Unexpectedly Intriguing!
02 August 2019
Trinity Nuclear Test - Source: Los Alamos National Laboratory - https://library.lanl.gov/infores/nuclear/trinity.htm

Alex Tabarrok recently kicked a hornet's nest when he asked "What is the probability of a nuclear war?", where he focused on survey results compiled by Luisa Rodriguez that put the unique event probability of a nuclear war breaking out anywhere in the world at 1.17%, where he went on to estimate that the probability of a nuclear war taking place during the 75-year lifespan of a child born today would be about 60%.

Here is how he arrived at those lifetime odds:

For a child born today (say 75 year life expectancy) these probabilities (.0117) suggest that the chance of a nuclear war in their lifetime is nearly 60%, (1-(1-.0117)^75). At an annualized probability of .009 which is the probability from accident analysis it’s approximately 50%.

That math formula provides the key to estimating the probability of any unique event occurring within any set period of time, which we've incorporated into the following tool. If you're accessing this article on a site that republishes our RSS news feed, please click through to our site to access a working version.

Probability of Unique Event
Input Data Values
Percentage Odds of Event Occurring in Any Given Year
Number of Future Years To Estimate Probability of Happening

Odds of Unique Event Happening During Period of Time
Calculated Results Values
Estimated Probability

The default numbers in our tool are taken directly from Alex' example, where we find the probability of a nuclear war happening sometime in the next 75 years is 58.6%.

But the tool, and the math behind it, can be used to consider the odds of any unique event, where you're welcome to substitute numbers that apply for whatever scenario you would like to consider.

Let's consider a more fun scenario. In 2019, the St. Louis Blues hockey team went from being in dead last place in the league at the beginning of January to winning the Stanley Cup for the first time ever in its 52-year history six months later. The team won an 'ESPY' for "Best Comeback" in sports.

As unique events go, the Blues 2018-2019 season stands out as especially unique. Let's consider some odds:

  • There are 31 teams in the National Hockey League that could potentially win the Stanley Cup in any given year, so the basic probability of winning the cup is 1-in-31, or 3.23%.
  • The St. Louis Blues were playing their 52nd season, without ever having previously won the cup. Based on history then, winning the cup for the first time would have odds of 1-in-52, or 1.92%.
  • In early January 2019, after the team had already chalked up the worst record in the NHL, Las Vegas' sports books were giving a 1-in-300 chance that the team would go on to win the Stanley Cup, or 0.33%.
  • One lucky gambler bet $400 at odds of 1-in-250 that the Blues would win in January 2019, representing a 0.40% probability of winning. (He would go on to win $100,000 on that long shot wager).

What would the odds be of the Blues repeating their Stanley Cup-winning season during their next 52 seasons?

Averaging all these percentage probabilities together gives us an aggregate probability of 1.47%. Over the next 52 years, the tool suggests the Blues have a 53.7% probability of winning the cup a second time.

That's more likely than a nuclear war breaking out somewhere on Earth during the next 52 years, which would have nearly a 46% probability of occurring. Which outcome would you rather cheer for?

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About Political Calculations

Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:

ironman at politicalcalculations.com

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