Probabilistic Thinking - Mental Model
“We will deliver this project on time” — But what is the probability of it?
There is a high probability that after reading this article, you will pay closer attention to probabilities around you.
Probability is important for making decisions and predicting the future. In this article, we will discuss a mental model that shows the importance of randomness in our lives.
It has helped me a lot as a manager: assessing project risks, managing expectations, and staying calm when unexpected events happen.
When we hear confident statements, they sound like facts:
“We will deliver this project on time.”
“We will never do any layoffs, business is doing great.”
“Do not worry about your horse-selling business. People will never buy cars; horses are better.”
“AI will never replace developers.”
In schools, we learn that not knowing something or not being certain is wrong. It is important to change our perspective on this. Life is full of uncertainty.
Reality and Estimations
The weather forecast is our daily dose of probability (and we are getting better at it: “A four-day forecast today is as accurate as a one-day forecast 30 years ago.”).
When it is predicted to rain with a probability of 80%, do you take an umbrella with you? And if it eventually does not rain, would you complain about carrying it around? The prediction was right — there was a 20% chance it would not rain.
When we estimate for our clients, it is good to apply probabilistic thinking. What is the probability of delivering on time, and how can we increase it? What would decrease it?
“This is a good library for the project — I am 100% certain.”
In reality, 100% certainty rarely exists... “So, I’m 90% sure that this is the right solution.”
What is in that 10% of uncertainty? Exploring these possibilities is a great way to start a conversation with others about their opinions.
“Instead of altering our beliefs to fit new information, we do the opposite, altering our interpretation of that information to fit our beliefs.”
— Annie Duke, “Thinking in Bets”
Our nature makes us interpret situations to fit our beliefs, but this does not help us make the right decisions.
To apply probabilistic thinking:
Focus on ranges and chances instead of stating binary yes|no, true|false.
Think of the probability range — then: How can we increase it? How can we decrease it?
Be aware of your beliefs — we tend to interpret information to fit our beliefs.
Never use Always — Language
Terms like 'always' and 'never' are certainties, not probabilities.
We often confuse certainty with credibility, and confident people can influence our judgement of real probabilities.
I am guilty of using ‘always’ and ‘never’ far too often, even when the probabilities are not 100%|0%. I need to have a plan, a clear path, and no surprises.
Using precise language to say if something is certain or probable helps us set expectations. We are hardwired to see patterns and look for reasons everywhere. We want to be sure of what happens next. Unfortunately, the world is much more random than we think.
Importance of Luck
What is the reason for your success? US researchers asked a group of NHL hockey players. (I heard this example in an episode of Veritasium.)
Players said that hard work, great coaches, and support from their parents contributed to their success.
No player mentioned that they were successful because they were born in January.
According to data for players that got into the NHL, 40% of hockey players were born in the first quarter of the year, compared to 10% in the fourth quarter. An early birthday can increase the probability of being a pro hockey player. The most likely explanation is that the cut-off date for kids to play in the same group is December 31st. Kids born at the beginning of the year will be stronger, bigger, and faster than younger colleagues playing in the same group from a given year. These differences are compounding over the years.
The luck of being born at the beginning of the year plays its role. One of the most important factors of luck is the place where we were born. I am lucky to be born in a prosperous country, so I can write this article, and you can read it. If we were born in a low-income country, or an unprivileged family, no matter how much we try, it will be unlikely to earn much as an adult.
We see winners, while hard-working and skilled people stay hidden from us. Luck alone is not enough — it is a mix of luck and skills. But do not assume it is only someone's skill and hard work.
Probability thinking requires considering both luck and bad luck.
Summary
The world is a random place, it is far from programming languages that make software work in the same way every time we run our tests.
To work with probabilistic thinking:
Think of the probability range and explore it.
Pay attention to stating certainties with ‘always’ and ‘never’, be precise with your language.
Take luck and bad luck into consideration.
What is your take on probability?
Thanks for reading!
Michał
PS: My interest in mental models has been growing over the years thanks to Farnam Street. Their podcast, The Knowledge Project, and their books. FS covered Probabilistic Thinking explaining: Bayesian thinking, Fat-tailed curves, and Asymmetries.
Post Notes
Discover Weekly — Shoutouts
Articles that might help you explore new perspectives, which I have read recently:
"Prioritize your Tasks Effectively" —
wrote a great article on using the Eisenhower Matrix."Why do companies keep so many secrets" —
’s take on putting a special umbrella (worth checking out the image of it) between the organisation and your teams."5 Writing Tips to Overcome the Blank Page" —
prepared an article that I enjoyed about overcoming writing blocks — publishing each week requires using many of his tips.“Communicate like a Senior: How to write well (Part 1)” —
shares great tips on writing at work — I found it relatable to Perspectiveship’s “On writing at work,” with a 3-step framework.
Good article, Michał! Probailities, circumstances and unkown factors influence estimations a lot. Overtime I came to the conclusion that the idea continuous delievery helps a lot to mitigate this problem in the entire vertical from business to engineering.
Great read!
Great article Michał! And congrats on the new branding :)
I remember my latest usage of probability. A couple of months ago, we had an urgent and unexpected project, and ~5 days to deliver it. It was very critical, so there were daily calls with the CEO. I remember starting the week with ‘there is a 20% we will finish on time’, and then updating the probability every day. As it went smoother than I expected (and people worked like crazy), in the last day I increased it from 80 to 95%, and we finished 1 hour before the deadline, like in the movies :)
Using probability, instead of words like ‘low chance / high chance’, gave everyone a good sense of where we stand.
I still stand behind that initial 20% probability - we didnt have any significant unexpected problem, which is very rare.