• whether an interval must be calibrated: whether a stated 68% interval must actually contain the outcome 68% of the time.

The last is materially stricter than a median error threshold. It is also the one most AVM disclosures avoid.

Where this report already goes beyond common practice, whatever the standard turns out to be: the comparables are named, every adjustment is itemized 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-centered 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-centered 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 in Part one 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 normalization. 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: with a handful of observations the 95th percentile is interpolated between the two largest errors, so it is an indication of the worst misses, not an observed exceedance rate. 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. These bands are therefore labeled error bands, not confidence or prediction intervals: they describe how far the held-out predictions missed, and no coverage probability for this property’s sale price is claimed.

RMSLE. RMSLE = [n⁻¹ Σ (ln(1+ŷᵢ) − ln(1+yᵢ))²]^1/2. Squaring in log space penalizes proportional rather than absolute error, which limits the influence of a single large dollar residual relative to RMSE. It is asymmetric in levels: under-prediction is penalized more heavily than over-prediction of the same absolute size, since |ln(1−δ)| > ln(1+δ). The 1+ offset is negligible at these magnitudes. RMSLE approximates a typical proportional error, but its main use is to rank methods on the same sales; quoted alone it says little.

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 favors 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 artifact 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 8.19%, RMSLE 0.1652 over a blind holdout of 19,621 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 checked. Nothing in this report is a proprietary formula whose behavior cannot be examined.

Two of these are ours to defend, rather than merely to cite. First, the distance caliper is set at twice the chi-square median. The subject and the comparable are two draws, so their difference carries twice the covariance. Second, the kernel bandwidth is the caliper itself, h = √(2χ²_6,0.5) ≈ 3.27, rather than a bandwidth read off the sample, so it is fixed before any sale is seen. The one exception: when the nearest available comparables lie past the caliper, the bandwidth is widened to d_max/0.75 so the furthest one is down-weighted rather than given zero weight. 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. After adjustment, each comparable’s value per SF (Pᵢ + Aᵢ) / sᵢ is taken to equal this property’s value per SF, plus a smooth allowance for the difference in size (the fitted size slope, below), plus comparable-specific error with mean zero. The raw indication for the subject is vᵢ = S·(Pᵢ + Aᵢ)/sᵢ. Size enters through the ratio and the slope, not through a dollar line, so a size difference is priced once.

Estimators. The Traditional Arithmetic row is the plain mean (1/n) Σᵢ vᵢ and the ordinary median of the vᵢ; 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%. The valuation itself is not that mean: it is the kernel-weighted local linear fit written out below, which equals the weighted mean of the size-carried indications shown in the ALEX AI Statistical Model row. Eligibility is the appraisal size standard |sᵢ/S − 1| ≤ 0.25, stepped out to 30% and 35% only as far as needed to reach five sales, and waived if fewer than three remain. Where the page converts V̂ to a contract price, it uses 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-centered 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 center is not the estimator being validated, which is why the re-centering 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%. This property’s own percentiles (diagnostic): 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); here Q(0.68) = 7.63% and Q(0.95) = 14.14%. They do not set the band: from 5 leave-one-out residuals a 68th percentile cannot be estimated with useful precision, and jackknife+ guarantees only 1 − 2α coverage from such residuals (Barber, Candès, Ramdas & Tibshirani 2021). Error bands (split conformal, calibrated). The same comparable engine valued m = 145 past Williamson County sales, each as of its own closing date with only earlier sales in its pool. With their absolute percentage errors sorted ascending, the (1 − α) band is the order statistic q̂ = |e|⃝⌈(m+1)(1−α)⌉⃝ (Vovk, Gammerman & Shafer 2005; Lei, G’Sell, Rinaldo, Tibshirani & Wasserman 2018). If this sale is exchangeable with the calibration sales, 1 − α ≤ P(|e| ≤ q̂) ≤ 1 − α + 1/(m+1). A county with at least 100 calibration sales gets its own quantile (Mondrian conformal prediction, Vovk 2012), otherwise the counties are pooled. Here q̂(0.68) = 8.08% (distribution-free 95% interval for the population quantile 6.4–9.6%, Conover 1999) and q̂(0.95) = 19.70% (15.6–23.2%), applied as V̂(1 ± q̂). Out-of-time check: calibrated once on the earlier half of the sales, the 68% band covered 84 of the 128 later sales and the 95% band 127. Banded the way the report bands a sale — each later sale from every sale that closed before it in its own county, refreshed sale by sale — the 68% band covered 83 of 128 (64.8%) and the 95% band 123 (96.1%). The fixed half-split understates coverage because it freezes the band at mid-sample while later errors drift; refreshed, the 68% band runs within the sampling error of a 128-sale check (a binomial standard error of about 4 points) of its nominal level. A recency-weighted band (non-exchangeable split conformal, Barber, Candès, Ramdas & Tibshirani 2023, weights halving every 60 days) covered 85 and 123: two more of 128 at 68%, within that error and with the half-life chosen on these same sales, so it is reported and not adopted. The guarantee holds on average over sales like this one, not conditionally on this house, and it describes this estimator only; it is re-measured whenever the engine changes. 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 AVM providers use when they publish an FSD. 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 on the arithmetic mean: its standard error 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 weighted fit’s own interval is given under Range, below. 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) minimize 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 minimizes the asymptotic mean squared error of this estimator among non-negative kernels — with dᵢ the matching distance defined in the selection section above and h the selection caliper itself, fixed before any sale was seen rather than read off the sample (widened only when comparables lie past the caliper) (h = 6.096).

