[This is one of a series of posts that explore real world examples of mathematical modeling to help educators better understand its applications. This is not intended to be a context for a student lesson. To learn about Spies and Analysts, I recommend watching this webinar (with elementary, middle, and high school versions) or reading this blog post.]

Perhaps you’ve heard of Zillow, which is a real estate website that can give you a rough estimate for how much a real estate property is worth. While the property values they share are not as researched or accurate as what you would get from a professional appraisal, the fact that they instantly provide this data for free for over 100 million homes is pretty amazing.

So, what if you worked for Zillow and they asked you to create a formula to more accurately predict how much a home is worth? Where would you begin? What information would you want to know? What would you do with that data once you had access to it? These are the topics I’m exploring in my spies and analysts post. I want to walk you through the process so that you can better appreciate the complexities of mathematical modeling.

The first part of the process requires the spies. So, I want you to stop and take thirty seconds to think about what information you would use to accurately predict a home’s value. Would you look at what the home previously sold for? Would you look at how close it is to freeways and schools? Would you look at the crime rate? Would you look to see what other nearby homes have sold for? The list of questions could go on and on. So, think about what information you’d pick if this was your job. Once you’ve determined what information you’d want, keep reading.

Spies
Zillow lists the following data as being a part of the formula they use. While it doesn’t include all the data I had mentioned, none of what they do list is very surprising:

Physical attributes: Location, lot size, square footage, number of bedrooms and bathrooms and many other details.

Tax assessments: Property tax information, actual property taxes paid, exceptions to tax assessments and other information provided in the tax assessors’ records.

Prior and current transactions: Actual sale prices over time of the home itself and comparable recent sales of nearby homes

So now that we know some of the data they use, how would we go about turning that into a price for the home? Is “lot size” more important than “number of bedrooms and bathrooms”? Remember, if your formula isn’t good, customers won’t spend their time on your site and you’ll be out of business.

This is where the analysts come in. Their job is to take the data, figure out what parts are more or less important, and break it down in such a way that it becomes useful. Take 30 more seconds to think about how you might even begin to work with the data.

Analysts
I hope you’re feeling a bit overwhelmed at this point. If figuring this kind of stuff was easy, then everyone would have a company worth over \$5 billion, like Zillow is. Here’s what Zillow does, according to their website:

We use proprietary automated valuation models that apply advanced algorithms to analyze our data to identify relationships within a specific geographic area, between this home-related data and actual sales prices. Home characteristics, such as square footage, location or the number of bathrooms, are given different weights according to their influence on home sale prices in each specific geography over a specific period of time, resulting in a set of valuation rules, or models that are applied to generate each home’s Zestimate.

Just when you thought it was hard enough to figure out what information you needed, you start to realize that even doing something with that information is challening too! The reality is that they created a formula to take all of that information, determine what was most important, and make it into a website that earns them significant revenue.

Conclusion
I’m hoping that at this point, you have a better appreciation for the complexities of mathematical modeling. Once the spies and analysts are done acquiring the information and putting it together, they still have to determine whether the formula (or mathematical model) they come up with is any good. For example, when they compare actual sales data to the predictions they made and see a big gap, it’s a sign that your mathematical model is not doing its job. Can you imagine the never-ending refinement that a model like this must require?

At this point, there are no computers or calculators that can figure this out on their own. This is where the jobs are at. If we truly want to focus our time and energy in a skill that will really help our students become college and career ready, mathematical modeling is where we need to be.