City building is both a creative and quantitative endeavor. It takes two sides of the collective brain. Unfortunately, both of these are fairly limited to trial and error as we design and continually evolve our cities.
Two separate equations produce nearly identical results. As you may know, I created a Spatial Integration map of Austin, Texas. I did this because I wanted to measure what kind of relationship there might be between the space syntax formula and real estate value.
Below is a sample Spatial Integration map I created for pre-highway Dallas. Each of those color codes is based on the mathematical formula measuring connectivity. The important thing to note about the color-coded map below is that red is highest and blue is lowest.
The program has no idea where it is. It doesn't know the above is Dallas or the model of Austin is Austin. All it knows is the road network and how interconnected it may or may not be. Every road has a numerical value assigned to it. The color code is just a visual gradient applied to the meta-data within the program, available when you click on each segment. Since every road has a value, therefore every two roads forming an intersection has a value. Since intersections have a value, therefore the four intersections that comprise a block within will also have a value.
Also, every block has a real estate value. I wanted to find the relationship between these two things.
So as part of the Austin study, I built a spatial integration map (above) and then I tabulated all the property data from the below blocks. I then averaged the blocks by their distance from I-35. For example, A4, B4, and C4 were lumped together in order to smooth out some of the noise within an individual block.
So I have every property within every block shown above listed into a database with values for amount of square footage by use, land value, assessed improvement value, amount of parking, lot area, etc. After summarizing each property within its block of three, I was able to put together the below chart:
It shows land value per square feet on the y-axis and distance each block of three is in relation to each other. It is shown in section from west to east with Congress and I-35 clearly shown as gray bars. As you can see, there is a clear value drop off away from Congress and towards I-35. To the east of I-35 is a near flatline. I wanted to know whether these values had more to do with Congress as proxy for the center of town as a value creator or 35 as a value 'deflator'. More on that specific analysis is at the link above.
Then after creating the spatial integration map, I went through every block and aggregating its block-value by averaging its four-intersections. That gave me an integration number for each block. When creating a similar chart to the one above, it produced this:
Strikingly similar. The beauty is the two data sources are completely independent of one another. But the real estate market inherently 'knows' or intuits that greater interconnectivity leads to greater demand, and thus the market builds more supply of improvements (square footage) towards that demand based on interconnectivity.
Because the graphs are so startlingly similar, I decided to cut out the middle man and find the equation of connectivity equals expected land value by eliminating distance from the equation, since distance was created solely for visual purposes and measured from the highway. The highway was shown to lower global connectivity, so therefore it is already factored into the equation.
Relating global connectivity to land value produced the following exponential equation:
71820 times Global Integration Integer to the 23.145 power. This may not be the exact equation in every city or even every area within a city, but it is at this particular area.
A remarkably high r-squared value of .9434. That means the degree of correlation is almost perfect (=1). In other words, we can say with near 100% confidence that higher degree of connectivity = higher land value. Furthermore, with this equation we can see if global connectivity is x than land value should be y.
We can also say with similar confidence that the highway is what lowers connectivity and thus diminishes real estate value. As one of my favorite quotes from a 1912 plan of Saint Louis states, "the art and science (two sides of the brain) of city building is to design streets and public spaces to maximize the private use of land." Clearly, when it comes to downtowns that means highways are antithetical to those aims.
We can then take these numbers and produce a suitable FAR (floor area ratio) or density based on expected value. Because the correlation is so strong, even in a dynamic, volatile market like downtown Austin, this means the real estate is already highly adapted to its current infrastructure. Hence, the tendency towards roughly conical skylines. The greatest density (most supply of square footage per acre) is at the core of the city where connectivity is highest (demand). Buildings respond to connectivity, supply to demand.
How do you increase demand? Well, some "urban designers" (note: anybody can and does call themselves or their firm this these days) don't believe changes are necessary to the infrastructural network when revitalizing areas (or clumsily attempting to). Draw a few buildings, wave a magic wand (of subsidy) and voila! Of course, as I often say, subsidizing supply again does very little for demand and a better, more targeted use of public funds is into driving demand via interconnectivity.
Having these kinds of formulas can allow us to determine which properties might be over-valued or under-valued based on current conditions. Or perhaps more critically, can determine what new potential value there might be with a couple tweaks to the surrounding infrastructure by improving connectivity. Strategy: buy a property, work with the city to improve connectivity, profit.