Small probabilities, big consequences

Sonnie Bailey

19 June 2020

Low probability events shape our lives, more than you'd think.

The probability of being born in the first place is infinitesimal. Every single person in your family tree, from your parents upwards, had to meet and conceive at just the right time for you to exist.

It's a wonder we're here.

The big events in your life may be predictable in their general contours.

However, the specifics are impossible to predict, and wildly improbable. For example: who you marry, how many children you have, their genders and characteristics, etc.

(And even then, there are no guarantees. Not everyone gets married. Not everyone has children.)

Yet here we are.

Good and bad, we need to give small probability events their due.

Take a 1% chance often enough and it’ll happen

Roll a 100-side dice, and eventually your number will come up. For better or worse.

A 99% likelihood that something will happen isn’t a guarantee that it will happen. It means that 99 times out of 100, that thing is likely to happen. On average, you should expect it not to happen 1 in 100 times.

On a more consequential note, this was the last snapshot of the major prediction sites regarding the 2016 US presidential election before polling started. The figures related to the likelihood of Hilary Clinton winning the US presidency.

The FiveThirtyEight figures seem remarkably prescient: they gave Trump an almost 1-in-3 shot.

Many of these institutions took a hit to their reputation when Trump was elected. The weird thing is, if you understand the probabilistic nature of these predictions, over a long enough time frame, unlikely events are almost certain to occur.

The shower is a killer

I recently mentioned Jared Diamond's New York Times article "That daily shower can be a killer" from 2013. I spoke about it in the context of COVID-19, before things worked out so well for New Zealand (for now, at least).

He stressed the "biggest single lesson that I've learned from 50 years of field world...: the importance of being attentive to hazards that carry a low risk each time but are encountered frequently".

Diamond encourages his readers to adopt a "hypervigilant attitude toward repeated low risks", which he calls "constructive paranoia". He acknowledges that "it exasperates many of my American and European friends". But he also notes that some of his friends have learned his attitude, "as I did, by witnessing the deaths of careless people".

Every moment or unique interaction you have might pose a very marginal threat of being infected or infecting someone on to you. Reducing the likelihood is a good philosophy.

Persistence > patience

Sometimes the same philosophy that stops bad things from happening also helps make good things happen

I've just finished reading Bluefishing: The Art of Making Things Happen. by Steve Sims. One of the sentences in the book captures Sim’s philosophy very well:

"Passion plus persistence will remove doors from their hinges, shred them, and throw them away."

Sims continues:

"It's not a coin toss. It's not a 50/50 proposition that you will succeed. When you go through something with passion and persistence together, you can't be blocked."

The message is that if you want something badly enough (passion), you need to keep trying (be persistent).

Of course, I'd add my own nuances. But the key message is powerful.

If something is a 1-in-100 possibility, then it's like rolling a 100-side dice. You might not get your number on the first roll, but keep rolling and eventually your number will come up.

I recently read/heard someone mention that they prefer the term persistence to patience. Patience implies passively waiting, while persistence implies being active. I like that distinction.

A personal story

The best example of persistence in the face of low odds from my own life was in 2008, when I decided that I might try practicing law, despite being insistent to that point that I didn't want to do so.

The odds weren't in my favour. I was living in Australia, and my law degree was from New Zealand. It was the middle of the GFC. I hadn't gone through the traditional route of doing clerkships and applying for graduate roles. I’d forgotten more than I remembered.

But I persisted. I applied for, or contacted, over 200 different firms over the course of around six months. I’ve still got the files on my computer: I created a new directory for each role, and in each role I retained a copy of my cover letter and the CV I tailored for the job, plus my research at the time.

After rolling the dice, I eventually found a role with a terrific firm. It was a firm that I had specifically reached out to. Because I wasn’t just applying for advertised jobs: I was approaching organisations that might value someone with my capabilities.

The firm I ended up working for was one of a handful of firms that met the exact criteria I was after: a small firm, working in the area of expertise I was interested in, that seemed to have values that were in alignment with my own.

They hadn't advertised a role, but I printed a CV and cover letter and physically dropped it off. They didn't contact me right away: in fact, it was several months before I heard from them.

That role has subsequently defined my career, and I am still on excellent terms with the firm and many of the people who work there. In one sense, I am especially lucky to have found that role. In another sense, I persisted until I won.

Keep taking shots

As Wayne Gretsky said: "You miss 100% of the chances you never take".

Keep taking shots, and the probabilities will wind up in your favour.

In most cases, you can also take steps to improve the probabilities. Increasing a 1% probability to 2% or 4% may not seem like a lot, but in most cases you'll roll your number quicker on a 25-sided dice than a 100-sided dice.

... and keep playing defence

And likewise, be careful of those 1-in-100 and 1-in-1,000 risks, especially where the consequences are large.

If you can make a 1-in-100 risk a 1-in-200 risk – or better yet, add a zero or two – you’re on the track.

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