Tag Archive for: formula

Formula for Allocating Future Flood-Mitigation Funding Deceives

How do you fairly allocate flood-mitigation funds? Voters have argued about that since the day Harris County Commissioners Court redefined the conventional meaning of “equitable” with the first equity formula in 2019. Since then the formula has changed several times to ensure low-to-moderate income (LMI) areas continue to receive the lion’s share of mitigation funding, even as some commissioners claim LMI areas get none.

On 6/28/22, the Harris County Community Resilience Flood Task Force proposed yet another formula for allocating potentially billions of dollars in future flood-mitigation funding. It purports to objectively calculate the benefits received by different areas. But it doesn’t in any conventional sense. And therefore, the results can be deceptively counter-intuitive.

Problems With Formula

The formula shows increased benefit when:

  • Risk remains unchanged.
  • Costs increase.
  • Population decreases.

The formula is…

Benefit = Total Cost/(Population X Risk)

On July 2, 2022, I posted about a variety of issues that affect the validity of this formula. Admittedly, the post got complex. So let me give you two simple examples that dramatize these problems.

In each example below, I’ll hold two of the three variables constant. That makes it easy to see whether “benefit” varies in a predictable direction. And whether that matches what people expect when they hear the word “benefit.”

Cost Example

The value of “10” applied to Risk in each case represents a 10% annual chance of flooding.

If you hold risk and population constant, while increasing cost

  1. Population = 5000, Risk = 10 and Cost = $100,000, then Benefit = 2
  2. Population = 5000, Risk = 10, and Cost = $1,000,000, then Benefit = 20

…benefit increases by spending more without reducing risk! A taxpayer nightmare!

Population Example

If you hold cost and risk constant, while increasing population

  1. Population = 2000, Risk = 10, and Cost = $1 million, then Benefit = 50
  2. Population = 5000, Risk = 10, and Cost = $1 million, then Benefit = 20

…benefit decreases by helping more people with the same dollars! Again, counter-intuitive.

Both takeaways are confusing. What is this formula measuring?!

I would argue that, in a flood context, most people strongly associate the word “benefit” with “risk reduction.”

But this formula doesn’t measure risk reduction. And it doesn’t measure efficiency either. It measures per capita investment associated with a certain level of flood risk and calls that “Benefit.”

So, the more people you help with any given sum, the more the benefit goes down. Voila! That makes it look as though the highly populated watersheds (that have received the overwhelming majority of prior investments) have received little benefit. And that may be the point of this formula. It will send even more money to those same areas.

In logic, they call this the fallacy of incomplete evidence – more commonly known as cherry-picking. You cherry pick data that favors your argument and ignore the rest. For instance, consider the image below.

Brays Bayou at Calhoun, photographed May 2021. Note abundance of multi-story apartments.

The total population in some areas includes many people in tall apartment buildings or high-rises. For many of them, flooding may be more inconvenient than financially devastating. Yet the formula assumes all people suffer equally.

The formula provides the appearance of objectivity and fairness. But it masks important information by lumping everything into a single number.

But the proponents of this formula don’t even want to discuss numbers. They want to render the results as heat maps, layered with Social Vulnerability Index, LMI and other data guaranteed to mask and perpetuate the lopsided distribution of flood-mitigation funds.

Omitting Benefits to Structures

By defining Benefit as the cost per person to achieve a certain level of flood risk, the formula omits any benefit to structures. That’s the traditional way to define the benefit of a flood-mitigation project. You measure “the value of damages avoided.” Whether one person lives in a house or two people live there, the cost to protect those people and that home remains the same.

For instance, widening a channel can reduce flood risk for a house. But with the proposed formula, that home and its value no longer count – only the number of people living within it. So, doubling the number of people in a representative home cuts the Benefit of a flood mitigation project in half.


The formula is a vast oversimplification. It omits valuable information such as avoided damages.

It’s also confusing and semantically deceptive in that results vary in counter-intuitive directions.

Finally, as I previously posted, the formula is not valid. It masks several apples-to-oranges comparisons.

Yet the majority of the Community Resilience Flood Task Force proposes using it to help guide (potentially) billions in future flood-mitigation investments. That could hurt taxpayers, flood victims, future bonds and the credibility of local government.

The formula can deceive people into making bad flood-mitigation investments. But in this case, there’s no Securities & Exchange Commission to protect investors. Only the ballot box.

Posted by Bob Rehak on 7/6/22

1772 Days since Hurricane Harvey