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 = $197.41 per SF, so V̂ = $417,312. The size slope is β̂₁ = -92.2 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 = 4.6 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 on the comparables only when n ≥ 5 and n_eff ≥ 4; the market slope, estimated on its own sales, needs neither.

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 ALEX’s valuation engine, 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 written to the same formulas so that, on identical inputs, they agree; until an agent edits something, the page shows the server’s figure.

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 slope β̂₁ estimates that departure and corrects for it. It is measured on the wider market where at least 25 usable sales allow, which assumes the size effect there holds at this property; otherwise it is measured on the comparables in hand, and where n_eff < 4 no slope is fitted, proportionality stands unaided, and the ±25% band bounds the resulting bias without removing it. Whatever the slope, the valuation is held inside the range of the comparables’ indications. (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 Minimum and Maximum cards in the Traditional Arithmetic row are minᵢ Iᵢ and maxᵢ Iᵢ, on the same net basis as the valuation. 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 6.096. 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 optimal kernel (Epanechnikov 1969), meaning that among non-negative kernel shapes it gives the smallest asymptotic mean 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 4.6 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: $389,728 to $440,977 at 68%, and $347,447 to $483,258 at 95%, using Student’s t with degrees of freedom based on the effective sample size. These are typically 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 how far this method typically misses, see the 68% Error Band in the row of statistics above.

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. The minimum, average, median and maximum cards are recomputed in the page from the comparables as they currently stand, including the agent’s adjustments, additions and removals. The held-out error measures are not; they describe ALEX’s own set.

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 negotiation pool (recent resales near this property in its price range), the recency-weighted median sale closed at 98.9% of the asking price, and 70% 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. 15 days. The report takes the largest of three figures: the MLS cumulative days on market, the days since the listing contract date, and the MLS days-on-market field. The last stops counting at the listing’s most recent change, such as a price reduction, so on its own it can understate how long a property has been for sale.

Accuracy on this property — 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. The fit is re-centered on that sale, with the kernel weights recomputed as distances from it. It is then read at that sale’s own size and adjusted back to a net sale price, less its own adjustments. That figure is compared with what the sale actually brought. 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.

The error bands. The bands are not taken from these five tests, which are too few to place a 68th percentile. They are calibrated on 145 past Williamson County sales valued by this same method: the 68% error band is ±8.08% ($383,593 to $451,031 when applied to this valuation) and the 95% error band is ±19.70% ($335,102 to $499,522). On this property’s own tests the 68th and 95th percentiles of the misses are ±7.63% and ±14.14%, a check on whether this comparable set behaves like the calibration sales. The construction is in the statistical appendix.

