# 100-Year Floods Are More Common Than You Think

I hope that all of you in the Atlanta metro area are safe and dry right now. I’d also like to take this chance to correct a common misconception, which is often promoted by the media every time a flood occurs. As just one example, take this CNN article:

He hustled out of bed and rushed to the door. There were his neighbors, surrounded by floodwaters the neighborhood is supposed to experience only once every 100 years.

The highlighted sentence is not accurate, and gets people thinking strange thoughts like “Oh the last flood was in 1969, I should be good until 2069 or so”. The fact is there is a reason we hear about such floods all the time. Let’s look at what FEMA has to say:

The term “100-year flood” is misleading. It is not the flood that will occur once every 100 years. Rather, it is the flood elevation that has a 1-percent chance of being equaled or exceeded each year. Thus, the 100-year flood could occur more than once in a relatively short period of time.

Again, if you live in a 100-year floodplain, you have 1 percent chance of being flooded every year. Think of how concerned you’d be if you were told there was a 1-in-100 chance of your house burning down every year. The way the math works out, this means that over a 30-year mortgage, there is a 26% chance you’ll have a 100-year flood during that time period (1 – (0.99)30). This is also why most people with home loans in such areas are required to buy flood insurance.

Many people are in 500-year flood plains, which gets people even less worried. “The last flood was in 1909, we’re good for another 400 years!” Actually, having a 0.2% chance of a flood each and every year works out to a 6% chance of occurring at least once over a span of 30 years, or 1-in-17.

If you haven’t already, take some time and check if you are in a flood plain here. Some may consider buying flood insurance even if you are not required to by your mortgage lender. We ended up buying a modest amount of building coverage from the NFIP.

1. Mark says:

I can attest to this. I live in a suburb of Chicago, and my office is in a 100-year flood plain, about 1/2 mile from a river. We have had catastophic floods in 1986, 1987, and 2008. The most recent flood caused about \$150,000 worth of damage to the building and it’s contents, not counting the lost revenue and stress.

2. Jeff says:

They should not call them 100-year floods then. I know it’s obvious, but the misnomer is the issue.

3. TL says:

It’s a misnomer on purpose. No one would buy a house in a zone with a 26% percent chance of flooding over 30 years.

4. Andrew says:

Most people are just awful at understanding probability and statistics, and it is to their significant detriment. Thanks for this illuminating post.

5. Justin says:

You’re assuming that each year is dependent on the year prior. If each year is independent of each other, then the chance of a flood in a 100-year flood zone would only be 1% every year, right?

6. Chris Brown says:

Any renters out there? Get renters insurance. It’s cheap! My house burned down and the landlord got a fat check for the building but I got a fat nothing for the contents.

7. @Justin – I’m not sure I understand what you are saying. Each year is independent of each other, AND the chance of a flood in a 100-year flood zone would only be 1% every year.

It’s like saying if there was a 100-sided coin/dice, you would roll it each year, and if it came up 1 out of 100, there would be a flood. Then the next year, there would again still be a chance you’d roll and get 1 again.

The chance of a 100-year flood occurring within a 100 year span is, weirdly, about 63%. 1-0.99^100

I’m going to add to the post that we did buy a small amount of flood insurance from NFIP.gov.

The real problem with trying to do probabilities like this is that, well, probabilities are made up imaginary things. Numbers used to describe observations.

That is to say, let’s imagine you level in a once in a century floodplain. So we say every year there’s a 1% chance of a flood. What’s the probability that next year will flood? It’s 1%.

But in reality that’s meaningless — it’s either going to flood or it’s not. 1 or 0. All we have is historical averages that over certain geologic timespans we can measure, and we can average. We believe the likelihood of a flood in any given year is 1%. But thanks to climate change, sunspots, UFOs or whatever, floods could be more or less likely. We don’t really KNOW what the probability for a specific year, or decade is. It’s somewhat like measuring average speed versus an instantaneous velocity.

