High Probability of Low Probability Events

The Paradox of Low-Probability Events

We tend to ignore low-probability events because, by definition, any one of them is unlikely to occur. But this oversight may be detrimental to our business, because the likelihood that one of the hundreds of low-probability events that could occur will occur, is surprisingly high. Ignoring these events can leave us unprepared for eventualities that, while rare, can have significant impact.

Low probability is more than just a label. In areas where certain events are rare, the lack of historical data can make it difficult to anticipate and prepare for these events. This is particularly critical in fields such as disaster preparedness, risk management, finance, and insurance, where understanding and planning for rare, high-impact events is essential.

Although we cannot predict the exact nature of a low-probability event, we should be prepared for significant impacts from unexpected sources. Often, these are elements we have not fully considered, which catch us off-guard when they occur, such as the 2008 financial crisis and various natural disasters.

Mathematical Perspective

The probability of experiencing at least one low-probability event from a group of independent events is calculated using the 'At Least Once Rule.' The formula is: one minus the product of (one minus the probability of each individual event), raised to the power of the total number of events. 1- (1-probability) ^# of events.

For example, if each event has a 1% chance of occurring and there are 42 possible events, the probability that at least one will occur is about 34%. (1- (1-.01)^42 = 34.4%) This probability increases to about 63% with 100 events. If the chance of any single event occurring is 5%, then with 42 events, the probability that at least one will occur jumps to approximately 88%, and with 100 events, it exceeds 99%. (1- (1-.05)^100 = 99.4%)

Relying solely on numerical data may not always provide a complete understanding, especially in complex or abstract scenarios.

Different Categories of Probability:

·???????? Objective Probability: Based on empirical evidence and statistical analysis, this type quantifies the likelihood of events using historical data and mathematical calculations. It is typically associated with random, repeatable events.

·???????? Subjective Probability: Influenced by an individual's personal judgment, biases, experiences, and beliefs.

·???????? Epistemic Probability: Focuses on probabilities derived from available knowledge and how it influences beliefs about future events.

·???????? Bayesian Probability: Begins with a prior probability and is updated as new evidence is integrated, reflecting an evolved belief.

Psychological Factors

Psychological factors, such as normalcy bias and confirmation bias, lead us to discount the probabilities of certain negative events occurring, or to inflate the probability of positive events. Understanding these biases can help you develop better strategies for managing these risks.

Related Concepts

The Butterfly Effect,[1] a concept from chaos theory, illustrates how small, initial changes in a system can lead to disproportionately large outcomes. This concept relates to the idea of high probability of low-probability events in that both underscore the unexpected occurrence of significant outcomes from seemingly trivial or minor conditions.

In this context, numerous seemingly insignificant events can collectively pose a high probability that at least one will lead to a substantial impact. The Butterfly Effect and the High Probability of Low Probability Events both highlight the limitations of linear predictions in complex systems and the need for robust analysis that considers a wide range of potential outcomes, no matter how unlikely they may seem individually. This interconnection stresses the importance of considering even the smallest factors in scenario planning and risk management because their aggregate effect can be unexpectedly large and transformative.

Another factor to consider is the Ripple Effect,[2] which describes how an initial event, although seemingly minor or localized, can propagate through interconnected networks, leading to widespread, significant impacts. It also describes how a series of events, which individually have a low probability of causing major disruptions, can collectively lead to a high likelihood of significant outcomes.

The combination of the High Probability of Low Probability Events and the Ripple Effect emphasize the importance of recognizing and planning for the cascading effects of small disturbances in complex systems. They underscore the need for robust strategies that account not only for direct impacts, but also for the potential chain reactions that might follow. This understanding is crucial in fields like disaster preparedness, where planners must consider not just the direct effects of a disaster, but also the subsequent series of events it could trigger.

Black Swan Events

Finally, no discussion of probabilities would be complete without mentioning Black Swan events, which are highly significant yet unexpected occurrences with profound impacts on systems and markets. The concept, popularized by Nassim Nicholas Taleb in his book, The Black Swan,[3] highlights the rarity of Black Swans in the known world until their discovery in Australia, which challenged established beliefs.

The unpredictable nature of Black Swan events means they do not align well with standard predictive models used in risk management or forecasting. This is primarily because the data required to predict such events is typically unavailable or overlooked due to their rarity.