FSD and RMSLE on this property. FSD 0.0895 — on the convention some AVM providers use for a confidence score, 1 − FSD that reads 0.9105, and in dollars ±$37,360. 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 predictions 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, no active listing and no outside 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 similarity-weighted fit through those indications, read at this property’s size (the ALEX AI Statistical Model average); the plain average and median are reported beside it as the Traditional Arithmetic row. Only comparables whose living area is within ±25% of this property’s are used — the appraisal size standard — stepped out only if needed to reach five, and waived if fewer than three would remain.

Why 5 is a small number, stated plainly. With 5 observations the valuation has real sampling uncertainty — each comparable moves it in proportion to its weight, and the effective number of comparables after weighting is smaller still — the median and extremes 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 $418,211 — our net figure grossed to a contract price by the neighborhood ratio described further down this drawer — 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. The vendor figures are estimates of a contract price; the county figure is a tax-roll market value. Each is compared with the grossed ALEX figure.

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 judgment 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 (formerly 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 neighborhood 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 = $418,211; HouseCanary +2.2%; the county roll −7.4%. Against the asking price, 100(G − list)/list = −0.4%.

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 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: the claim, but not the calculation. Cotality, the third vendor named above, supplied no estimate for this report.³

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 localized price indices; (3) train machine-learning models on time-adjusted historical prices. Models are fitted at census-tract level, borrowing from neighboring tracts where a tract has too few sales to model alone, with neighbors 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 machine-learning models per tract are then fitted to explain that deviation and combined into one estimate. Inputs include data from more than 3,100 county assessors and more than 2,700 county recorders covering 20 years, MLS property 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 forecast standard deviation (FSD), and a caveat it states itself. 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 testing by a third party. 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. HouseCanary reports 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 describes a typical home; it does not describe this particular property and its own comparables. Reading a vendor figure as a promise about this house would be a mistake, and so would judging this report’s figure against a national figure computed on millions of sales.

What this report exposes by contrast. The estimator is stated, the comparables are named with MLS numbers, every adjustment is itemized with its reason, the price index is the repeat-sales regression published by Bailey, Muth and Nourse in 1963, 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 for this report.

The model

Specification. A three-stage ensemble fitted to the natural log of the net sale price (close price less seller-paid closing costs and repair credits), f(x) = a + Σⱼ wⱼ gⱼ(x) + s(lat, lon). Stage 1 is four learners: LightGBM, XGBoost, CatBoost, and Ridge. Stage 2 is a ridge-regression stack whose weights are w = 0.3652 on LightGBM, w = 0.4194 on XGBoost, w = 0.2079 on CatBoost, w = 0.0003 on Ridge, with intercept a = 0.06492. Stage 3, s, is a distance-weighted 25-nearest-neighbor regression on latitude and longitude, fitted to out-of-fold Stage-2 residuals.

Data. 384,015 closed sales on or before 03/30/26, 215 model columns (35 features once category indicators are grouped). Sale prices are restated to March 2026 by a monthly price-per-square-foot index built from the training sales, so the model’s dollars are March 2026 dollars. Model file ensemble-20261008-211134.

Accuracy. On 19,621 sales that closed after 03/30/26 and were never seen in fitting, the median absolute percentage error was 8.19% and 58.4% of estimates fell within 10% of the sale price.

How each effect is computed

Shapley values. Each line is a SHAP value (Lundberg & Lee, 2017): the Shapley (1953) share of the prediction assigned to one feature, the unique attribution that is additive, gives nothing to a feature the model does not use, and treats features symmetrically.

The boosted trees. For LightGBM, XGBoost and CatBoost the values are computed exactly by each library’s native TreeSHAP (Lundberg et al., 2020), which evaluates the expectation over the tree’s own training-path coverage in polynomial time: gⱼ(x) = bⱼ + Σₖ φⱼₖ(x).

The ridge learner. Linear after standardization, so its attribution is exact in closed form with the training mean as the reference: φₖ = βₖ(xₖ − μₖ)/σₖ.

Through the stack. Because Stage 2 is linear in the learners, the ensemble attribution is the weighted sum φₖ = Σⱼ wⱼ φⱼₖ with baseline b = a + Σⱼ wⱼ bⱼ. Stage 3 is reported as its own line, the location residual (-3.83% here). Indicator columns of one category are summed into that category.

