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\section{Introduction}
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The sales comparison approach is the workhorse of residential property valuation. Appraisers, assessors, lenders and courts rely on it daily: a small set of recent sales of similar properties is selected, each sale price is adjusted for the differences between the comparable and the subject, and the adjusted prices are reconciled into a single opinion of value \citep{appraisal2020,iaao2017}. The approach is taught in every valuation curriculum and codified in professional standards, and its logic---that the market itself reveals what buyers pay for a bundle of characteristics---is compelling. Yet the \emph{operating rules} that turn this logic into a number are, to a remarkable degree, matters of convention rather than evidence. How many comparables should be used? Three is the traditional answer; some standards say ``at least three.'' How far should one search, and how far back in time? Which adjustments are warranted, and of what magnitude? Should comparables be weighted equally, by proximity, by recency, or by similarity? Should adjusted prices be averaged, or should the appraiser ``reconcile'' them by judgement? Each of these questions has been debated for four decades \citep{colwell1983,vandell1991,gau1992,pace1996,isakson2002,lai2008}, but the empirical evidence remains thin, dated, and almost always drawn from a few hundred sales in a single metropolitan area.

This paper provides a population-scale, out-of-sample validation of the sales comparison approach. We exploit a research database---Vrai Prix---that links the universe of registered residential transactions in Quebec to the municipal assessment roll, giving us \nSalesClean{} arm's-length single-family sales from January 2021 to September 2026 with harmonised physical characteristics, coordinates and assessed values. On this base we build a \emph{point-in-time backtesting} engine. For each of \nTargetsAll{} target sales occurring in 2024, 2025 and 2026, the sale price is masked and the property is valued as an appraiser would have had to value it on the day of the sale: only transactions closed strictly before that date are admissible as comparables; the price index used to time-adjust them is re-estimated every month from prior sales only; the adjustment grids and machine-learning benchmarks are re-estimated every quarter from prior sales only. The masked price is then compared with the estimate. Because every configuration of the method is applied to exactly the same targets, differences in accuracy are paired differences of forecast losses in the sense of \citet{diebold1995}, and we quantify their uncertainty with a cluster bootstrap over municipality--quarter cells \citep{cameron2008} that respects the spatial and temporal dependence of valuation errors. Because configurations are chosen on 2024 sales and evaluated on 2025--2026 sales, the headline figures are protected against the data-snooping bias that a search over thousands of specifications would otherwise create \citep{white2000,hansen2005}; we verify directly that the configuration chosen on 2024 ranks \mZeroRankTest{}nd among the \nConfigsCov{} eligible configurations in 2025--2026.

Within this engine we run \nConfigs{} configurations of the sales comparison approach. A first experiment maps the \emph{error surface} $\mathrm{Error}(k, d, t)$ over the number of comparables $k \in \{1,\dots,50\}$, the search radius $d \in \{0.5,\dots,25\}$~km and the look-back window $t \in \{3,\dots,24\}$ months, for three selection rules (nearest, most physically similar, and a compromise) and two adjustment regimes (time only, hedonic grid). A second experiment is a full factorial design over the \emph{rules} of the method at three anchor configurations: four selection criteria, eight adjustment schemes (none; time only; a stylised conventional grid; a global hedonic grid; a regional grid; a locally re-estimated grid; non-linear adjustments from a gradient-boosting model; and the assessment-ratio adjustment), five weighting schemes, and two reconciliation rules. Sixteen named models, from ``median of the three nearest sales'' to a quarterly-retrained gradient-boosting model and a hybrid, are then placed in a horse race, and five hypotheses about the trade-offs between proximity, similarity, sample size, local estimation, weighting and market liquidity are tested directly.

Five results stand out. First, \emph{adjustments dominate}. Averaging the five nearest time-adjusted sales yields a median absolute percentage error (MdAPE) of \mdapeMtwo{}; applying a hedonic adjustment grid to the same five sales cuts it to \mdapeMseven{}, and a stylised conventional grid---half the comparable's price per square metre for living area, half the implied land value per square metre for lot size, half a percent per year of age---captures most of that gain (\mdapeMsix{}). What matters is \emph{that} one adjusts, far more than the sophistication of the grid: regional, local and non-linear refinements add little, and the locally re-estimated grid is less accurate where sales are sparse. Second, \emph{similarity beats proximity}. With no physical adjustment at all, selecting the five most similar sales within a wide radius rather than the five nearest yields \mdapeMthree{}, essentially the same accuracy as adjusting the nearest ones. A nearby but dissimilar sale is a worse comparable than a more distant but similar one. Third, \emph{three comparables is too few}. Without physical adjustment, accuracy improves up to about ten comparables and then deteriorates as more distant sales are added; with a grid it improves up to roughly \kOpt{} and stays flat to fifty, in sparse and dense markets alike. Three-month windows are dominated everywhere, whereas the search radius, once enough similar sales are retained, matters little. Fourth, \emph{weighting and reconciliation matter little}: the choice between median and mean, or between equal, distance, recency and similarity weights, moves the MdAPE by a few tenths of a point, an order of magnitude less than selection and adjustment. Fifth, \emph{the cost of transparency is small}. The best configuration of the method chosen on 2024 data reaches \mdapeMzero{} out of sample in 2025--2026, against \mdapeMelevenB{} for a gradient-boosting model retrained every quarter with access to the assessed value, and \mdapeMtwelve{} for a hybrid that combines the two; the paired difference of \transparencyCost{} points is precisely estimated, and it falls to about a point and a half in homogeneous submarkets. Accuracy is, above all, a function of submarket liquidity: the same method is two and a half times more accurate where hundreds of sales occur within two kilometres in a year than where fewer than five do. A wide-net rule that retains the most similar sales within a large radius adapts to this on its own, and rules tuned stratum by stratum do not improve on it.

The paper contributes to three literatures. It extends the theoretical and small-sample studies of comparable selection and weighting \citep{colwell1983,vandell1991,gau1992,green1994,pace1996,epley1997,lai2008} to a population-scale, out-of-sample, point-in-time setting, and resolves several of their open questions with confidence intervals rather than illustrations. It speaks to the literature comparing hedonic and grid-adjustment techniques \citep{kang1991,lipscomb1990,pacegilley1998} and to the comparisons of machine learning with traditional valuation \citep{mccluskey2013,mayer2019,bogin2020,pace2020}, by holding the information set fixed across methods and measuring the price of interpretability in a transparent method tuned to the same data. And it offers the profession and its regulators a reproducible empirical basis for rules that are currently taught as conventions. We are careful about what the evidence can and cannot say: we validate the \emph{predictive accuracy of simulated professional rules} on observable characteristics, not the judgement of actual appraisers, whose files, comparables and adjustments we do not observe.

The remainder of the paper is organised as follows. Section~\ref{sec:literature} reviews the literature on the sales comparison approach, adjustment estimation and automated valuation. Section~\ref{sec:data} describes the Vrai Prix database and the construction of the analysis sample. Section~\ref{sec:methodology} presents the point-in-time backtesting protocol, the configuration space, the benchmark models and the inference strategy. Section~\ref{sec:results} reports the results, Section~\ref{sec:robustness} examines their stability across submarkets, time, specifications and the selection step itself, and Section~\ref{sec:conclusion} concludes.