Risk and Uncertainty in Leadership: 2-Dimensional Thinking
How to think in terms of impact × probability • When to avoid Russian Roulette and when to play • Examples of risk and uncertainty in business (and what to do about it)
Russian Roulette is a morbid game played as follows:
Load a revolver’s cylinder with a single round (bullet).
Spin the cylinder at random.
Aim the gun at your own head.
Pull the trigger.
If the revolver fires on an empty chamber, there’s a loud –click– that results in the player’s survival. If the gun fires on the loaded chamber, there’s a loud –bang– that results in a corpse.
We’ll be returning to the Russian Roulette analogy several times throughout the series on risk and uncertainty.
Risk & Uncertainty in Terms of Impact × Probability
Not all risks are equally dangerous. The Fog of Uncertainty is not uniformly opaque. To improve your decision-making, think about the concept of risk and uncertainty in terms of how impactful they are, and how likely they are to happen. That is, think about risk and uncertainty in terms of Impact × Probability.
The following illustration shows the Impact × Probability framework for thinking about risk and uncertainty in two dimensions:
We’ll be discussing the Impact × Probability framework for most of this article. Notice how each quadrant contains two categories that we introduced in Anti-Fragility and Asymmetry: Leadership's Best-Kept Secret.
Fragile things have more to lose than to gain. They’re easier to break than to build. In the context of risk and uncertainty, higher impact = more dangerous.
Anti-fragile things have more to gain than to lose. They improve because of volatility and disorder, not merely in spite of them. In the context of risk and uncertainty, higher impact = more beneficial.
Recall from Risk and Uncertainty in Leadership: 1-Dimensional Thinking that the Fog of Uncertainty can hide both unpleasant surprises (dangers) and pleasant surprises (serendipity). When evaluating risk & uncertainty, think about bonanzas and perils in the same way – except that one category is helpful while the other is harmful.
Upper-Right Quadrant (High Probability, High Impact)
Fragile/Risky: Darwin awards
Imagine pole-dancing on a lightning rod in the middle of a thunderstorm, or drunk driving at 100 mph (161 kph). These are high-probability, high-impact risks because they’ll probably get you killed. If you do something spectacularly stupid or reckless, you might even win a Darwin Award for contributing to human evolution by unnaturally selecting yourself out of the gene pool!
In Leadership Land, high-probability, high-impact risks usually send people to the Career Swamp rather than the morgue. Examples of risk and uncertainty in business include antagonizing customers, going to a job interview naked1, committing crimes and bragging about it, trusting people with long rap sheets of malfeasance, and hiring someone whose toxicity seeps into the organization’s culture and curdles morale.
— What to do with this information —
Avoid these risks, obviously. If you can’t, segregate your risks into silos to limit the damage (e.g. isolate toxic people so they don’t infect everyone else).
Insurance for high-probability, high-impact risks will be prohibitively expensive. If you want to be robust, you’ll need to self-insure.
Beware the moments of weakness that can make high-probability, high-impact risks seem like a good idea. We’re not just talking about drunkenness; the feeling of invulnerability stemming from success can also impair your judgment. So can rage, despair, terror, greed, envy, and lust. If you’re prone to acting on powerful emotions, prepare a fail-safe ahead of time.
Anti-fragile/Advantageous: Daily self-improvement
Eating healthier and exercising, building a financial buffer, and honing your leadership skills has a high probability of making a big impact on your life. There’s no telling what the future holds, so continuous self-improvement will better prepare you for whatever comes your way.
Personal self-improvement is just as important as organizational self-improvement. Examples of preparing your organization for the vicissitudes of fate include:
Building a fortress balance sheet
Training your employees and maintaining their readiness with drills2
Fighting diseases from the Plague Plateau that emerge once an organization reaches a certain size (see the first half of Social Loafing and Pseudo-Productivitis: An Infectious Disease)
Aligning employee incentives with the organization’s goals as much as possible (see the second half of Social Loafing and Pseudo-Productivitis: An Infectious Disease)
Hiring someone with rare skills doesn’t merely make your organization 10% better, they could make your organization 10× better (see The Lollapalooza Effect: When 1+1=2 Becomes 1+1=11)!
— What to do with this information —
Everything we wrote in this section is easier said than done. Why is it so hard to follow through? If you find yourself struggling to execute on something you know you should do, it’s probably your feelings holding you back. Is shame preventing you from confronting your problems head-on? Are the dark whispers of anxiety crowding out your voice of reason? Is the fake mask you wear for social approval erasing the true person behind it?
Upper-Left Quadrant (Low Probability, High Impact)
Fragile/Risky: Russian Roulette
Let’s play Russian Roulette with mathematics instead of bullets. Imagine a gambling game where you have a 99.9% chance of winning $1 and a 0.1% chance of losing $10,0003. Would you play that game?
