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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 = 0.0945.

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 0.0847.

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 0.0847. 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: 3.75%. The mean of the same errors (MAPE) is 6.73% and the largest single one is 12.91%.

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 = 3/5 = 60%. 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 23% to 88%. 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 $1,065,936 — 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 Ranch At Brushy Creek (the subject's subdivision) in the last 24 months, n = 75, with a minimum of 15 sales before the level is used at all. Here ρ̂ = 0.9987, an implied seller contribution of 0.13% 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 = 75 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.
• 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; on this property the pool share could not be computed, so no difference between them is stated. 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 = $1,065,936 ÷ 0.9987 = $1,067,324.

Assumptions and limits of ρ̂. The sample is every closed sale with a positive close and net price whose subdivision name begins with Ranch At Brushy Creek, 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 four 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.

Relaxed for this property: View. Applying it would have left no comparable at all, which means that rule has stopped describing this market rather than that the difference stopped mattering. Read the valuation accordingly.

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. Inside this property’s own subdivision — the same street, the same phase and the subdivision as a whole — the window can reach further, back to August 1, 2022, but only after every one of those rungs has failed to fill at 13 and at 24 months. Comparable sales come only from this subdivision; a wider area is searched only when the subdivision holds no eligible sale since August 1, 2022, and the report says so. July 2022 is when this market changed: as mortgage rates rose from 3.1% to 5.5%, July 2022 was the first month ABOR single-family homes no longer sold above their original list price (100.0%, from 104.5% in April) and the median time on market doubled, so sales after it belong to the market that exists today and earlier ones do not. Tested on 142 Williamson and Travis County sales from April to October 2026, each valued only from sales before it, the rule changed the comparables of 13, all of which then came entirely from their own subdivision, and lowered the median absolute error from 5.57% to 5.27% (sales valued within 5% of the price: 43.7% to 47.2%). This report used a 13-month window.

Step 5 — the distance itself. Each eligible sale is placed in a 7-dimensional space — living area (logarithm), year built, lot size (logarithm), distance from this property, in miles, months between the sale and today, bedrooms, and 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 7 covariates (metric from 49 sales in the market area), within Ranch at Brushy Creek, all phases and sections; 6 of the 16 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 ≤ 12.69. 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.

This property, in numbers. 49 closed sales survived step 1, 20 of them admissible under step 2, 6 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. 67 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 67, medium.

Formally. With τ the stopping stratum’s position on a ladder of T strata (0 the tightest), ē the engine’s mean held-out error in percent, ā the mean comparable age in days and ḡ = n⁻¹ Σ 100|Σₖ aᵢₖ|/Pᵢ: f₁ = round(25 − 13τ/(T−1)); f₂ = max(12, 25 − round(ē)); f₃ = max(12, 25 − ⌊ā/15⌋); f₄ = max(12, 25 − round(ḡ)). Over the m factors that could be measured, Q = min(100, round(4Σf/m) + B), with B = round(15(1 − 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 3.75%, FSD 9.45%, RMSLE 0.0847, 68th-percentile miss ±10.17%, 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 6.73% against 3.75% indicates no single dominating residual.

Hit rates. PPE_k = n⁻¹ Σ 1{|ŷᵢ−yᵢ|/yᵢ ≤ k} at k = 0.10 and 0.20 — the empirical CDF of absolute percentage error at two points. On this property: 3 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 3/5 spans roughly [0.23, 0.88].

Bias check. Mean signed error n⁻¹ Σ eᵢ = −0.16%, median signed error −1.09% (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 Standard Arithmetic Model row is the plain mean (1/n) Σᵢ uᵢ and the ordinary median of uᵢ = S·Cᵢ/sᵢ, with Cᵢ the sale price and no adjustment of any kind; 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 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| = 3.75%; mean absolute percentage error MAPE = (1/n)Σ|eᵢ| = 6.73%. 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) = 10.17% and Q(0.95) = 12.86%. 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 = 0.0945; 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) = 0.0847, symmetric in proportional over- and under-prediction. Share within 10%: 3 of 5, Wilson 95% score interval [23%, 88%].

