..

analyses/school_catchment_model.ipynb

@@ -5,7 +5,7 @@
    "id": "46a28f40",
    "metadata": {},
    "source": [
-    "# School catchment model — the working\n",
+    "# School catchment model: the working\n",
     "\n",
     "The postcode features **\"Good+/Outstanding primary/secondary school catchments\"** count the\n",
     "rated state schools whose modelled *admission cutoff radius* covers a postcode. This notebook\n",
@@ -17,7 +17,7 @@
     "Pupil Database. What *is* public: where every school is and how many pupils it has (GIAS), how\n",
     "many children live where (Census 2021), and the fact that most English admissions are run as\n",
     "**deferred acceptance with distance tie-breaks**. That is enough to *solve for* each school's\n",
-    "cutoff distance — the \"last distance offered\" that councils publish each offer day — and those\n",
+    "cutoff distance (the \"last distance offered\" that councils publish each offer day) and those\n",
     "published figures give us ground truth to calibrate against.\n",
     "\n",
     "The production code is `pipeline/transform/school_catchments.py`; the calibration harness is\n",
@@ -81,14 +81,14 @@
    "id": "e13f2bc4",
    "metadata": {},
    "source": [
-    "## 1. Supply — schools and their phase fill targets\n",
+    "## 1. Supply: schools and their phase fill targets\n",
     "\n",
     "Every open, **non-selective** state school (academies, LA-maintained, free schools) takes part.\n",
     "Grammar schools are excluded outright: their intakes are test-based and region-wide, so any\n",
     "distance-based catchment would be fabricated. Independent, special and Welsh schools don't\n",
     "admit by distance either.\n",
     "\n",
-    "A school's *fill target* is `max(capacity, headcount)` — an over-full school keeps its\n",
+    "A school's *fill target* is `max(capacity, headcount)`: an over-full school keeps its\n",
     "demonstrated size, an under-full one can admit up to capacity (the feature asks \"would you get\n",
     "a place?\", not \"does a pupil already live there?\"). The target is prorated over the cohort ages\n",
     "the school teaches, parsed from its age range: nursery years weigh 0.5 and sixth-form years 0.6,\n",
@@ -182,16 +182,16 @@
    "id": "2905514f",
    "metadata": {},
    "source": [
-    "## 2. Demand — children per postcode\n",
+    "## 2. Demand: children per postcode\n",
     "\n",
     "Census 2021 (TS007A) gives children by five-year band per LSOA. Bands don't align with school\n",
-    "phases, so phases take fractional shares — primary (ages 4–10) = ⅕·(0–4) + (5–9) + ⅕·(10–14);\n",
-    "secondary (11–15) = ⅘·(10–14) + ⅕·(15–19) — and each LSOA's total is split evenly across its\n",
+    "phases, so phases take fractional shares: primary (ages 4–10) = ⅕·(0–4) + (5–9) + ⅕·(10–14);\n",
+    "secondary (11–15) = ⅘·(10–14) + ⅕·(15–19), and each LSOA's total is split evenly across its\n",
     "live postcodes (LSOAs hold ~40 postcodes, small enough at catchment scale).\n",
     "\n",
     "Not all of those children compete for state places: births fell ~10% between 2016 and 2021\n",
     "(exactly the gap between the census stock and the cohorts reaching Reception by mid-decade) and\n",
-    "~7% attend independent schools or are home-educated. `DEMAND_SCALE = 0.8` absorbs both — without\n",
+    "~7% attend independent schools or are home-educated. `DEMAND_SCALE = 0.8` absorbs both, without\n",
     "it, modelled cutoffs run systematically tight and half the genuinely undersubscribed schools\n",
     "look full (this was the single biggest correction the ground truth forced; see §7).\n"
    ]
@@ -241,18 +241,18 @@
    "id": "20d44b21",
    "metadata": {},
    "source": [
-    "## 3. Preferences — grade bonuses and logit choice\n",
+    "## 3. Preferences: grade bonuses and logit choice\n",
     "\n",
     "Families don't just pick the nearest school. Two ingredients:\n",
     "\n",
-    "- **Grade bonus** — a school's *effective distance* is its real distance minus an Ofsted-grade\n",
+    "- **Grade bonus**: a school's *effective distance* is its real distance minus an Ofsted-grade\n",
     "  bonus (+0.6 km Outstanding, +0.3 km Good, −0.3/−0.6 km for grade 3/4). A family accepts that\n",
     "  much extra travel for a better school.\n",