Here’s how the Impact × Probability math works out:
Win $1 (Impact) × 999/1,000 (Probability) = +$0.999 (Expected gain)
Lose –$10,000 (Impact) × 1/1,000 (Probability) = –$10 (Expected loss)
Net Expectation: +$0.999 – $10 = Loss of –$9.001
This game has an expected loss of $9 per play, making it a terrible gamble. Why would anyone play this numerical version of Russian Roulette? By extension, why would anyone take a low-probability, high-impact risk?
Two reasons.
Reason 1: our brains are terrible at probabilistic thinking
To illustrate, let’s see what would happen if you were to play this mathematical version of Russian Roulette.
You fire the Russian Roulette gun, and –click– a dollar pops out of the barrel. Ooh! You pull the trigger again, and –click– another dollar pops out. Oooooh! Pull it again! –Click– out comes a third copy of George Washington’s green stoic face. Now it’s getting fun!
We’re easily lulled into a sense of complacency when the probability of harm is 1) abstract and 2) very low. The actual experience of playing Russian Roulette feels completely disconnected from the mathematical expected loss of –$9 each time you pull the trigger. How long can you keep playing before the gun stops shooting dollar bills and sucks $10,000 out of your wallet? We ran the numbers:
99.5% chance of winning $5
95.1% chance of winning $50
60.7% chance of winning $500
0.67% chance of winning $5,000
Isn’t it weird that more than half of all players can gain $500 without experiencing a $10,000 loss? By the 500th trigger pull, you’ve become desensitized to the risk. The adrenaline rush has abated, replaced by the monotony of adding yet another $1 to your stack of bills with each pull of the trigger. At this point, losing $10,000 feels like a distant prospect – like something that only happens to other people.
Reason 2: our brains are terrible at dealing with survivorship bias
For every 1,000 people who play our version of Russian Roulette, an average of seven people would win $5,000. Those are the people who would proudly attribute their “success” to their trigger-pulling skills or to some superstitious nonsense. Those 7 lucky fools would write books entitled How I Made $5,000 in Thirty Minutes with Zero Effort and post pictures of their $5,000 tropical vacation on social media. What about the 993 people who lost $10,000? They’re too busy digging themselves out of the financial hole to write books or take fancy vacations. Since we only see the people who played Russian Roulette and lived to tell about it, we overweigh the probability of success and underweigh the probability of failure.
Every human brain is hardwired with these two cognitive defects. Together, the two defects make people more eager to take low-probability, high-impact risks, like:
Trading naked options with 10× leverage
Having unprotected sex and using the pull-out method
Engaging in extreme sports (e.g. BASE jumping, free solo climbing, gladiatorial combat)
Driving without a seat belt
Organizations can take low-probability, high-impact risks too. Examples include:
Borrowing heavily at unsustainable rates to chase the latest industry fad
Accounting gimmicks to create the illusion of steadily-growing profits
Covering up deficiencies from regulators or watchdogs
Middle managers spending wastefully at the end of a fiscal year so their budgets aren’t cut next year
All eight examples provide some kind of small reward or cheap thrill in exchange for one ticket to the “anti-lottery.” Low-probability, high-impact risks are insidious because they get people into the habit of buying more tickets to the anti-lottery. Just like the real lottery, you’re unlikely to “win” the anti-lottery with a single ticket. But if you keep buying tickets day after day, year after year, you’re going to eventually “win.”
The grand prize for winning the anti-lottery is a one-way ticket to the Career Swamp, bankruptcy court, unplanned and unwanted parenthood, or the morgue.
— What to do with this information —
Spend some time studying Leadership Land’s Silent Graveyard. It won’t call to you (it’s very silent) so you’ll have to go out of your way to visit. The Silent Graveyard is full of people who “won” the anti-lottery and are no longer around to serve as cautionary tales.
If you’re a member of an organizational board, be careful what incentives you provide for your executives. If you set aggressive short-term goals, you are encouraging executives to borrow from the organization’s future to turbocharge near-term results. The managers often play Russian Roulette for years and then retire – leaving behind explosive risks to detonate in their successors’ faces.
Build a portfolio of insurance against a variety of low-probability, high-impact risks. The premiums tend to be reasonable because the total cost is distributed among many people who will never win a particular anti-lottery. In some cases (recent example: fire insurance in California), you might find mispriced (i.e. cheap) insurance because the insurer underestimated the Impact × Probability of a risk.