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 = 4.701).

The slope held at the market’s. On this valuation β₁ is not estimated from the comparables. It is fixed at the market slope b̂ₘ, the coefficient on ln s in the ordinary least squares regression y = γ₀ + bₘ(ln s − ln S) + γ₁·year built + γ₂·ln(lot + 1) + γ₃·(beds + ½baths) + γ₄·months since sale + u fitted on m = 7,044 sales in the ABOR market: resales priced $1,000,000 and up, closed since July 2023 (last 24 months, living area within 40% of S). The level is then the weighted mean of the comparables carried to this property’s size along that slope, β̂₀ = Σᵢ wᵢ (yᵢ − b̂ₘ[ln sᵢ − ln S]) / Σᵢ wᵢ, and its standard error carries the slope’s own: SE(β̂₀)² = σ̂²Σᵢ(wᵢ/Σw)² + (x̄ₛ·SE(b̂ₘ))², with x̄ₛ the weighted mean of ln sᵢ − ln S and σ̂² the weighted residual variance on n_eff − 1 degrees of freedom.

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 = 3,714 sf, n = 5, each sale carried to this size by the measured size effect and weighted, so V̂ = ΣwᵢVᵢ = $1,065,936, which is $287.00 per SF. The size slope is the market slope b̂ₘ = -96.4 dollars per SF per log-foot (7,044 sales in the ABOR market: resales priced $1,000,000 and up, closed since July 2023; standard error 59.7), 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 3,714 SF it is that comparable’s indication Iᵢ = (Pᵢ + Aᵢ) / sᵢ × S. The lowest and highest Iᵢ are the two ends, on the same net basis as the valuation. The Traditional Standard Arithmetic Model row’s Minimum and Maximum are simpler: the lowest and highest sale price per SF times this property’s SF, with no adjustments. 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 4.701. 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: $1,005,987 to $1,087,562 at 68%, and $947,310 to $1,146,239 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, reduced from $1,245,000 — a change of -4.02%. 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 a share of its asking price — 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. 74 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. This listing’s MLS status is Withdrawn, and it left the market on October 19, 2026, so the days since the listing contract date are counted to that date, not to the date of this report: a house that is no longer offered for sale is not accumulating time on the market.

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% ($979,808 to $1,152,064 when applied to this valuation) and the 95% error band is ±19.70% ($855,947 to $1,275,925). On this property’s own tests the 68th and 95th percentiles of the misses are ±10.17% and ±12.86%, 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 0.0945 — on the convention some AVM providers use for a confidence score, 1 − FSD that reads 0.9055, and in dollars ±$100,773. RMSLE 0.0847, 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 3.75%; mean 6.73%; worst single error 12.91%. 3 of 5 held-out valuations landed within 10% (Wilson 95% interval 23%–88%), 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 3,714 SF. The valuation is the similarity-weighted fit through those indications, read at this property’s size (the ALEX Model average); the Standard Arithmetic Model row beside it is simpler: each sale price divided by its SF, averaged, times this property’s SF, with no adjustments. 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 Ranch At Brushy Creek

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 $1,067,324 — 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.

Where they disagree with this report, and why

Why their figures sit closer to the asking price. HouseCanary lands 1.8% below the $1,195,000 asking price, Zillow lands 4.5% below the $1,195,000 asking price. This report is 10.7% below it. The reason is simple: they use the asking price; we do not. HouseCanary’s own brief lists MLS “listed prices and contract prices” as inputs and says a new listing triggers an immediate re-valuation. Zillow publishes separate accuracy figures for homes on and off the market: 1.79% median error on-market against 7.20% off, and states that on-market estimates are more accurate because listing details are available. The gap between those two figures is consistent with the asking price informing the on-market estimate. A list price is real information about what a seller wants; it is not independent evidence of value, which is what this report was asked for. Ours uses only what five nearby sales actually sold for.

