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The Ethics of Uncertainty, Survivors Bias, And The Law of Large Numbers

A great line from the hit series “Narcos” illustrates the law of large numbers idea more poetically. “The bad guys have to keep getting lucky. We only have to get lucky once.” No one outruns the law of large numbers forever.

Ed Latimore
Ed Latimore
Writer, retired boxer, self-improvement enthusiast

“If you replayed the circumstances of my early life repeatedly, nine times out of ten, I suspect I’d end up in jail.”

-Rob Henderson, Cambridge PhD student

Accepting luck’s role in your success takes a certain level of maturity and humility. 

It takes the same maturity and humility to accept your role in creating your problems.

Some things you control.

Some you can’t.

All contribute to your quality of life.

By luck, I mean things that affect the outcome that you don’t control.

By skill, I mean things that affect the outcome that you control.

I think about one of the defining moments in my life. I stopped drinking after a night when I couldn’t remember how I got where I woke up. I just knew that I drove there.

This was not the first time I’d driven drunk, but it was the last.

I’m not proud of the behavior. Although no one got hurt, the risk I took doing that still fills me with guilt, but my emotional regrets and remorse are not why I bring this up. I bring it up to illustrate the probabilistic nature of life. 

When you focus only on the outcomes, you create a particularly devastating illusion. 

The ethics of uncertainty and drunk driving

In 2016, a little more than 1 million drivers were arrested for driving under the influence of alcohol or narcotics. That’s less than one percent of the 111 million self-reported episodes of alcohol-impaired driving among U.S. adults each year. 

This means that if you’ve been drinking, getting arrested for a DUI is the least likely outcome. If you have a DUI, the numbers suggest that you got unlucky. And not just kind of unlucky. However, it was your fault for getting behind the wheel intoxicated.

Your lack of skill in making the best decisions coincided with landing on the wrong side of the coin toss. When you look at it from this perspective, neither outcome feels right. Either you got away with a dangerous activity or you got caught when MOST people don’t.

We want the world to behave predictably and deterministically. If every time someone got behind the wheel with a BAC over .08%, we want to know they’d be arrested. At the very least, we’d sleep better knowing that it happened more than 1% of the time. We’d also have fewer drunk drivers since they almost always get arrested instead of developing a case of survivor bias.

That’s disheartening, but think about the families of murder victims. There’s a 40 percent chance they’ll never know who did it—and murder has one of the better clearance rates of violent crime. (Source)

Survivor’s bias is a dangerous logical fallacy

Survivor's bias discounts those who didn't survive
Survivor's bias discounts those who didn't survive

Survivor bias is the logical error of concentrating on those who passed a selection process while overlooking those who did not. The most famous example of this is the case of the Allied forces in World War II investigating where most bullet holes were concentrated in their planes that had returned from battle.

The Allies analyzed bullet hole patterns on their planes, thinking more armor may be useful where the planes were getting hit the most. However, analyst Abraham Wald pointed out that the correct conclusion was the opposite - they should reinforce where there were the least bullet holes. Why?

Because the planes they were looking at were the ones that had survived and returned. 

The areas with fewer bullet holes were likely the most critical - planes getting hit in those places likely didn’t make it back.

Survivor's Bias and where the bullet holes are not
Survivor's Bias and where the bullet holes are not

So, those least damaged areas represented the most vulnerable parts. The lesson here is that when you only look at successful people as an example of what to emulate, you do two disservices:

  1. You ignore everyone who didn’t make it despite having the same conditions and circumstances. At best, this creates a blind spot. At worst, it creates an impossible burden of expectation.
  2. You follow the wrong metrics for success. You set yourself up for failure because you’re operating under conditions that usually lead to failure. This is a big problem if you ever want to improve.

Because I never got caught drinking and driving, I thought I could keep getting away with it. Most people who habitually engage in risky behaviors believe something to this effect. They view their “success” as a sign of competence. Or maybe, they don’t care. Either way, the law of large numbers catches up to everyone.

You can’t outrun the law of large numbers

Coin toss and the law of large numbers
Coin toss and the law of large numbers

The law of large numbers refers to the tendency for results involving randomness to stabilize or converge as more trials or instances occur increasingly. While small sample sizes show wide variation and flux, larger data sets reveal more predictable average outcomes from the collective results.

A simple example is coin flips. Flip a coin 10 times, and heads or tails could dominate heavily by chance - the ratios will visibly differ from the 50-50 probability. But if you complete 10,000 coin flips, you’ll likely end up close to 50% heads and tails as outliers balance out. The enormous volume normalizes around the expected value.

A great line from the hit series “Narcos” illustrates this idea more poetically. “The bad guys have to keep getting lucky. We only have to get lucky once.” Maybe I would have kept getting lucky; however, no one outruns the law of large numbers forever. 

But because I was one of the 99% who never got a DUI, I was able to change my life around and not suffer any consequences (jail time, criminal record, inability to get a passport, etc.). Although I got sober of my own volition, I don’t feel like this is an ethical and fair outcome. It is simply a lucky one that I capitalized on.

Skill and insight are required for the things you can control, but you need luck to survive the things you can’t. Opportunity is when you survive the latter long enough to make progress based on the former. If you push your luck and take more risks than you need to, you will eventually come up on the wrong side. At that point, no amount of skill can save you.

Push your luck too much, and eventually, your luck will push back

I regularly feel guilty because every time I bet on tails, I won. Just because I made the correct call doesn’t mean it was the right one. This has given me a powerful framework for assessing people.

I don’t look down on (most) criminals because I know that a stupid decision can have life-changing effects if you land on the wrong side of uncertainty. Some people never have a chance to learn and get their lives right before the law of large numbers forces them to do so.

I’m not saying that people who break the law shouldn’t be imprisoned. What I’m saying is that many of the people you know and respect were only able to become that way because they were on the right of uncertainty in their idiotic moments.

Of course, this also means that you could be dealing with legitimate violent criminals who never got the rightful designation. It’s the most unfair coin toss in the universe because if the perpetrators win the toss, then another person may be at risk.

We don’t all become redemption stories. We don’t all get in front of our problems before the law does. With that said, if you’re currently engaging in any behavior where the law of large numbers is currently on your side, my recommendation to you is to stop before the math catches up to you.

The ethics of uncertainty and the law of large numbers give you a chance to get right before the universe intervenes. And it always does, one way or the other. 

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I’m a former heavyweight pro-boxer (13-1-1) and alcoholic (Sobriety date 12/23/13), current writer, and aspiring chess master. I was raised in the projects by a single mom and failed high school, but I eventually earned a bachelor’s degree in Physics.

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Ed Latimore
About the author

Ed Latimore

I’m a writer, competitive chess player, Army veteran, physicist, and former professional heavyweight boxer. My work focuses on self-development, realizing your potential, and sobriety—speaking from personal experience, having overcome both poverty and addiction.

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