Module 5
Uncertainty and simulation
By the end of this module you can explain why an average cost is not a budget, read a distribution of outcomes, use percentiles to talk about bad years, and say what a simulation can and cannot tell you.
Part 1. The lecture
Why one number misleads
Alderwick has four legal matters that might cost money in the next year. Each has its own chance and its own range. If you add up the expected costs you get one number, about $120,000. A manager asks: “So should we set aside $120,000?”
In some years nothing happens. In others two matters strike together and the cost is several times the average. A budget of $120,000 would be too small in nearly half of all years. The average is true over a long run, but the client lives through one year at a time.
Simulating many possible years
The idea is simple. Play the year out on a computer, once: for each matter, draw a random number to see whether it happens, and if it does, draw a cost between its low and its high. Add up the costs. Now repeat it ten thousand times. You have ten thousand possible years, and a picture of how the total is spread.
This is called a Monte Carlo simulation, after the casino. It does not discover anything new. It shows what your own estimatesmean when put together, which is hard to do in your head.
Reading the picture: percentiles
- The 50th percentile (the median) is the middle year: half cost less, half cost more.
- The 90th percentile is a bad year: one year in ten costs more than this. Many organisations set reserves or insurance limits with a figure like this in mind.
- The 95th percentile is a very bad year.
- The gap between the average and the 90th percentile tells you how risky the portfolio is. A wide gap means a budget at the average will often fail.
What a simulation cannot do
- Fix bad inputs. A hundred thousand trials of a poor estimate still rest on a poor estimate. Ten thousand is plenty for a steady picture.
- See links between matters. If an inquiry makes a lawsuit more likely, the matters are not independent and the real bad years are worse than shown.
- Find risks you did not list. It can only combine what you put in.
- Choose for the client. Whether to hold a reserve at the 90th or the 95th percentile is a business decision about how much shortfall risk is acceptable.
Common mistakes
- Reporting only the average of a simulation.
- Treating the result as a forecast of the next year.
- Using the same low and high for everything because the real range is unknown, without saying so.
- Ignoring that some matters cause others.
- Running the model once and trusting a single picture. Change the seed and see how stable it is.
Part 2. Lab: Simulator
Alderwick’s four matters for the next twelve months. Change a chance or a range and the picture changes at once. Try making two of the matters more costly and see what happens to the bad years.
Each matter may or may not happen in the next twelve months. If it happens, its cost is somewhere between the low and the high, most often near the most likely value. The simulator plays out 10,000 possible years and shows how the total is spread.
| Matter | Chance (%) | Low | Most likely | High |
|---|---|---|---|---|
| Contract dispute with the buyer | ||||
| Regulatory inquiry | ||||
| Employee claim | ||||
| Stalled cross-border payment |
Average year
$120,973
The expected cost
Middle year (50th percentile)
$106,766
Half of years cost less
Bad year (90th percentile)
$261,646
One year in ten costs more
Very bad year (95th)
$309,428
One year in twenty costs more
In 20% of simulated years nothing at all happens, and in the worst tenth the cost is at least $261,646, which is 2.2 times the average. A budget set at the average would be too small in about 45% of years.
About 5.8% of simulated years cost more than $300,000.
Average cost by matter, and what the simulation assumes
- Contract dispute with the buyer$37,333
- Regulatory inquiry$26,667
- Employee claim$18,000
- Stalled cross-border payment$20,750
It assumes the matters are independent and that each cost follows a simple triangle between the low and the high. If one problem makes another more likely (an inquiry that triggers a lawsuit, for example), the real bad years are worse than shown. Different random numbers change the picture a little:
Part 3. Check your understanding
Ten questions drawn from a larger pool. In this pilot your score is shown but not saved.
This course teaches a method with invented figures and fictional parties. It does not give legal advice, and its numbers are for practice. Never paste a real client’s confidential details into any public tool.