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 (Ranch At Brushy Creek, n = 75, ρ̂ = 0.9987), 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 = $1,067,324; HouseCanary +10.0%; Zillow +6.9%; the county roll −10.3%. Against the asking price, 100(G − list)/list = −10.7%.

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 (9.45%) 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.” Its published nationwide median errors, on-market and off-market, are quoted above; a median error means half of Zestimates fall within that percentage 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 95% confidence reported for this property corresponds to an FSD of 0.05. 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 9.45% 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.

Market timing: adjusting a past sale to today

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.

What each row means

The house.

• Distance from this house is the straight-line distance from this house to the sale, in miles, with the compass direction the sale lies in.
• Living area is the square footage of living space on each home’s MLS record. It drives the size adjustment further down, so there is no separate dollar line for it.
• Bedrooms is the number of bedrooms on each home’s MLS record, and it sets the Bedroom count line in the adjustments.
• Bathrooms is the number of full baths with the half baths after the point, so 2.1 means two full baths and one half bath, from the MLS record.
• Year built is the year each home was built, from its MLS record. In the adjustments, the Year built line moves the sale by 1% of its net sale price for each year of age difference, with no cap.
• Lot area is the size of each lot in SF, from the lot size on its MLS record. The Lot size line in the adjustments prices the difference.
• Garage is the number of garage spaces on each home’s MLS record. Where the counts differ, a Garage line in the adjustments prices each space of difference as a percentage of the sale’s net price that depends on its price range.
• Levels is the number of stories each home has, as entered on its MLS record.

The sale.

• Listing date is the date the listing contract began on each home’s MLS record.
• Close date is the date each sale closed, as recorded in the MLS for that home.
• Days on market is the number of days each home was on the market, from its MLS record.
• Original list price is the first asking price on each listing. Where the MLS has no original price, the last list price is shown instead.
• Last list price is the final asking price on each listing, after any price changes it had.
• Buyer closing costs paid by the seller is the amount the seller put toward the buyer’s closing costs, as reported in the MLS. It is taken off the sale price.
• Repairs at the buyer’s request is the amount the seller paid for repairs the buyer asked for, as reported in the MLS. It is also taken off the sale price.
• Net sale price is what each home sold for, less the seller-paid closing costs and repairs above. Every adjustment that follows starts from it.

The time adjustment.

• Months from sale to today is how many months the market index carries each sale forward, from the month it closed to the most recent month the index measures.
• Market trend to today is the dollar change in each sale’s net price from its closing month to today, read from ALEX’s repeat-sales index of home prices. The index is the county’s where it has enough sales, otherwise the metro’s.
• Time-adjusted net sale price is the net sale price plus the market trend, so every sale is stated in today’s market.
• Per SF is the time-adjusted net sale price divided by the sale’s own living area, rounded to the dollar.
• Time-adjusted net sale price per SF is the time-adjusted net sale price divided by the sale’s own living area, rounded to the dollar, so sales of different sizes can be compared.

The AI lines.

