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Flooding the Return Period

Flooding the Return Period

What does finding someone who shares your birthday, and a 1:100 storm have in common? They both happen more often than you’d expect. In fact, once there are 23 people in a room, you’ve got as much chance of guessing a coin-toss as finding two people born on the same day. That’s probability for you, about as intuitive as a rock in the face- or something like that.

The cynic in me notes that the Return Period phrasing seems designed to dismiss the event as impossible to predict, whilst giving the client the impression that it’ll never happen again.

Having enjoyed my wettest cycle of the year (yes, I know we’re only nine days in); I had good cause to reflect on the irony of having experienced so many “1:100” year storms during my lifetime- while ringing out my socks into the cistern. Perhaps the greatest concern is that the more “1:100” year rains I cycle through, the more likely I am to get equally soaked- confused yet?

The “1 in X” year description of an extreme event is an odd one (know as a Return Period). The cynic in me notes that the phrasing seems designed to dismiss the event as impossible to predict, whilst giving the client the impression that it’ll never happen again. In fact, I sincerely hope that Wikipedia’s article on the subject is accurate when it credits Civil Engineering for the terminology.

In an attempt to demonstrate the wonderful world of Return Periods, I’ve made this little widget. The graph shows the probability of a “1 in X” year event happening over a period of years. By moving the slider you can can change the return period and see how it affects your chances.


Years

 

Despite everything, however, Return Periods should give hope to all those searching singles; despite there only being a 63% chance that you’ll meet that one “once in a lifetime” person, there’s a 1 in 5 chance that you’ve already met them.

Isn’t probability wonderful.

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Comments

  1. Damian

    “In fact, once there are 23 people in a room, you’ve got as much chance of guessing a coin-toss as meeting someone born on the same day as you.”

    This isn’t quite right. Should be “if there are 23 people in a room, you have as much chance of guessing a coin-toss as meeting two people born on the same day”.

    The probability of your example is still pretty low, like intuition would suggest: 1–(365/366)^23 = 6%

  2. Andy T

    Another correction (sorry Tom!):
    Your graph should not say “Years Since Event Last Happened” on the X axis – that’s irrelevant. What it should say is “Period (Years)” and the title of the graph should be “Chance of an event with X return period occuring in a given Period”. I think…
    Hmm, my wording’s still messy, but hopefully it makes my point.

    • Although, as the axis is continuous, isn’t the terminology correct?

      • Andy T

        Afraid not. As the graph is currently worded, it implies that if there hasn’t been a 1in10 year event for the past 9 years (i.e. Years Since Event Last Happened = 9) that there’s a 60% chance of it happening this year. That is incorrect. The fact that it hasn’t happened for 9 years is irrelevant when it comes to predicting what will happen this year.

        What the graph actually shows (and hence should be worded for) is the chance of the event happening in a given time frame. i.e. In a 9 year period, the chance of a 1in10 year event happening is 60% (surprisingly low!).