Huff Gravity Model Simulator

Each colored region shows the dominant store — the store with the highest Huff probability for consumers in that area. Boundaries between colors are where two stores have roughly equal pull. These are the market boundaries in retail geography.

The heatmap view shows continuous probability (0–100%) for a selected store, revealing how influence fades with distance — even inside a competitor's dominant zone, there's still some probability of visiting.

The Converse Breaking Point between two stores is the location where a consumer is equally likely to visit either store. It's calculated as:

Where D_AB is the distance between stores A and B. A more attractive store "pushes" the breaking point farther away from itself — its trade area extends past the midpoint.

In the Breaking Points view, dashed lines connect each store pair through their breaking point. The more attractive store's side extends farther.

The U.S. Census counts people where they sleep (residential population). But retail gravity models need to know where people shop — and those are different things. A university campus tract might house 5,000 residents but have 30,000+ students and staff present on a typical weekday. A downtown office district might have 3,000 residents but 50,000 daytime workers.

Real-world site analysts address this with "effective consumer population" (sometimes called "daytime population" or "ambient population") — a composite that blends residential counts with daytime activity estimates from universities, employers, and transit hubs. It answers the question: how many potential customers are physically present in this zone during business hours?

This simulator uses that approach: Census 2020 residential data as the base layer, plus documented adjustments for university presence and major employment centers.

Every population center starts with the POP100 value from the 2020 Decennial Census Redistricting Data (PL 94-171), Table P1 — total population of the enclosing census tract.

Census tracts are small geographic units (typically 1,200–8,000 people) designed to be relatively homogeneous in population characteristics. We retrieved each tract's POP100 by converting the population center's lat/lng coordinates into a FIPS code via the Census Bureau Geocoder API. Each center's GEOID (state + county + tract FIPS) is documented in the source code for reproducibility.

Limitation: POP100 is a residential headcount, not a consumer demand estimate. For purely residential areas (suburbs, family neighborhoods), it's a reasonable proxy. For areas with heavy daytime inflows (campuses, downtowns, malls), it dramatically undercounts the people actually present and available to patronize a store.

Two scenarios center on university districts where census residential counts miss the dominant consumer group — students and staff who commute in daily.

The "50% average weekday presence" multiplier is a simplification. On any given weekday, some fraction of enrolled students are on campus at any time (attending class, studying, eating, socializing). The 50% figure is a rough midpoint — peak midday presence is higher; evenings and breaks are lower. For a coffee shop gravity model, this captures the order-of-magnitude reality that matters: a campus tract has many times more potential coffee buyers than its residential count suggests.

Source: Enrollment and staff figures from Wikipedia, citing UT System Smartbook (June 2025) and SDSU Analytic Studies & Institutional Research enrollment tables.

The Bank Siting scenario includes two zones where daytime employment significantly exceeds the residential population:

Banking customers visit branches both near home and near work, so employment-weighted population is appropriate for this product category. The Grocery Wars scenario uses census-only values because grocery shopping is overwhelmingly a near-home activity.

Note: Employment estimates are approximate and not sourced from a single authoritative dataset. The Census Bureau's LODES/LEHD (Longitudinal Employer-Household Dynamics) data would provide precise workplace counts by census block but was not used here. The adjustments are order-of-magnitude estimates intended to produce realistic relative variation, not precise counts.

Real population isn't evenly distributed within a census tract — people cluster along streets, in apartment complexes, and in specific developments. Modeling this exactly would require block-level or parcel-level data and add complexity without pedagogical benefit.

Instead, each population center is modeled as a 2D Gaussian (normal) distribution ("blob") centered on its lat/lng coordinates. The sigma parameter (σ) controls how spread out the population is:

• σ = 0.004 (≈ 0.4 km): Tight cluster — a campus or apartment complex
• σ = 0.006 (≈ 0.7 km): Moderate spread — an urban neighborhood
• σ = 0.008 (≈ 0.9 km): Broad spread — a suburban residential area

At each grid cell, the engine sums the Gaussian contribution from every population center to produce a continuous density surface. This is conceptually identical to kernel density estimation (KDE) — a standard technique in spatial analysis.