• Age is priced at what ABOR closed sales show the market pays in this price range: -0.21% of price per year of age. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Updated or remodeled is priced at what ABOR closed sales show the market pays in this price range: +6.3% of price per updated or remodeled home. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Bedroom count is one of the variables ALEX tests for every sale. ABOR closed sales in this price range show no measurable price effect, so the line is $0.
• Full bath is priced at what ABOR closed sales show the market pays in this price range: +2.8% of price per full bath. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Half bath is priced at what ABOR closed sales show the market pays in this price range: +1.2% of price per half bath. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Garage is priced at what ABOR closed sales show the market pays in this price range: +2.5% of price per garage space. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Fireplace is priced at what ABOR closed sales show the market pays in this price range: +1.2% of price per fireplace. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Pool is priced at what ABOR closed sales show the market pays in this price range: +7.9% of price per private pool. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Lot size is priced at what ABOR closed sales show the market pays in this price range: +5.5% of price per doubling of lot area. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Stories is priced at what ABOR closed sales show the market pays in this price range: -2.5% of price per home of two or more stories; -4.4% of price per home of three or more stories. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• View is priced at what ABOR closed sales show the market pays in this price range: +1.7% of price per greenbelt view; +2.4% of price per golf view; +2.3% of price per water view; +1.2% of price per panoramic view. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Cul-de-sac is one of the variables ALEX tests for every sale. ABOR closed sales in this price range show no measurable price effect, so the line is $0.
• Corner lot is priced at what ABOR closed sales show the market pays in this price range: -0.7% of price per corner lot. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Study office is priced at what ABOR closed sales show the market pays in this price range: +1.1% of price per study or office. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Guest suite is priced at what ABOR closed sales show the market pays in this price range: -0.7% of price per guest suite. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Outdoor kitchen is one of the variables ALEX tests for every sale. ABOR closed sales in this price range show no measurable price effect, so the line is $0.
• Patio is priced at what ABOR closed sales show the market pays in this price range: +0.7% of price per covered patio. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Fence is priced at what ABOR closed sales show the market pays in this price range: +1.1% of price per privacy fence. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Foundation is held constant when ALEX measures the other lines but is not applied: its price difference tracks older locations rather than the feature itself, so the line is $0.
• Septic is one of the variables ALEX tests for every sale. ABOR closed sales in this price range show no measurable price effect, so the line is $0.
• Well is one of the variables ALEX tests for every sale. ABOR closed sales in this price range show no measurable price effect, so the line is $0.
• Flood plain is one of the variables ALEX tests for every sale. ABOR closed sales in this price range show no measurable price effect, so the line is $0.
• Solar is one of the variables ALEX tests for every sale. ABOR closed sales in this price range show no measurable price effect, so the line is $0.
• Casita is one of the variables ALEX tests for every sale. ABOR closed sales in this price range show no measurable price effect, so the line is $0.
• Outbuilding is one of the variables ALEX tests for every sale. ABOR closed sales in this price range show no measurable price effect, so the line is $0.
• Visible disrepair is priced at what ABOR closed sales show the market pays in this price range: -4.3% of price per home whose photos show visible disrepair. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Kitchen is priced at what ABOR closed sales show the market pays in this price range: +2.6% of price per renovated kitchen in the photos; -8.4% of price per dated kitchen in the photos. The line is that share of the sale's time-adjusted net price, for the difference between this home and the sale.
• Bathrooms is one of the variables ALEX tests for every sale. ABOR closed sales in this price range show no measurable price effect, so the line is $0.
• Closing date repeats each sale’s close date beside the adjustment lines, so the age of the evidence stays in view.
• Primary bath starts at $0 for every sale, because nothing in the listing data measures it. Diane enters an amount where the sale differs from this home.
• Full bath 2 starts at $0 for every sale, because nothing in the listing data measures it. Diane enters an amount where the sale differs from this home.
• Full bath 3 starts at $0 for every sale, because nothing in the listing data measures it. Diane enters an amount where the sale differs from this home.
• Interior quality starts at $0 for every sale, because nothing in the listing data measures it. Diane enters an amount where the sale differs from this home.
• Interior lighting starts at $0 for every sale, because nothing in the listing data measures it. Diane enters an amount where the sale differs from this home.
• Deck starts at $0 for every sale, because nothing in the listing data measures it. Diane enters an amount where the sale differs from this home.
• Exterior condition starts at $0 for every sale, because nothing in the listing data measures it. Diane enters an amount where the sale differs from this home.
• Front yard starts at $0 for every sale, because nothing in the listing data measures it. Diane enters an amount where the sale differs from this home.
• Back yard starts at $0 for every sale, because nothing in the listing data measures it. Diane enters an amount where the sale differs from this home.
• Total ALEX Model & Diane adjustments is the sum of the ALEX Model lines above, the full effect of the ALEX Model lines on each sale. Where Diane typed in an amount on a line, that amount replaces ALEX’s figure rather than adding to it. It also includes the fields Diane added to every sale, and any overall adjustment entered for a sale; these have no ALEX line to replace, so they add.