I don’t remember my math enough–given Mark’s anecdote, he suffered 3 floods in 22 years from 1986-2008 in a supposedly 1% area. How do you calculate the probability?

P_three_floods * P_19_no_floods = (.01)^3 * (.99^19) = ?

But would that mean 3 floods in a row followed by 19 no floods?

9. Alvin says:

Out of curiosity, how much do you pay for your “small amount of flood insurance”? I know it’s heavily dependent on many factors, but I am just curious about your situation. Perhaps if I have a 500-year flood zone, can I and should I pay less?

10. I don’t have my cost with me right now, but you get a no-obligation quote from many insurance agents (start with your homeowner’s?). The cost will be the same everywhere, as it is directly from the government and any commission is built in. Cost is dependent on flood map area and you can choose your coverage amount,

11. Flood insurance is relatively cheap and does drop for folks in non-flood zones as opposed to someone with a beachfront view in Florida.

It is hard to determine if you should get insurance for a 100 year flood. What people need to remember about insurance is you are guarding against a cost that you cannot afford yourself. So if a flood, however remote the possibility, would really hamper you financially then you should look to get flood insurance. If you could afford to replace your furniture and goods (in the basement and main floor) then you don’t need insurance.

Also, you can get levels of flood insurance. Rather than covering all your household goods, you could get a lower replacement value. This keeps premiums lower and still helps if the rare flooding event happens.

The number of floods ‘X’ in a period spanning ‘n’ years is simply a binomial random variable (repeated Bernoulli trials). The probability of exactly ‘k’ floods in ‘n’ years is:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

where ‘p’ is the probability of a flood occurring (say, 0.01) and C(n,k) is the combinatorial coefficient. For 1 or more floods in 30 years, we get Jonathan’s simplified expression:

P(X >= 1) = 1 – P(X=0)
= 1 – C(30,0) * (0.01)^0 * (0.99)^30
= 1 – (0.99)^30
= 0.26

Now if only we could compute the flood insurance premium that easily!

13. teeej says:

anyone have any good advice or experiences with renters insurance? I need some, and haven’t done much research yet, but I rent a 2br house with less than 10k in material goods. I’d like to go low deductible in the event of a stolen bike, ipod, etc, as theft is the most likely event I would use it for.

I’m in Phoenix, and don’t think I’m in a monsoon floodplain or flashflood path, but Sedona just got hammered with bad flooding last week.

14. Debbie M says:

Not only that, your chance of flood each year is 1/100 if you’re on the edge of a 100-year flood plane. If you’re in the middle of it, your chances of flooding might be even worse. You might be on the edge of the 72-year flood plane, for example.

15. Debbie M says:

@teeej, insurance is most cost-effective to prevent financial catastrophe. Renter’s insurance is best for things like flood and fire, not minor thefts or damage to electronics from a nearby lightning strike. (I don’t have an answer to your actual question, though; I wasn’t smart enough to get renter’s insurance back when I was still renting.)

16. Margaret T says:

We purchased flood insurance for our home and it was \$350.99 for the year. A tad on the high side but we have had two occasions in the past year or so when the heavy rain has brought the water level almost up to the front door – despite the fact that we are built fairly high from the road. The city has been lowering roads and making all kinds of changes which has changed the gradings somewhat. I think in the past three years the increase in our premium has been about \$100.00. I feel like an imposter on this site as all the readers seem to be so smart. Never could figure algebra let alone figure the probability of flooding by this method. I do however appreciate it’s value.

17. Jon says:

This article/discussion may be making a mistake. The assumption that 100-yr flood plain means a 1% chance of being flooded can be questioned based on conflict of interest. The same agency which collects the insurance money is the one which sets the flood plain map. Based on this conflict it would be reasonable to question the validity of the designation.

If your house gets designated you are forced by FEMA to pay up for insurance even if you don’t want it. And you are forced to pay for insurance on the entire value of your home — even though the probability of a flood destroying your home is very unlikely (The 1% flood is only a few inches above floor level — a massive flood forcing you to wait on your roof for help is much much smaller probability).