The resulting surface is proportionally correct (high-population zones pull harder) but geometrically simplified (actual building footprints aren't represented). For a gravity model exploring the interplay of population × distance × attractiveness, this level of abstraction preserves the key dynamics.

Professional retail site analysts at firms like Esri, Placer.ai, and Buxton go further than this simulator in several ways:

• Block-group or block-level data: Instead of one population center per neighborhood, they use hundreds of census blocks, each with its own population count and demographic profile.
• Road-network distances: Instead of straight-line (Euclidean) distance, they compute actual drive times using road networks, traffic data, and turn penalties.
• Consumer segmentation: Population is weighted by spending propensity using geodemographic systems like Tapestry or PRIZM that classify neighborhoods by lifestyle, income, and consumption patterns.
• LEHD/LODES employment data: The Census Bureau's Longitudinal Employer-Household Dynamics program provides workplace-area counts at the census-block level, enabling precise daytime-population models.
• Mobile location data: Companies like SafeGraph and Placer.ai provide observed foot-traffic counts at individual stores, allowing analysts to calibrate (rather than assume) model parameters.

This simulator intentionally simplifies these layers to keep the focus on the core Huff mechanics: how attractiveness, distance decay, and population interact to shape market share. The effective consumer population approach captures the most important real-world adjustment (daytime ≠ nighttime population) without overwhelming the pedagogical experience.

• Coordinate system: WGS 84 (EPSG:4326). The Huff engine computes Euclidean distance from lat/lng, which introduces minor distortion at these latitudes (~1–2% vs. true geodesic distance). Acceptable for the distances involved (< 20 km).
• Grid resolution: 40 × 40 cells across the map viewport. Finer grids increase accuracy at the cost of computation time — and don't change qualitative conclusions.
• Huff formula: P(i→j) = S_j^α · d_ij^−β / Σ_k S_k^α · d_ik^−β — identical across all scenarios. Only the parameter defaults (α, β) differ.
• Distance units: Degrees (not km or miles). Since all scenarios are within a single metro area, the degree-to-km conversion is effectively constant and cancels out in the Huff ratio.

In practice, α and β are not guessed — they're estimated from observed data. Researchers collect actual customer visit data (surveys, loyalty cards, or mobile pings), then use maximum-likelihood estimation or log-linear regression to find the α and β that best predict observed shopping patterns.

Calibrated parameters vary dramatically by product category: β for convenience stores may be 3.0+, while for specialty furniture it might be 0.8. Without calibration, the Huff model is an illustration tool; with calibration, it becomes a predictive engine.

Traditional gravity models relied on surveys to learn where people shop. Today, mobile location data (from GPS, Wi-Fi, and app SDKs) reveals actual visit patterns at massive scale. Providers like SafeGraph, Placer.ai, and Gravy Analytics supply anonymized foot-traffic counts by store and time period.

This data lets analysts directly observe what the Huff model tries to predict — the probability a consumer visits each store. Modern workflows use gravity models to fill gaps where mobile data is sparse, creating a hybrid approach that's far more accurate than either method alone.

The original Huff model uses a single "attractiveness" number (usually floor area). The Multiplicative Competitive Interaction (MCI) model extends this by decomposing attractiveness into multiple attributes — each with its own weight:

This means a store's pull depends on its brand recognition, price level, parking availability, product variety, and more — each weighted by how much consumers care about that attribute for this product category. The MCI model is now the standard in academic retail geography.

The Huff model was built for a world where shopping meant physically visiting a store. In the omnichannel era, consumers might browse online, order for pickup, or have items delivered. This changes the meaning of "distance" — for online orders, the relevant distance might be delivery time rather than driving distance.

Researchers are adapting gravity models by adding an "online channel" as a virtual store with zero physical distance but its own friction (shipping time, return hassle, lack of tactile experience). Hybrid models combine physical Huff probabilities with online choice data to predict total demand across channels.