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D3 · The Going-Rate Atlas

Capstone dossier · what every dish-type costs in Amsterdam, with honest ranges

Dossier, not the essay. Backstage layer for technical readers; the capstone essay is the general-audience artifact. Corpus: Snapshot · June 2026, ~900 priced venues, roughly 4 in 10 of Amsterdam’s ~2,028 restaurants.

The verdict

Amsterdam has a going rate for everything, and now it is written down. The Dish Atlas prices 200 dish-type cells (147 at full confidence, 53 stabilised by pooling), covering 96% of 32,651 clean dishes: each cell gets a typical price (the empirical median) and a 90% range (where 90% of that dish-type’s prices actually fall). Carpaccio as a starter: €15, range €11.50 to €23. Friet: €5.80. Bitterballen: €7.20. A dorade main: €24.50. No venue is named anywhere in the atlas; it prices dish-types, never restaurants.

Two design decisions carry the credibility. Typical = the median, not the mean, because on skewed price distributions the model’s own pooled mean misleads by 27 to 38% (the cheese-board cell reads €10.50 by geometric mean and €14.50 by median; the median is what a diner actually encounters). And the range is the partially-pooled quantity: big cells show their own percentiles, thin cells borrow spread from their parent cells, so a 20-dish cell cannot fake a precise range it has not earned.

suppressPackageStartupMessages({library(dplyr); library(ggplot2)})

atlas <- readr::read_csv("../../data/processed/dish_atlas.csv", show_col_types = FALSE)

picks <- c("side · vegan · none · other", "snack · meat · fried · other",
           "sweet · any · baked · other", "starter · meat · raw · plate",
           "main · meat · none · sandwich", "main · vegetarian · baked · pizza",
           "main · meat · baked · pizza", "main · meat · none · pasta",
           "main · meat · stew · curry", "main · meat · none · plate",
           "main · fish · none · plate", "main · meat · grilled · plate")

sel <- atlas |> filter(cell %in% picks) |>
  mutate(label = sprintf("%s  ·  %s", exemplar, sub(" · none", "", cell)))

ggplot(sel, aes(x = typical_eur, y = reorder(label, typical_eur))) +
  geom_linerange(aes(xmin = ppi_lo_eur, xmax = ppi_hi_eur),
                 colour = "#b5623f", alpha = .45, linewidth = 1.6) +
  geom_point(colour = "#b5623f", size = 2.6) +
  geom_text(aes(label = sprintf("€%.2f", typical_eur)), vjust = -0.9, size = 3) +
  labs(x = "Typical price (median) with 90% range (€)", y = NULL) +
  theme_minimal()

Figure 1: The going rates: typical price (dot) and 90% range (line) for twelve recognizable cells. Each label is the cell’s exemplar, the most common cleaned dish name inside it; it stands for the whole cell, not for one dish.

Why the obvious approach lies, twice

The first lie is averaging across products. “The average dish price in Amsterdam” mixes a €2.50 side with a €49 Wagyu; it measures menu composition, nothing else. The coordinate system (dossier D1) fixes that: prices are only ever summarised within a cell, where dishes are the same kind of thing.

The second lie is subtler: the mean lies even within a cell. Dish prices are right-skewed (a long tail of expensive versions), and the model is fitted on log-prices, whose natural “average” back-transforms to the geometric mean. On skewed cells that number drifts far from what a diner actually meets. The skew check that caught this compared the model’s pooled mean against the empirical median across all confident cells: gaps up to 27 to 38%. Verdict: the model keeps the mean internally for validation, and the atlas displays the median. The variance components confirm the median is reliable even at 15 dishes per cell; what is unreliable in small cells is the tails, and that is exactly where pooling is aimed.