Murphy’s Law states: “Anything that can go wrong will go wrong.” In a 40-year, upwardly mobile career, this adage is generally true. You’re probably accumulating tickets to multiple anti-lotteries in the course of daily life, thus steadily growing the number of pathways to career failure. You only need to “win” one single anti-lottery to wipe out decades of hard work. Avoid wipe-out risks (low-probability, high-impact events where you multiply your accumulated success × 0) as much as you can manage. If you’re taking wipe-out risks in a discipline where calamities happen more often than once every few decades or so, find a new career as soon as you can. Minimize your collection of anti-lottery tickets, and you have a better chance of retiring comfortably before the Sword of Damocles falls.
Anti-fragile/Advantageous: Proto-geniuses
Let’s imagine a game of Reverse Russian Roulette where winning brings you good luck instead of bad luck. When the gun fires on a loaded chamber, it doesn’t turn your skull inside-out with a –bang–. Instead, a genie emerges from the revolver’s muzzle with a –poof– and grants you a wish.
If playing Russian Roulette is akin to playing the anti-lottery, then playing Reverse Russian Roulette is akin to playing the regular lottery. More broadly, we’re talking about any kind of low-probability, high impact event that benefits you instead of harming you. You can find several examples in Anti-Fragility and Asymmetry: Leadership's Best-Kept Secret. In that article, we used the term “proto-geniuses” to describe Reverse Russian Roulette players because other people will worship the winners as “geniuses” and “visionaries” only after they become famous – never beforehand.
Remember the two cognitive defects that make people more willing to play Russian Roulette (where the prize is “winning” a quick death)? Those very same defects also make people more willing to play Reverse Russian Roulette (where the prize is winning at life). Our brains aren’t wired for probabilistic thinking and we’re prone to survivorship bias, so the likelihood of winning Reverse Russian Roulette always feels higher than it truly is. The dual cognitive defects cause:
People to overpay for lottery tickets
Organizational leaders to overcommit resources to pie-in-the-sky goals (that will require a “strategic pivot” later when reality fails to meet expectations)
Hordes of aspiring actors, musicians, and writers to wait tables in between waiting for their “big break.”
We (the authors) are dreamers suckers for the two cognitive defects. Every article we write feels like the one that’ll put Adventures in Leadership Land on the map. But our logical, calculating brains know that we’re statistically more likely to end up in the Silent Graveyard. Our hearts propel us onward and upward with delusional optimism. Our pessimistic brains are preparing us to become one of the poor souls who drink away their broken dreams in Billy Joel’s Piano Man.
— What to do with this information —
The answer seems to be simple: collect as many lottery tickets as you can. Follow your heart! Chase your dreams! Proto-geniuses have more to gain than to lose, so if you keep playing the lottery, you’ll eventually win, right?
Not quite. Like a real lottery, it might take you longer than a human lifespan (on average) to hit the jackpot. Worse still, tickets to the proto-genius lottery aren’t free. They cost time. They cost energy. They cost opportunities, because an aspiring actress (AKA “barista”) who spends all her time auditioning and networking isn’t studying for medical school.
Spending your entire life in the antechamber of hope: is that a life worth living? The answer depends on your circumstances, your temperament, and which proto-genius lottery you’re interested in playing. Once again, it’s helpful to study Leadership Land’s Silent Graveyard. The Graveyard is full of smart, talented, courageous people who never won the proto-genius lottery during their lifetimes and died in obscurity. Count the number of proto-geniuses against the ones who “made it” to get a better sense of your odds.
Lower-Right Quadrant (High Probability, Low Impact)
Fragile/Risky: Inconveniences, annoyances, and minor slights of everyday life
A bean-counting bureaucrat rejects your TPS report because you forgot the cover sheet. Sloppy data entry slows down your analysis. The new aspiring actress barista is rude, puts too much ice in your Frappuccino, and misspells your name on the cup. There’s a paper jam in the printer – again – which means no handouts for your upcoming meeting. The restroom is so dirty that you have to stand far away from the urinal (common in men’s rooms) or hover over the toilet seat (common in women’s rooms). End result: you contribute to the restroom’s growing filthiness, forcing the next bathroom visitor to become an artillery operator who bombards the porcelain target from afar with biological weapons.
— What to do with this information —
Triage your time and energy. Many low-impact inconveniences are solvable, but not all solutions are cost-effective. Implementing a cost-effective solution saves you a lot of chronic stress, and overcoming the challenge feels satisfying in its own way. Contrast that with fighting every tiny injustice without regard to cost-efficiency. Spending too much time on futile gestures of self-righteousness guarantees a life of mediocrity (at best) or miserable failure (at worst).
Some cost-effective solutions come in the form of systemic changes that save a little time across a lot of people (at which point it’s no longer “low-impact”). Putting people on rails (e.g. data validation) can prevent slop from ever entering your database – an example of good bureaucracy. Dismantling rails that no longer function properly is an example of destroying bad bureaucracy. Sometimes a small change is all it takes, like painting a tiny seashell or insect on the inside of a urinal to leverage the male instinct for target practice.