Estimating the probability of a Black Swan event occurring is therefore challenging and often only qualitatively assessed until the event unfolds. Subsequent analysis may reveal signs that were missed or underestimated, suggesting that the event might have been anticipated with different analytical approaches. Examples include the rise of the Internet, the 2008 housing market crash leading to the Great Recession, and the global spread of COVID-19—all of which had unforeseen, widespread economic and social effects.

Because Black Swan events are so rare and impactful, they are often overlooked in risk assessments and scenario planning. This oversight can be harmful, as such events can derail economies, disrupt industries, and cause significant societal upheaval. Preparing for Black Swan events involves incorporating robust risk management strategies that account for unforeseen disruptions, recognizing that conventional predictions and models often fail to anticipate such anomalies.

Strategic Implications

The greatest risk in basing strategy on individual probabilities is that the effects of rare, but severe events can greatly differ from those of common, but minor events, even if the calculation of impact times probability produces the same number and, therefore, the same priority. High-Impact Low Probability (HILP) events, such as disasters, pandemics, cyber-attacks, terrorism, and nuclear incidents, although rare, can have devastating consequences.

In decision-making, where information is often incomplete—as in statistics, artificial intelligence, and philosophy—these types of probability are crucial. Qualitative factors like industry cycles, management expertise, and labor relations, although hard to quantify, also play a significant role in assessing organizational trajectories and potentials. Thus, incorporating both quantitative data and qualitative insights is vital for informed decision-making.

Initially, it is prudent to include a margin of error or "wiggle room" in our plans, anticipating that tasks may require more time and effort than expected. Planning only for best-case scenarios leaves us ill-prepared for potential setbacks.

Setting up an early warning system that provides clues about emerging changes can give you more time to decide if, when and how to respond effectively. Such a system can also indicate when your business may need to drastically alter its course to survive.

Scenario planning and stress testing are effective for preparing for unlikely, but possible events. They help you anticipate and adapt to changes, ensuring you're prepared for any eventuality.

Vigilance is a Virtue

As we navigate the complexities of a world that defies simple calculations and predictable patterns, the imperative to remain vigilant and prepared has never been more crucial. Our understanding of High-Impact Low Probability events should not just provoke thought, but inspire action. Whether it is the unpredictable fury of nature, the volatility of financial markets, or the sudden disruption caused by technological failures, these events demand a robust strategy that goes beyond conventional planning.

Embrace Proactivity: Act Now, Not Later

I encourage you to transition from passive observer to active participant in shaping your future. It's not enough to acknowledge the existence of these phenomena; we must integrate this knowledge into every layer of decision-making. From personal finance to corporate strategy, from public policy to individual lifestyle choices, the approach to risk management must be comprehensive and adaptive.

Implement Dynamic Systems: Prepare for the Inevitable

Incorporate advanced analytics and flexible strategies to detect and respond to signs of potential disruptions. Use scenario planning and stress testing as tools not merely for prediction, but for preparation. Establish systems that are not just resilient, but also regenerative, capable of adapting and thriving in the face of challenges. (Taleb’s book Antifragile is a great source on this topic.[4])

Cultivate Awareness: Educate and Inform

Spread awareness about the nature of these risks and the best practices for mitigating them. Education at all levels, from the boardroom to the broom closet, should include an understanding of the Butterfly, Ripple, and Black Swan effects as fundamental concepts that influence modern risk assessments and strategy development.

Join Forces to Fortify

Collaborate to create more resilient infrastructures and support systems that can withstand the shocks of high-impact events. Share resources, knowledge, and strategies to enhance collective security and well-being.

Do not wait for the next unforeseen event to highlight and exploit your vulnerabilities. Act now, with foresight and diligence, to build a future where we are not merely survivors of the next disaster, but architects of a resilient tomorrow. Let's turn our awareness into action and our action into assurance. Together, we can redefine the landscape of risk and readiness.

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Bob Roitblat, hailing from Chicago, knows a thing or two about changing the game for businesses. He writes, speaks, and consults, drawing from a well of experience. If you're on the hunt for practical advice, fresh insights, and smart strategies to give your business a boost, why not follow his LinkedIn newsletter? It's where Bob shares his wisdom on making your business better. https://www.dhirubhai.net/newsletters/7099140608132358144

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[1] A term coined by mathematician and meteorologist Edward Norton Lorenz.

[2] A term purportedly coined by management theorist Jacob Kounin.

[3] Taleb,?Nassim Nicholas.?The Black Swan.?United States:?Random House,?2009.

[4] Taleb,?Nassim Nicholas.?Antifragile: Things That Gain from Disorder.?United Kingdom:?Random House Publishing Group,?2012.