The Character of Prediction Errors
For some long-tailed duration models, an unfinished project’s expected remaining time increases as more time passes. Taleb contrasts this with a life-expectancy example in which remaining time falls with age. The effect depends on the distribution, rather than on delay alone.
THE IDEA
The Character of Prediction Errors
Like many biological variables, life expectancy is from Mediocristan, that is, it is subjected to mild randomness. It is not scalable, since the older we get, the less likely we are to live. In Taleb’s insurance-table illustration, a newborn female in a developed country is expected to die at around 79. When she reaches her 79th birthday, her life expectancy, assuming that she is in typical health, is another 10 years. At the age of 90, she should have another 4.7 years to go. At the age of 100, 2.5 years. At the age of 119, if she miraculously lives that long, she should have about nine months left. As she lives beyond the expected date of death, the number of additional years to go decreases. In this example, the conditional expectation of additional life drops as the person gets older.
With human projects and ventures we have another story. These are often scalable, as I said in Chapter 3. For some long-tailed duration models, the effect reverses, as the following illustration shows. Let’s say a project is expected to terminate in 79 days, the same expectation in days as the newborn female has in years. On the 79th day, if the project is not finished, it will be expected to take another 25 days to complete. But on the 90th day, if the project is still not completed, it should have about 58 days to go. On the 100th, it should have 89 days to go. On the 119th, it should have an extra 149 days. On day 600, if the project is not done, you will be expected to need an extra 1,590 days. As you see, the longer you wait, the longer you will be expected to wait.
Let’s say you are a refugee waiting for the return to your homeland. Each day that passes you are getting farther from, not closer to, the day of triumphal return. The same applies to the completion date of your next opera house. If it was expected to take two years, and three years later you are asking questions, do not expect the project to be completed any time soon. If wars last on average six months, and your conflict has been going on for two years, expect another few years of problems. The Arab-Israeli conflict is sixty years old, and counting—yet it was considered “a simple problem” sixty years ago. (Always remember that, in a modern environment, wars last longer and kill more people than is typically planned.) Another example: Say that you send your favorite author a letter, knowing that he is busy and has a two-week turnaround. If three weeks later your mailbox is still empty, do not expect the letter to come tomorrow—it will take on average another three weeks. If three months later you still have nothing, you will have to expect to wait another year. Each day will bring you closer to your death but further from the receipt of the letter.
This subtle but extremely consequential property of scalable randomness is unusually counterintuitive. We misunderstand the logic of large deviations from the norm.
When to use it
Project management: When a project misses its deadline, use this principle to recalibrate completion estimates instead of assuming steady progress.
Conflict resolution: revise duration estimates using the history and causes of delay, rather than assuming that a long-running conflict must be close to ending.
Customer service: use response-time data and the cause of a delay to estimate the remaining wait for an overdue request.
Personal goal setting: review progress and obstacles when a goal takes longer than expected, rather than assuming that time spent guarantees a short remaining effort.
FROM THEORY TO EVERYDAY LIFE
In practice
Life Expectancy (Mediocristan)
In Taleb’s insurance-table illustration, a newborn female has an expected lifespan of 79 years. At age 79, expected remaining life is 10 years; at 90 it is 4.7 years; at 100 it is 2.5 years; and at 119 it is about 9 months. These are the source’s illustrative figures, rather than current estimates for an unspecified population.
Project Completion (Extremistan)
In Taleb’s project illustration, the initial expected duration is 79 days. If unfinished at day 79, expected remaining time is 25 days; at day 90, 58 days; at day 100, 89 days; at day 119, 149 days; and at day 600, an additional 1,590 days. These figures illustrate a duration model with an increasing expected remaining wait.
Refugee Return
Taleb uses a refugee’s prolonged wait to illustrate how an unresolved situation may lead to a longer estimate of the remaining delay. This is an analogy, not a rule that every day of waiting makes return more distant.
Author Letter Response
Taleb imagines an author whose usual turnaround is two weeks. If no reply arrives after three weeks, the estimated additional wait becomes three weeks; after three months, it becomes a year. The particular estimates depend on the assumed pattern of delays.
A MOMENT TO REFLECT
Put it to work.
Think of a project you are currently working on that is overdue. According to this concept, what does the elapsed time suggest about the expected remaining time?
Identify a personal or professional situation where waiting longer has actually increased your expected wait. How can you adjust your planning or expectations?
Why do humans intuitively misunderstand the difference between scalable and non-scalable randomness? Give an example from your own life.
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)