The Problem With Probability

Read time —
6 Minutes
Last updated
March 29, 2024

Imagine trying to calculate the probable outcome of every decision.

Yes, it sounds kinda painful. But would it improve the quality of our decision-making?

Yes, it would. But it would also do something else.

It would allow us to appreciate that no decision comes with a guaranteed outcome.

The 18th-century journalist, Walter Bagehot was frighteningly right when he said, life is a school of probability.

Probability is the mathematical way of accounting for uncertainty.

It is so logical, that our emotional mind can’t stand it.

That’s the problem with probability.

This article covers:

The Upside to Thinking with Probability

Uncertainty is a part of life.

None of us can predict the future with great accuracy, although it doesn’t stop us from trying.

Entropy; the supernatural collective of uncertainty, randomness, and disorder is always amongst us.

Yes, we create systems which we believe are contained enough to stop entropy from appearing. We forget nothing is ever isolated. The universe is one complex adaptive system most fail to grasp.

Everything is linked, even if we can’t see the connections.

And this brings us back to thinking with probabilities.

Nassim Nicholas Taleb said: "Probability is not a mere computation of odds on the dice or more complicated variants; it is the acceptance of the lack of certainty in our knowledge and the development of methods for dealing with our ignorance."

For me, the most important word is acceptance.

Thinking with probability brings acceptance of uncertainty. After all, the only real certainty is uncertainty.

Even though we know this, we struggle with this acceptance. It goes against our instincts to take comfort in a future we can’t define. Our minds want to know what’s going to happen. We want safety, but in reality, the only thing we are creating is complacency.

There are two upsides to thinking with probability. First, the acceptance, but then also the methodology for valuing the level of uncertainty.

It's why we should overcome our problem with probability.

5 Simple Ways to Think with Probability

Apart from the acceptance, we shy away from probability thinking because we believe it to be difficult.

Probabilities bring equations.

For most of us, the thought of this type of math petrifies us. And for most everyday decisions, is more than we need.

But here's the thing. Probability thinking doesn’t need math. No, it needs a more open-minded approach to the big decisions we face.

Here are five different ways you become a probabilistic thinker without an equation:

  1. Avoid singular outcomes
  2. What don’t you know
  3. Pattern Matching
  4. Focus on probable outcomes
  5. Create a decision tree

Let me explain how these work.

Avoiding Singular Outcomes

Frequently, we see a decision creating only one outcome.

It is an outcome we like. We want it so much — because it’s so attractive — that we go all in. There can be no other outcome.

And then disappointment abounds.

Hindsight often comes from a loved one — “I knew this would happen!” — as you deal with the consequences of not being right.

They didn’t know, it’s hindsight bias talking.

But, we need to be honest with ourselves (acceptance…). We should consider a range of outcomes instead and think about how probable each one might be.

A decision is this: Information + Action = Outcome

Your decision is a consideration of each of these. The unsurprising lesson is that each is open to variation. It’s your job as a decision-maker to consider this variation.

Let’s consider outcomes for a minute.

Jeff Bezos compared business to baseball. He said, "The difference between baseball and business, however, is that baseball has a truncated outcome distribution. When you swing, no matter how well you connect with the ball, the most runs you can get is four. In business, every once in a while, when you step up to the plate, you can score 1,000 runs."

Amazon taking a swing produced 1000 runs, like the Kindle. Or it ended with a strike-out, as the Fire phone crashed. Some might not have hit the centre of the bat. The resulting dribble down the field still gave Amazon insights to help swing again.

Essentially, the point is to question the outcome you’re chasing.

  1. How likely is it?
  2. What else might happen?
  3. What can do to limit the damage if things go wrong?

What Don’t You Know

Every decision begins with information.

The problem we have is this information is often incomplete. Or, to the point, a collection of prior beliefs and opinions.

Yes, those dreaded assumptions.

Rather than accepting assumptions as facts, we should see them as incomplete information.

Questioning, so we can identify what is true and what isn't, is critical. It reveals what we don't know.

With these points, we can now question their probable impact. Understanding this allows us to be more informed before deciding.

We can reduce the uncertainty by knowing what we don’t know.

No one likes surprises. Especially when they come from information that you should know isn’t complete.

Pattern Matching

I’ve written at length about pattern matching and base rates before.

Probability thinking brings both into play.

Historical data gives us a degree of understanding of what is likely to happen given a situation where the scenario is similar. Patten matching draws more on our experiences.

It won’t tell us what will happen. But it can increase our confidence in the potential outcome.

Stock control software works in the same way. But this isn’t about building an algorithm. It’s about building probability into your decision-making process.

Pattern matching appears more frequently than we realise.

It’s an intuitive skill our mind uses to make rapid decisions. We use it to decide whether to eat new foods and go to places we haven’t been before. We are comparing what we see with our past experiences.

This guides us to act.

With probability thinking, we can extend the scope to ask a question. Given the similar pattern, how likely is the same outcome?

This comparison gives us some confidence in deciding.

Base rates need more thought.

We can use external data to compare possible outcomes with past ones. Using base rates gives us confidence when our experiences might be lacking. The probability question still arises though. Given what happened in the past, how likely is the same outcome?

Focus on Probable Outcomes

It seems obvious, but the best decision should support the most likely outcome.

Frequently, we go with a choice because it is the one we most like. When an outcome offers an attractive incentive, it is easy to become blind to reality.

That’s why lotteries offer big prizes.

We are suckers for incentives, especially huge ones that come with a low cost.

A probable outcome brings a much-needed perspective to our decision-making. It forces us to ask what the likely outcome is going to be.

We tend to look for the probable outcome when we assess a decision rationally. That’s the thing with probability thinking. It holds no place for emotion in our decision-making.

It is a truth few like, but a logical approach will increase your chances of being right.

Create a Decision Tree

A decision tree is a way of simply mapping out a decision.

From a probability thinking perspective, it gives you a visual framework to consider the initial decision (the root) and the possible pathways (branches) that follow. These pathways end with decisions (leaves), which help you see a more logical path.

Here is an example of a decision tree I created to help me decide whether to write this article.

An example of a decision tree from The Resolve Blog
Example of a decision tree

The question is, how does a decision tree align with thinking probabilistically?

For me, it has four upsides:

  1. I can see my decision before me. I can see the information I have, I can define what action I can take, and see the outcomes it creates.
  2. I can assess possible outcomes. Seeing the outcome path leads me towards potential consequences. It also allows me to consider different scenarios.
  3. It becomes quantitative. I can assess outcomes and consider the probability of achieving them. It makes the concept of probability more concrete.
  4. I can make an informed decision. By seeing my decision, I can base my decision on best guesses and existing information. This aligns with the principles of probability thinking.

The Problem With Probability

These 5 simple ways to think with probability will be helpful.

But what I can’t do is do them for you. You have to challenge yourself to grasp the opportunity probability brings. And that’s the problem with probability.

But it goes further.

Neil deGrasse Tyson explains: "When a coincidence seems amazing, that's because the human mind isn’t wired to naturally comprehend probability & statistics."

Luck has to be the most misaligned word in the human language. We call coincidences lucky or unlucky, depending on whether they fall in our favour or not. Probability, and statistics — which I haven’t mentioned — give us the ability to explain the reality of luck.

It’s called entropy.

This give us a rational explanation, be it a complex one. And when it becomes complex, we back away and live with stories that don’t stack up. Survivorship bias does a great job of clouding the view probability brings.

What I hope is that you overcome the problem of probability thinking.

Then, this article and the techniques I've listed with prove to be most helpful to you.

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