Size and the final value.

• Scaling to 3,714 SF restates each sale at this home’s size: the sale’s adjusted price is divided by its own living area and multiplied by this home’s 3,714 SF. The row shows the dollar difference that makes.
• Statistical size adjustment corrects that scaling for the fact that larger homes sell for less per SF. It applies the size effect ALEX measured from 7,044 ABOR closed resales priced $1,000,000 and up: price rises with living area to the power 0.47, not in proportion, so the further a sale’s size is from this home’s, the larger the correction.
• Total size adjustment is the sum of the scaling and the statistical size adjustment for each sale.
• Weight in the ALEX Model is the share of the valuation each sale carries in the ALEX Model. Sales closer to this home in the matching measure carry more weight.
• Time adjustment repeats the market trend to today from the time adjustment table above.
• ALEX Model & Diane adjustments repeats the Total ALEX Model & Diane adjustments row from the table above.
• Size adjustment repeats the Total size adjustment row from the size table above.
• Final adjusted value is the net sale price plus the time, ALEX Model & Diane and size adjustments above it. It is what each sale says this home is worth.
• Final adjusted sale price per SF is the final adjusted value divided by this home’s living area, rounded to the dollar.

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 R502472 (S9830 - RANCH AT BRUSHY CREEK SEC 7B, BLOCK D, Lot 11): 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.

What each row means

• Improvement value is what Williamson Central Appraisal District assigns to the buildings and other improvements on the parcel, for 2026 and 2025.
• Land value is the appraisal district’s value for the land alone. It is the one roll figure the valuation uses: the land section prices lot-size differences at this parcel’s county land rate.
• Total market value is land plus improvement: the district’s mass-appraisal market value as of January 1 of each roll year. It is not the taxable value, which exemptions and the homestead cap can lower.

Against its peers

This comparison asks whether the appraisal district revalued this parcel more or less than the parcels around it. Each group’s figure is the median change in total market value from 2025 to 2026 across every parcel in that group on the Williamson Central Appraisal District roll carrying both years, set beside this parcel’s own change. Parcels valued at $10,000 or less in either year are left out.

• Neighborhood is the appraisal district’s own neighborhood code for this parcel, L543514A - Ranch at Brushy Creek - Section 8A: every parcel the district appraises as one neighborhood. Its figure is the median change across those 1,488 parcels.
• ZIP 78613 is every parcel on the roll whose property address is in that ZIP code. Its figure is the median change across those 25,682 parcels.
• Cedar Park is every parcel on the roll whose property address names Cedar Park as its city. Its figure is the median change across those 25,814 parcels.
• Williamson County is every parcel on the Williamson Central Appraisal District roll. Its figure is the median change across those 286,358 parcels.
• Improvement value per SF is this parcel’s 2026 improvement value divided by the square footage on the roll, set against the median for neighborhood parcels over 500 SF that carry an improvement value.

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 −$25,000 and improvement −$28,657, which is why the shares can read as 47/53 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 −8.9% to −0.9%). 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 Cedar Park (CCP); Williamson CO (GWI); Aus Comm Coll (J01); Wmsn CO FM/RD (RFM); Round Rock ISD (SRR); Upper Brushy Creek WCID (W09).

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 $17,115 a year. Divided by the 2026 county market value of $957,600 from WCAD, that is 1.79% — 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 = 19.5%. The effective rate is τ = annual tax ÷ M₂₀₂₆ = 1.79%. 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.