Additivity check. b + Σₖ φₖ + s = f(x) holds by construction and is verified for every report: for this property the gap is 4.3e-06 in log price (XGBoost stores its trees in 32-bit floats; the other learners agree to rounding error).

From logs to dollars. The model works in logs, so effects multiply. Dollars are allocated by the logarithmic mean (Vartia, 1976; Ang, 2005): $ₖ = φₖ · (eᶠ − eᵇ) / Σφ, which makes the baseline plus every line equal the estimate to the cent. Each line is then rounded to the dollar and the totals are the sums of the rounded lines.

The prior-sale model

Not used for this property: no closed sale of this parcel in the 1996+ history. The estimate is the base model’s.

Specification. The prior-sale model is the same ensemble refitted on the same sales, cut and settings with four added features: the last prior sale restated to the model’s month, months since it, the count of earlier sales, and an indicator. The repeat-sales index is Case & Shiller’s (1987) weighted estimator, monthly, fitted only to consecutive sales of the same parcel whose second sale closed by the model’s cut. A prior sale counts only if the parcel number looks like an ID, the sale closed at least 31 days before the valuation date, and the record describes the same structure: year built within two years and living area within 20% wherever both records carry them.

Why it is gated. The prior-sale model is used only where such a sale exists; everywhere else the base model is used unchanged, because on properties without a prior sale the refitted model is no better.

The recent-sales correction

What it does. A model fitted once is then used for months, and its misses cluster on the map: where it has recently priced homes too low, it tends to price their neighbors too low as well. The correction moves the estimate by part of the average miss on the nearest recent sales: V = Vₘ · exp(λ · r̄), with r̄ = (1/10) Σⱼ ln(Pⱼ / P̂ⱼ) over the 10 nearest arm’s-length sales the model had not seen in fitting and that closed at least 60 days before this valuation, so they were known when it was made. This property is never one of its own neighbors.

The weight λ. Re-estimated for each valuation date from known sales only: the least-squares slope of each known sale’s miss on the average miss of its own 10 nearest known neighbors (itself excluded), limited to the range 0 to 1. It is the spatial-error coefficient of Anselin (1988) estimated by its neighbor regression.

For this property. 14,579 known sales (closed 03/31/26 to 08/10/26); λ = 0.6249; the 10 nearest sold for +3.57% against the model on average (r̄ = +0.03512); the factor is exp(0.6249 × +0.03512) = 1.02219, a change of +2.22%, or +$8,449.

Measured effect. Checked on every rebuild by applying the same rule, day by day, to the 8,609 arm’s-length sales that closed 06/30/26 to 09/30/26: the median absolute error went from 8.07% to 7.51%, a change of -0.56 points (95% paired bootstrap interval -0.74 to -0.39, 1,000 resamples). The median λ over those days was 0.56.

What these figures are not

Not causal. A SHAP value apportions this model’s output among its inputs. When features are correlated — living area, the tax-assessed value, the taxes and location move together — the trees use them interchangeably and the credit is split according to how the trees happened to split, so one feature can carry credit that belongs to another. No line is the price effect of changing that feature, and none should be quoted as one.

Not a valuation. The estimate is a statistical prediction from listing records, separate from the comparable-sales valuation; it is not inside that valuation’s error band and was not used to produce it. The model dollars are March 2026 dollars; only the recent-sales correction carries information from later sales.

Gaps in the record. Not on this property’s MLS record, and filled with the training median: tax_rate, estimated_taxes, and hoa_fee.

