2. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory

3. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History William Reilly, 1931, “Law of Retail Gravitation”. Developed a formula to find the retail break-point between two cities based on their populations. Break Point for city-a when comparing city-a to city-b ●

4. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History William Reilly, 1931, “Law of Retail Gravitation”. Developed a formula to find the retail break-point between two cities based on their populations. Example: ●

5. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History William Reilly, 1931, “Law of Retail Gravitation”. Developed a formula to find the retail break-point between two cities based on their populations. Example: Used to define a trade area ●

6. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History Walter Christaller, 1933, “Central Place Theory”. Described how retailers must distribute themselves over distance. “Threshold”: Minimum area needed for the goods and services to be viable. “Range”: The maximum distance the retailer could expect to reach consumers with goods or services. When the offerings are larger, both the threshold and the range could be expected to increase. ●

7. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History Walter Christaller, 1933, “Central Place Theory”. Described how retailers must distribute themselves over distance. Threshold Range This is how Christaller pictured it in 1933 ●

8. Range New threshold! Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History Walter Christaller, 1933, “Central Place Theory”. Described how retailers must distribute themselves over distance. How online retailers have changed it. ●

9. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History Isaac Newton (or Thomas Hooke), 1686, “Universal Gravitation”. Described the force celestial bodies exerted on each other. ●

10. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History The Gravity Model Has Been Adapted to a Variety of Uses Migration Patterns ●

11. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History The Gravity Model Has Been Adapted to a Variety of Uses World Trade Patterns (both WTO and NAFTA) ●

12. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History The Gravity Model Has Been Adapted to a Variety of Uses Ethnic and Linguistic Expansion Models ●

13. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History The Gravity Model Has Been Adapted to a Variety of Uses ???????? ●

14. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History The Huff Model P ij = Probability of shopper “i” shopping at store “j” d ij = Distance of shopper “i” from store “j” A j = Attractiveness of store “j” λ = Some measure of trade area friction ●

15. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History The Huff Model P ij = Probability of shopper “i” shopping at store “j” P ij = Attractiveness of Store j Attraction felt by all stores 1. A move from dividing line to probabilities. 2. Probability applied to Wallet = Expected Value. 3. Multiple shopping destinations, different amounts! Three big steps forward: ●

16. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History The Gaussian Model Where: A ij = The attractiveness of consumer “i” and store “j” ●

17. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History The Gaussian Model Normal “Bell” Curve ●

18. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory A Brief History The Gaussian Model Distance Distance Decay Function Attractiveness ●

19. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Why Gravity? Regression Method: Formula with multiple variables and coefficients predicts results. Variables = x 1, x 2, x 3, … Coefficients = m 1, m 2, m 3, … Best used to compute small cells, then aggregate. (See “Analog Regression”, 1978, H. Green and D. Rogers.) ●

20. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Why Gravity? Regression Method: Disadvantages Difficult to simulate curves. Tendency towards extreme values. Little room for analyst judgement. Heterogeneity of sample stores. Coefficients probably change with T.A. (Disaggregation may help.) Autocorrelation can cause serious trouble. ●

21. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Why Gravity? Analog Method: Use historic data (spotting?) to predict sales by matching conditions. ● Surrounding competition ● Surrounding population / demographics ● Store format and size Use Excel to build a spreadsheet of smaller areas and analog forecasts, then sum. ●

22. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Why Gravity? Analog Method: Disadvantages Match is never exact How to handle new sizes and formats? New trade areas? Harder to predict impacts New competition? Great for reality checks! ●

23. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Why Gravity? Gravity Method: Advantages Non-linear, matches spotting data Closed monetary system We know where money comes from Works with complicated scenarios Shows changes to all stores Model conditions can be changed quickly ●

24. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Where Do Gravity Models Work? Destination-type trips, returning home Where accurate competitive sales can be obtained Where accurate per-capita expenditures can be estimated Where perceived distances can be measured Grocery, liquor, scripts, hardware BLS Annual Consumer Expenditure Study Distance, drive-time, walk-time, bicycle-time Closed system demands an accurate pool ●

25. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions All customers behave the same. Original Huff Model All customers have the same-sized pocket. All stores are the same, except for size. Disaggregation model. Small individual probabilities are not expected to be accurate; aggregations are accurate. This contributes to model robustness. ●

26. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions All customers DO NOT behave the same. ●

27. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions All customers DO NOT behave the same. We create consumer profiles. We recognize store types. We research preferences. e.g. FIT Each product implements differently. How we “fix” that violation: ●

28. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions All customers DO NOT have the same-sized pockets. (1) Household Size(2) Household Income (3) Race/Ethnicity Region Rural/Urban BLS Annual Diary of Consumer Expenditures ●

29. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions All Stores are NOT the same except for size. Difference in power (image) Difference in curve DistanceAttractiveness Two outward signs of heterogeneous store formats. ●

30. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions All Stores are NOT the same except for size. Tremendous differences in format types, SKUs, prices, quality, … ●

31. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions Speaking of Curves (Gaussian model) … DistanceAttractiveness Radius (2 ?) Area under the curve is proportional to sales for Store i Area (from 0 to Radius) = Area (from 0 to infinity) = Sales Percent ●

32. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions Speaking of Curves (Gaussian model) … DistanceAttractiveness Radius (2 ?) Area under the curve is proportional to sales for Store i Assumption: Perfectly homogeneous population density and homogeneous store density. ●

33. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions Speaking of Curves (Gaussian model) … The software has now defined the role of radius and curve Remember the Gaussian definition of “x”? Now we only need to figure out “Power” (or “Image”) ●

34. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions Our Original Gaussian Model “x” is also proportional to standard deviation of distribution. “X” can then be defined so that distribution of “Power” (“Image”) has a known and predictable standard deviation. ●

35. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Basic Gravity Model Assumptions Our Original Gaussian Model “X” can then be defined so that distribution of “Power” (“Image”) has a known and predictable standard deviation. 100-SD 100 100+SD Power Distribution SITESPLUS has SD = 17 ●

36. Presented at the 2016 International Store Location Conference by Jim Puffer Gravity Modeling Theory Simple Modeling Example: 1 Sector Let Sector i be a population center with potential = $120,000 Let A ij be any Measure of Attraction Between Sector i and Store j (This measure includes effect of distance.) then Store-1Store-2Store-3 Attraction12080150 Sum of Att.350 Probability.34.23.43 Exp. Sales$40,800$27,600$51,600 Modern gravity software simply does this for all population sectors. ●