The model: pooling for the tails

The fit is a nested random-effects model on log price:

\[ \log(\text{price}) \sim \text{role} + (1 \mid \text{role:protein}) + (1 \mid \text{role:protein:method}) + (1 \mid \text{cell}) + (1 \mid \text{venue}) \]

The nesting is the point: a cell sits inside a role:protein:method family, which sits inside a role:protein family. A thin cell (say, 18 lamb stews) does not have to estimate its price spread alone; it borrows from its parents in proportion to how little data it has. The displayed 90% range blends the cell’s own 5th-to-95th percentile span with the model’s pooled predictive spread, weighted by cell size (weight = n/(n+40)). Big cells are effectively empirical; thin cells are honestly wider than their own data would naively suggest. The venue random effect keeps one expensive restaurant’s menu from imprinting on a cell.

Escalating to a fully Bayesian fit (brms) was considered and declined, on the light-first rule: with 31,000+ dishes the residual spread is pinned, the median would not move, and the extra machinery would change nothing a reader can see. The lme4 empirical-Bayes fit runs in four seconds and reproduces to the cent.

What it found, beyond the lookup

Sure bets and gambles. Range width is information. The most price-predictable dishes in the city are the cuisine-format ones: pizza (a diavola’s 90% range spans only ±35% of its €17.50 typical) and curries. The widest are the catch-all and sharing formats: a borrelplank runs €9.80 to €49.70 around an €18.50 typical, and a sharing-size kipsaté anywhere from €12.70 to €60. The practical reading for a diner: you can trust a pizza price sight-unseen; never assume a sharing platter.

Why widths differ this much: the quality ceiling. The model cannot see undisclosed portion size or ingredient quality, and dish names differ enormously in how much they pin those down. A borrelplank has no quality ceiling: the same menu line covers kaasblokjes with supermarket worst and an ibérico charcuterie board, and the price honestly spans that distance. A pizza, even loaded with the most premium ingredients, still has a pizza ceiling: the format bounds the plate, and the city carries a reference price for it. Range width is that invisibility made visible. Wide cells are cells where the name does not pin the product; tight cells are cells where it does. (Seen through dossier D4’s decomposition: the ranges are its non-dish 41%, venue character plus item noise, displayed cell by cell; D4’s “ladder and the rungs” section shows the two dossiers are one set of numbers.)

ww <- atlas |> filter(tier == "confident", n >= 100) |>
  mutate(relw = (ppi_hi_eur - ppi_lo_eur) / typical_eur,
         label = sprintf("%s  ·  %s", exemplar, sub(" · none", "", cell)))
wide   <- ww |> arrange(desc(relw)) |> head(6) |> mutate(group = "widest (gambles)")
narrow <- ww |> arrange(relw)       |> head(6) |> mutate(group = "narrowest (sure bets)")

ggplot(bind_rows(narrow, wide),
       aes(x = relw, y = reorder(label, relw), fill = group)) +
  geom_col(width = .7) +
  scale_fill_manual(values = c("widest (gambles)" = "#b5623f",
                               "narrowest (sure bets)" = "#7a9e7e"), name = NULL) +
  labs(x = "90% range width ÷ typical price", y = NULL) +
  theme_minimal() + theme(legend.position = "top")

Figure 2: Sure bets vs gambles: the narrowest and widest 90% ranges relative to the typical price, among confident cells with at least 100 dishes. Cuisine-format dishes price tightly; sharing and catch-all formats do not.

The atlas is a lookup table. The ten biggest cells, as they ship:

atlas |> arrange(desc(n)) |> head(10) |>
  transmute(cell, exemplar, n, venues,
            typical = sprintf("€%.2f", typical_eur),
            `90% range` = sprintf("€%.1f – €%.1f", ppi_lo_eur, ppi_hi_eur)) |>
  knitr::kable()

Table 1: The ten biggest atlas cells. Typical = empirical median; the range is the 90% partially-pooled interval.