References

Lundberg, S. M. & Lee, S.-I. (2017). A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems 30, 4765–4774.
Lundberg, S. M., Erion, G., Chen, H., DeGrave, A., Prutkin, J. M., Nair, B., Katz, R., Himmelfarb, J., Bansal, N. & Lee, S.-I. (2020). From local explanations to global understanding with explainable AI for trees. Nature Machine Intelligence 2, 56–67.
Shapley, L. S. (1953). A value for n-person games. In Contributions to the Theory of Games II, Annals of Mathematics Studies 28, 307–317.
Vartia, Y. O. (1976). Ideal log-change index numbers. Scandinavian Journal of Statistics 3(3), 121–126.
Ang, B. W. (2005). The LMDI approach to decomposition analysis: a practical guide. Energy Policy 33(7), 867–871.
Case, K. E. & Shiller, R. J. (1987). Prices of single-family homes since 1970: new indexes for four cities. New England Economic Review, Sept./Oct., 45–56.
Anselin, L. (1988). Spatial Econometrics: Methods and Models. Dordrecht: Kluwer.

Starting value

V₀ = $417,312, ALEX’s valuation as printed at the head of this report, to the dollar. The forecast service was given exactly this figure and returned it unchanged; the section is not shown if the two differ. The valuation has its own error: on past sales in Williamson County, the comparable method’s 68% band is ±8.1% and its 95% band ±19.7% (145 sales; split-conformal, see the statistics section). The outlook ranges include that starting error. Each run adds an independent draw of the valuation model’s own log error, centered on zero, measured on 2,445 sales from July 2026, September 2026 that the model valued at 2026-06 without having seen them (construction: b: issue_v2 draws + independent v14 log-error draw (median-centered), scaled about the median by k_h).

Price relative to the area: log(V₀ / m) = -0.158, where m = $488,500, the median net sale price over the three months to the origin in this ZIP code (−14.6%). It is one of the home traits the drift model reads.

Model

For horizon h ∈ {6, 12, 24, 36} months the log change in value is a sum of two independent draws:

log(V_h / V_0) = k_h · (M_h + D_h + E − median) + median, E = valuation error draw

Widening factor k_h, fitted in the consumer calibration and applied about the median: 6 months 0.915 (tested); 12 months 0.815 (tested); 24 months 1.000 (not tested); 36 months 1.000 (not tested).

Market draw M_h. The county distribution is an equal-weight quantile average (Vincentisation) of three forecasts, each with residual-based ranges (method B): no change (random walk); the FHFA purchase-only index’s 12-month growth × h/12; and a Minnesota-prior Bayesian VAR on index growth, mortgage rate, payroll growth and log months of supply with a 60-month half-life. The weights are 1/3 each and are not estimated.

Home drift D_h. A ridge location model with a Gamma-log scale GLM and an empirical standardized shape, fit on repeat sales in the five-county MSA closed before the origin year. Short-hold resales are disproportionately renovated flips, so the home tool takes this home’s relative drift at the median training hold (5.17 years), net of the median there, and applies it pro rata (× h / hold). This home’s relative drift: +1.79% a year.

Chance of a decline = the share of the 2,000 draws with V_h < V₀.

The figures, unrounded

Dollar figures are rounded half-up to $1,000 where they first appear; each change is computed from the rounded figures shown (middle ÷ $417,312 − 1). Chance of a decline is rounded to a whole percent.

Accuracy and back-test

In back-tests on 14,415 Austin-area home sales that closed between September 2025 and August 2026, with each forecast starting from our valuation model's estimate made 6 or 12 months before the sale, the 80% range contained the actual sale price 80% of the time at 6 months and at least 80% at 12 months; the middle estimate was within 12% (6 months) and 11% (12 months) of the sale price for half of the homes. Source: v2/consumer/CALIBRATION.md.

The market model’s own disclosure, verbatim: “v2 accuracy is not yet established prospectively (V2_SPEC.md sec. 7, A4). In the exploratory 2005-2026 replay, forecasts started from the earlier sale price brought forward by the county index had 80% ranges that covered 77% (6 mo), 75% (12 mo), 70% (24 mo) and 63% (36 mo) of later sale prices; 24- and 36-month figures are scenarios, not forecasts.” Those replay ranges were measured with a different starting value (the earlier sale brought forward by the county index), not a valuation like this report’s, and the replay is exploratory: the model was designed after its last years were seen.

Accuracy going forward is being measured on a hash-chained ledger written before the outcomes exist; no prospective result exists yet.