-    "- **Logit smearing** — even so, not everyone at a postcode ranks the same school first. Each\n",
+    "- **Logit smearing**: even so, not everyone at a postcode ranks the same school first. Each\n",
     "  postcode's children split across the nearby feasible schools with weights\n",
     "  `softmax(−effective_distance / τ)`, τ = 0.3 km. This matters more than it looks: with\n",
     "  deterministic choice a popular school fills entirely from its nearest band, putting its\n",
-    "  marginal admitted child — and therefore its cutoff — unrealistically close (about 2× too\n",
+    "  marginal admitted child (and therefore its cutoff) unrealistically close (about 2× too\n",
     "  tight against published cutoffs).\n",
     "\n",
     "Below: the share of applications a Good school captures against an unrated neighbour 1 km away.\n"
@@ -306,7 +306,7 @@
    "id": "04bcfbcf",
    "metadata": {},
    "source": [
-    "## 4. The equilibrium — cutoff dynamics\n",
+    "## 4. The equilibrium: cutoff dynamics\n",
     "\n",
     "English admissions run deferred acceptance with distance priority; in a continuum economy that\n",
     "is equivalent to finding **market-clearing cutoff distances** (Azevedo & Leshno 2016). The solver:\n",
@@ -314,7 +314,7 @@
     "1. start every school's cutoff at ∞;\n",
     "2. every child unit applies to its preferred school(s) among those whose cutoff still covers it;\n",
     "3. every oversubscribed school tightens its cutoff to the distance of its **marginal admitted\n",
-    "   child** — exactly the published \"last distance offered\";\n",
+    "   child**, exactly the published \"last distance offered\";\n",
     "4. repeat. Cutoffs only ever tighten, so the iteration converges to the deferred-acceptance\n",
     "   outcome. Schools that never fill keep no binding cutoff; their radius falls back to the\n",
     "   distance within which the local child population would cover their fill target.\n",
@@ -533,7 +533,7 @@
    "metadata": {},
    "source": [
     "The bimodal logic is visible: oversubscribed urban schools cluster well under 1 km while schools\n",
-    "with spare places reach further. A concrete slice — Cambridge and its villages. Circles are the\n",
+    "with spare places reach further. A concrete slice: Cambridge and its villages. Circles are the\n",
     "calibrated catchment radii of Good+ primary schools: tight in town, wide in the villages.\n"
    ]
   },
@@ -600,11 +600,11 @@
    "id": "25770af8",
    "metadata": {},
    "source": [
-    "## 6. Calibration — modelled vs published cutoffs\n",
+    "## 6. Calibration: modelled vs published cutoffs\n",
     "\n",
     "Councils publish each school's **last distance offered** in their allocation reports. We scraped\n",
     "783 rows from nine authorities (Hertfordshire, Surrey, Stockport, Manchester, Bristol, Barnet,\n",
-    "Redbridge, Ealing, Lambeth — `property-data/ground_truth/`), matched them to GIAS URNs, and\n",
+    "Redbridge, Ealing, Lambeth: `property-data/ground_truth/`), matched them to GIAS URNs, and\n",
     "compare against the modelled radii. Faith schools are reported separately: their published\n",
     "cutoff applies *within* faith priority, which a postcode model cannot see. \"All applicants\n",
     "offered\" schools test whether the model agrees there was no binding cutoff at all.\n"
@@ -823,11 +823,11 @@
    "source": [
     "## 8. Limitations\n",
     "\n",
-    "- **Faith admissions are not modelled** — whether a faith school's catchment is open to a given\n",
+    "- **Faith admissions are not modelled**: whether a faith school's catchment is open to a given\n",
     "  family depends on the family. Their fit is accordingly worse (the orange triangles above).\n",
     "- **Cutoffs are single-year snapshots**; real ones move with each cohort. The model is a\n",
     "  steady-state estimate, not this September's number.\n",
-    "- **Straight-line distance** is used throughout — it is the modal LA tie-break, but some\n",
+    "- **Straight-line distance** is used throughout. It is the modal LA tie-break, but some\n",
     "  authorities measure walking routes, and none of sibling priority, feeder schools or\n",
     "  designated catchment polygons are visible to the model.\n",
     "- Census 2021 child counts age; `DEMAND_SCALE` should drift upward as the birth-rate dip works\n",