cell	exemplar	n	venues	typical	90% range
main · meat · none · plate	kalfslever	2097	449	€21.70	€11.0 – €37.1
main · meat · none · sandwich	carpaccio	1998	394	€12.50	€5.5 – €21.6
sweet · any · none · other	affogato	1916	518	€7.70	€3.0 – €13.7
main · fish · none · plate	dorade	969	339	€24.50	€12.0 – €38.7
side · vegan · none · other	friet	937	421	€5.80	€2.5 – €9.6
main · meat · grilled · plate	bife de chorizo gr	912	309	€25.50	€14.0 – €48.3
main · meat · baked · pizza	diavola	905	112	€17.50	€12.3 – €22.4
sweet · any · baked · other	cheesecake	751	324	€6.00	€3.0 – €12.9
main · vegetarian · baked · pizza	margherita	719	116	€16.00	€9.9 – €22.3
main · vegetarian · none · sandwich	mozzarella di bufala	650	276	€9.50	€4.9 – €18.0

The stress-test battery

The threat	The test	The verdict
The displayed center misleads on skewed cells	geomean vs median across all confident cells	gaps up to 27–38% (cheese board €10.50 vs €14.50): median displayed, geomean demoted to a validation column
Package lines masquerade as dish-types	cell-contents audit, triggered by a band-width sort on the public atlas page	four package coordinates (444 items: promo bundles, prix-fixe lines, high teas, desserts-for-two) quarantined whole to dish_atlas_excluded.csv; survivors’ typicals unmoved, range endpoints shift ≤ €0.30
The pooling constant is arbitrary	audit re-ran with alternative K_W values	ranges move 3–4%: not sensitive
The pipeline drifted from the canonical corpus	adversarial data-layer audit, reproduced from scratch	lineage faithful: the atlas dish table is a bit-identical subset of canonical items.csv (set-difference zero both ways)
Ranges are fantasy	hand-validation of 10 cells against real menu dishes	exemplars faithful; ranges correctly exclude real extremes (a €49 Wagyu, a €78.50 T-bone, a €67.50 Dover sole all sit outside their cells’ 90% bands, as 5%-tails should)
Dessert prices biased by a silent filter	audit reproduction	985 sweets (34%) were being dropped, skewing sweet cells ~15–20% low; fixed, desserts recovered (the cheesecake cell grew 436 → 751 dishes)
Per-piece prices contaminate cells	mechanism-matched hygiene guard (D1)	main · fish · raw · sushi median €4.40 → €16.50
A heavier model would change the answer	lme4 vs brms escalation decision	declined on light-first grounds: 31k dishes pin the spread, the median cannot move; lme4 reproduces to the cent in 4 seconds

What this is, and what it isn’t

• No venue is named, structurally. The atlas aggregates over venues by construction; the per-venue claims that sank the earlier Value Atlas cannot be expressed in it.
• The exemplar is a label, not a promise. “Butter chicken” is the most common name inside the meat-curry cell, but actual butter chickens cluster in the upper part of that cell’s range. Read “meat curry, e.g. butter chicken”, never “butter chicken costs €20.80”. (This framing is a known presentation task carried forward from the audit.)
• Within-cell quality and portion are invisible. A €12 and a €19 carpaccio may differ in provenance and grams; the atlas sees neither. It prices the type, honestly wide.
• Menu price, not paid price. No service, no specials, no portion inflation observed.
• A snapshot. One city, one month, ~4 in 10 restaurants. The going rates are solid within that scope and dated by construction.

Lineage

• Method + brief: docs/m5_typical_menus.md (§4 method, §6 evidence base); audit record docs/m5_data_audit_findings.md.
• Code: R/50_dish_atlas_hygiene.R (cells + hygiene), R/51_dish_atlas_fit.R (the nested lme4 fit, the median decision, the K_W=40 blend).
• Data: data/processed/dish_atlas.csv (200 cells), dish_atlas_dishes.csv (32,651 dishes), dish_atlas_excluded.csv (the four quarantined package coordinates, with reasons).
• Journal trail: 2026-06-30_001 (the atlas crystallises), 2026-06-30_002 (the fit + the skew catch + 10-cell hand-validation), 2026-06-30_005/_006 (audit + fixes), 2026-07-07_013 (the package-cell curation).
• Sources: restaurant websites (menus), OpenStreetMap (venue universe). All open data. Snapshot · June 2026.