• Tested on 12 monthly forecast dates (March 2025 to February 2026) in a single market period; the 12-month figure rests on 6 of them, whose outcome windows overlap, so the results are not independent draws.
• The range-scaling factors (0.915 at 6 months, 0.815 at 12 months) were fitted on these same dates; held out one date at a time, the 80% range still contained 80% and 80% of sale prices.
• Middle estimates ran low in the test: actual sale prices were a median 9% (6 months) and 6% (12 months) above them. The ranges allow for this only through their width.
• Test starting values came from the valuation model applied to each home as last listed, not from a full report valuation with current details; if a report value is more accurate, these ranges are somewhat wider than needed.
• Only homes that had sold before were tested; new construction was not.
• 24- and 36-month figures are scenarios; their ranges were not tested.

Ledger record

Forecast origin September 2026. Ledger row e79670256f6f64e97b2e54d8819c0a2dec3d3a292bd2502d81c055d1c73cc290, previous row c23a13cc659188367504f3ed30b3c1eeb4fb53cd39d482258a611394e98342f3, issued 2026-10-08T21:09:19-05:00, code 9b35d33b0a16, V2_SPEC.md through A6. Drift model: 279,351 training pairs, fit year 2026, parameter hash b47dd40dd52e870e. Each row is written before any outcome after its origin exists; the forecast here can be re-derived from that row and this home’s traits.

Known weaknesses

• In the replay, 80% ranges held fewer than 80% of outcomes, and fewer the further ahead.
• Forecasts 24 and 36 months ahead missed badly in 2023–2026 in the earlier model; the long-horizon middle runs high in the replay.
• Averaging three forecasts narrows the range when they disagree.
• The model does not see this home’s condition, renovations, or anything after the origin month.

References

Lichtendahl, K. C., Grushka-Cockayne, Y. & Winkler, R. L. (2013). Is it better to average probabilities or quantiles? Management Science 59(7), 1594–1611.
Smith, J. & Wallis, K. F. (2009). A simple explanation of the forecast combination puzzle. Oxford Bulletin of Economics and Statistics 71(3), 331–355.
Giacoletti, M. (2021). Idiosyncratic risk in housing markets. Review of Financial Studies 34(8), 3695–3741.
Bańbura, M., Giannone, D. & Reichlin, L. (2010). Large Bayesian vector auto regressions. Journal of Applied Econometrics 25(1), 71–92.

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. The pool covers listings asking between $357,000 and $483,000 (the band actually observed runs $359,000 to $482,500), closed August 26, 2025 through August 25, 2026: 148 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;
• p_cut = Pr(original list > list), the share that had reduced the asking price before the sale;
• p_C = Pr(C > 0), the share where the seller put something toward the buyer’s closing costs;
• p_R = Pr(R > 0), the share that credited repairs.

All four are properties of this pool, not forecasts for this property. p_C and p_R 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 148. 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 = 129.5 against 148 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 30.7% [23.4%, 39.1%]; had cut the price 70.1% [61.7%, 77.3%]; paid closing costs 56.9% [48.2%, 65.1%]; credited repairs 22.2% [15.9%, 30.1%]. 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 p_cut 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 = 129.5 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 behavior 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 = 1.36%, 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 ZIP 78628, asking price within ±15% of this property’s, at least 15 days on market, closed August 26, 2025 to August 25, 2026 with a 45-day settle window so pending sales cannot enter, and a 12-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 adjustment schedule, because the county has no land rate 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 Central Appraisal District 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 38/62 while the net change can be smaller than either 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 neighborhood 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 neighborhood, 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 neighborhood 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 — normally the current owner’s bill, under the current owner’s exemptions. The effective rate divides that amount by the county market value, so it can sit below the adopted combined rate, and a buyer’s bill can differ.

The annual tax figure on the header, in full. The listing reports $7,037 a year. Divided by the 2026 county market value of $387,192 from WCAD, that is 1.82% — an effective rate, not the adopted rate. The adopted rates of each authority, where published, are shown under “What it is taxed at.” Two things move a buyer’s bill away from the listed figure: the exemptions the current owner holds, which do not carry over to a buyer, and reappraisal, since the roll is set once a year as of January 1.

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 neighborhood 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 Central Appraisal District parcels with both rolls on file.