In this “post-Harvey” period there are many suggestions about how best to spend the $10 or $20 billion we hope to get from the federal government, the state of Texas, local property taxes, potentially new sales tax collections, and (of course) cash proceeds from new local government bond sales.

For example, some folks are suggesting we should spend $6 billion to buy out homes in the western fringe of the Addicks and Barker flood pools and along Buffalo Bayou from Highway 6 to downtown, and channelize or modify the bayou corridor so it can convey 15,000 cubic feet per second. Others are pushing for the so called coastal spine to protect the region from storm surge.  Still others are suggesting that we build a third flood control reservoir in the Cypress Creek area.

I’m concerned that we are letting our emotions and a few cognitive biases harm our decision-making. Our emotions are telling us that flooding is terrible. People’s homes were destroyed. Their lives were horribly disrupted.  Photo albums destroyed.  Mold grew in bedrooms and living rooms. People died. This high level of emotion impacts decision making.  This high level of emotion increases our willingness to pay for projects that will (supposedly) cost-effectively reduce flood risks and damages. This is known as the “affect heuristic” cognitive bias, which basically means emotions can take over decision-making.

In addition, the “availability heuristic” cognitive bias, makes us all feel that flooding has a much higher likelihood of occurring in the near future if a flooding event has happened recently, regardless of the mathematical probability of the future occurrence.  A vivid example of this relates to how we perceive the risk of dying from a shark attack compared to the risk of dying from a falling airplane part.  Most people mistakenly believe that a shark death is more likely than a death from an airplane part because stories about shark attacks are widely reported and deaths from airplane parts are not.  What we hear about or experience recently is weighted more heavily in decision-making.

To avoid falling into the trap of these and other cognitive distortions we should decide how best to use post-Harvey funds using a risk-based decision making framework.  Here’s how I think it should work.

We need to think about potential projects in two distinct ways.  First, we need to think about the risk of a particular flooding event being addressed (over an appropriate period of time) and, second, we need to think about the consequence of that particular event occurring at any point in time. To help illustrate this approach we will consider two hypothetical projects, each with their own risk level, consequence, and cost.

But first we need to talk a bit more about risk and probability.  I created a graph that displays an array of various risk levels that we will use to help make the best decision.

The graph was constructed using basic probability calculations and it shows the probability of various rainfall events being exceeded during various time periods.  The vertical axis shows the probability from 0% chance to 100% chance.  The horizontal axis shows various time periods ranging from 1 to 10 to 10,000 years. It is plotted using a log scale, which allows us to see a very long period of time in a reasonable graph width. The various colored lines illustrate the probability of a particular 24-hour rain event being exceeded during any time period (duration) of interest.  The smaller events are much more common. The larger events are less common.  By examining the red line (13.2 inches in 24-hours) you can see that the likelihood of that storm falling on your home during your 30-year mortgage is about 26%.

The important thing to notice about this chart is that the longer we are willing to wait, the more likely any storm event becomes.  Let’s take a look at the very rare 18.9 inch rain storm in light blue. Over a 1 year time period we feel safe, because that much rain only has a 0.2% of happening during that time period. But the likelihood of that much rain falling on your home during your 30 year mortgage is about 6%. The chance of that storm hitting your home during 250 years is about 50%. So the crazy thing is that ALL of Houston has a non-zero probability of getting hit with a Harvey type storm or larger. It’s just a matter of time and the longer we wait the more certain the storm becomes. All of the curves eventually hit 100%.

These curves describe the risk of a certain rainfall depth hitting a certain location. Another similar set of curves could be created to illustrate the risk standing or flowing water achieving a certain elevation as a result of runoff from a rain event. This could be from bayou flooding, inundation of a low area, coastal surge, or reservoir pools filling up.

Ok, back to our two hypothetical projects. Here are the estimated or calculated facts about each of the projects. In real life all of this information would be estimated or calculated using engineering principles, computer models, construction cost estimating techniques, appraised property values, land values, and other sources and methods.

Project One – Conveyance Improvements: 

• Description: Acquire land and enlarge bayou channel to increase the channel’s conveyance capacity.
• Design Basis: Improve conveyance of stormwater runoff. Change stormwater carrying capacity to handle runoff from a 9.6 inch storm (4% annual chance) to 13.2 inch storm (1% annual chance).
• Cost: $450 million
• Benefit: Reduces flooding risk for 1,350 structures worth $675 million from a 9.6 inch storm (4% annual chance) to 13.2 inch storm (1% annual chance).

Project Two – Buyouts: 

• Description: Acquire land, demolish structures, regrade land to provide detention, and re-landscape to make park area.
• Design Basis: Remove home from high risk area which floods from 6.2 inches of rain (20% annual chance of flooding).
• Cost: $720 million
• Benefit: Reduces flooding risk for 1,350 structures worth $675 million from 4% per year (rain depth of 9.6 inches) to 0% forever.

Let’s look at each project from a benefit / cost perspective, while factoring in the cumulative risks.

Before Project One the risk of loss over 100 years can be determined from the graph by finding the intersection of the 9.6 inches curve with the 100 year line. This risk is 98%. The value of the loss (the consequence) is $675 million in present dollars. Multiplying the risk times the consequence provides the risk weighted loss for a 100 year period, which, in this case is $661.5 million.

After Project One the risk of loss over 100 years can be determined from the graph by finding the intersection of the 13.2 inches curve with the 100 year line. This risk is 63.5%. The value of the loss (the consequence) is still $675 million in present dollars. Multiplying the risk times the consequence provides the risk weighted loss for a 100 year period, which, in this case is $428.6 million.

Project One reduces the risk weighted loss by the difference between $661.5 million and $428.6 million. This reduction is the project benefit, which equals $232.9 million. The benefit to cost ratio is calculated by dividing the risk weighted benefit of $232.9 million by the project cost of $450 million. For this project the benefit to cost ratio is 0.52, which would not justify doing the project. Most project sponsors would only move forward if the benefit / cost ratio was greater than 1.0.

Now let’s look at Project Two.

Before Project Two the risk of loss over 100 years can be determined by multiplying the 20 year risk weighted loss by five. The 20 year risk can be obtained from the graph by finding the intersection of the 6.2 inches curve with the 20 year line. This risk is 99%. The value of the loss (the consequence) is $675 million in present dollars. Multiplying the risk times the consequence provides the risk weighted loss for a 20 year period, which, in this case is $668.3 million. Multiplying this by five, provides the 100 year risk weighted loss of $3.34 billion. (This assumes that the homes are repeatedly rebuilt and flooded.)

After Project Two the risk of loss over 20 years is zero because the structures are gone. The value of the loss (the consequence) is also zero because the structures are gone. This means the 100 year risk weighted loss is also zero.

Project Two reduces the risk weighted loss by the difference between $3.34 billion and $0.00. This reduction is the project benefit, which equals $3.34 billion. The benefit to cost ratio is calculated by dividing the risk weighted benefit of $3.34 billion by the cost of $720 million. This division yields a benefit to cost ratio of 4.6, which is an excellent ratio which indicates the project should proceed.

These two examples are admittedly simplistic, but we really need to use the methods illustrated to make smart decisions.  Let’s use the change in the risk weighted loss (pre to post project) to derive the project benefit value. Let’s compare that to the project cost.  Let’s calculate the project benefit to cost ratio over an appropriate time frame. Let’s do the projects with benefit to cost ratios of more than 1.0.