Anti-fragile/Advantageous: Hands-on learning
When learning something new, there’s a high probability of making mistakes. When those mistakes are also low-impact, you’ll learn very quickly by screwing around, tinkering, breaking things, and re-assembling them. When learning to draw, play music, or program a computer, you can quickly and cheaply start over after making a mistake. It does not work when you’re learning to pilot a stealth bomber, perform open heart surgery, or build a succession plan. “Fail fast, fail often” doesn’t work when mistakes are costly.
— What to do with this information —
The key is to unlearn the notion that all mistakes are costly. Most of us learned in school that even minor mistakes will result in black marks on our permanent records. The students with the highest grades learned to never make mistakes, thus depriving themselves of anti-fragile learning – the type of learning that actually matters in real life.
Lower-Left Quadrant (Low Probability, Low Impact)
Fragile/Risky: minor accidents
Being struck with staircase wit. Forgetting to bring a gift to a party, forcing you to send it separately to the host a few days later.
— What to do with this information —
There’s not much to do about trivial problems that happen infrequently. What’s more important is what NOT to do, which is to overreact. Imagine the following:
Alice makes a mistake that happens once every two years, on average. The mistake is severe enough to require the intervention of Bob (Alice’s supervisor) and Catherine (Bob’s supervisor).
Bob doesn’t want Catherine to think that he isn’t taking this seriously, so he implements a new procedure that all employees must follow so no one can repeat Alice’s mistake.
It took Alice, Bob, and Catherine a combined total of 20 person-hours to resolve a problem that recurs every two years on average (~10 person-hours per year). With Bob’s new procedure, all 25 people on Catherine’s team must spend five extra minutes completing the procedure every week. That maths out to 108 person-hours per year spent on preventing a problem that costs 10 person-hours per year to fix.
Bob wandered into the Desert of Good Intentions because he thought “an ounce of prevention is worth a pound of cure.” In reality, however, he was being “penny-wise, dollar-foolish.” He overreacted to a low probability, low(ish)-impact problem by creating a fix that’s 10× worse than the problem it aims to resolve.
Bureaucratic bloat accumulates because of leaders who can’t accurately judge risks in terms of Impact × Probability. Maybe they’re not analytical. Maybe they are analytical, but they have incorrect or incomplete data. Each piece of anxiety-reducing busywork feels lightweight to the person who created it, but everyone uses that excuse to add more mass to the anchor that weighs down the organization.
Don’t overreact like Bob did and be ready to backtrack when you misjudge the Impact × Probability of a risk. If you’re in Catherine’s position, don’t let the Bobs of the world overreact to low-probability, low-impact events, either. Be kind about it; they’re probably trying to appease you while seeking refuge from their negative emotions.
Anti-fragile/Advantageous: minor windfalls
Discovering $5 tucked in the pocket of some clothing you last wore ten years ago. Procrastinating until a problem resolves itself.
— What to do with this information —
Enjoy them when they happen, then spend your limited resources on higher-impact things.
Risk and Uncertainty: Alternate Form of Two-Dimensional Thinking
Impact × Probability is our favorite framework for thinking about risk and uncertainty in two dimensions. However, Impact × Probability is neither the only way nor always the best way. The Awareness × Understanding framework is also worth a brief mention:
This 2 × 2 framework comes from Donald Rumsfeld’s famous quote “there are unknown unknowns.” In retrospect, the above illustration would’ve been a great companion to Why Epistemology is Important in Leadership (And How to Apply It) and How to Discover Secrets in Leadership Land.
The Awareness × Understanding framework is philosophical, while Impact × Probability is more practical. When we come back next week with Risk and Uncertainty in Leadership: 3-Dimensional Thinking, we’ll develop the Impact × Probability framework further by adding a third axis.
This is post #8 in the Leadership Land Consistency Challenge, Phase I. We experienced a bout of temporary insanity last week when we got swept up in recent events and started armchair psychologizing. Last week’s post doesn’t count toward the “10 articles in 10 weeks” total, but it does expand the Consistency Challenge’s timeframe to 12/20/24 – 3/7/25.
Unless you’re auditioning to be a sex worker.
Most bureaucratic organizations have training programs for their white-collar workers. However, civilian orgs rarely put their employees through drills to maintain their readiness. In the absence of regular practice, “professional training” degrades into “self-improvement theater” with all of the form and none of the substance. Without drills, training programs become expensive money-sinks for organizations and boring time-sinks for the employees who are merely going through the motions.
We’re borrowing this example from Nassim Nicholas Taleb’s Fooled By Randomness, Chapter 6 (Skewness and Asymmetry). You can find the same example in Table 6.1.