18. John says:

@Debbie, why should a renter care about flood or fire if he does not have many material possesions in his house? Isn’t that one of the benefits of renting.

19. John,

Not that I carry it, but renter’s insurance is primarily for liability purposes (e.g. if your actions caused material damage to the unit and you get sued by the landlord, etc.). Unless you own really high end furniture and electronics, renter’s insurance usually isn’t worth it to protect personal property that is perhaps worth a few thousand dollars.

On another note, I should qualify that ‘k’ in the probability calculation a few posts earlier does not strictly refer to the number of floods – rather, it is the number of years in a total of ‘n’ that flooding will occur, since the event under consideration is “whether or not we will experience a flood in a given year”. The distinction is important as there can be multiple floods in a year.

20. I think this is a great point.

Definitely use common sense. Flood insurance is extremely affordable in designated “low risk” areas.

Under-insurance is a HUGE issue where I live.

Firstly, our low lying (basin) location, protected by nearby river levies, prompted us to raise our eyebrows at our home’s 200-year-flood zone designation. We bought flood insurance the day we moved in. (\$295 per year or so – hasn’t increased in a decade. Insurer is the government). This seemed rather no-brainer to us. I personally think you would be an idiot not to. (Plenty more think we are idiots to live here).

In recent years, we have been reclassed to a 10-year-flood zone. I knew there was flood risks, but we were not informed how bad it really was. Lord knows why buildings were ever permitted. Politics, politics, politics. Levies, levies, levies. Even so, there seems to be little interest in most residents here, to buy flood insurance. There have been a lot of campaigns to try to inform residents, and even discounted offers of \$295 annual insurance policies for the next couple of years, presumably until levies are improved, etc. We should end up with a 500-year-flood zone. As long as I live in a low lying area next to a river, I will always have insurance. I don’t care what the flood maps say.

It just amazes me how few in my neighborhood actually have flood insurance. Extreme case, but I am sure there are many others across the country.

21. Wes says:

S – I kind of have to disagree with you.

1) Take an honest inventory of your whole apartment – furniture, electronics, clothing, jewelry, appliances. I believe for most people that’s a lot more than a few thousand dollars.

2) Renters insurance will also pay hotel or other housing expenses in case your place burns down.

I speak from experience, unfortunately. Back in the day, our apartment burn down. We were fortunate to have renters insurance. All of our belongings were paid for (over 20k). We stayed with my sister for a few months and the insurance was able to pay “rent” to her, which was almost \$3k.

22. Wes,

I should mention that I am one of a dwindling species that believes in a “less is more”, minimalist lifestyle, more out of choice than necessity. I can honestly say that the total value of my material possessions does not exceed \$8,000. This includes my automobile.

While I’d like to continue living this way, I understand it may not be possible due to spousal considerations, societal pressures, etc. However, right now, renter’s insurance is probably overkill for protection of my personal property. I’m also fortunate to have family close by, should I need temporary accommodation for a brief period.

23. Justin says:

@ Jonathan:

My point is that because each year is independent of the year prior. There will always be a 1% chance, for that year. Sort of like spinning a coin. No matter how many times you spin the coin, the chance of that coin landing on heads is always 50%. I hope what I’m saying makes sense..

24. Justin,

For any given year, you are right, the probability of flooding in that year is always 1%. This is analogous to a coin flip, and is known as a Bernoulli trial.

http://en.wikipedia.org/wiki/Bernoulli_trial

However, when we consider a period spanning ‘n’ (say, 10) consecutive years (or coin flips), we have to account for all possible ways in which floods (or heads) may be distributed throughout those years (flips). What is the probability of 3 heads in 10 coin flips? More generally, what is the probability of ‘k’ “successes” in ‘n’ independent Bernoulli trials? This is given by the Binomial distribution.

http://en.wikipedia.org/wiki/Binomial_distribution

25. Wes says:

Justin, actually that is not correct. Check wikipedia for either Mony Hall or Probably of having a certain gender with your third child.