The **Monte Carlo Method** used in predicting project results is what we would like to discuss with you today. Let’s see what it is.

Almost all project managers have experienced, at least once in their career, a **missed deadline** for a project.

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The most common reasons that lead to missed deadlines are erroneous cost estimation or incorrect duration estimation of one or more activities.

Most managers treat estimates – both of the cost and duration of activities – as deterministic, thus not acknowledging that these values are actually probabilistic.

Unambiguous estimates are used with a false idea that the future can be predicted accurately.

Here is how it becomes useful to predict the results of a project using the **Monte Carlo method** to perform a quantitative analysis of the project’s risks.

## What is Monte Carlo method or simulation?

**Monte Carlo simulation** is a mathematical technique developed by **John Von Neumann** and **Stanislaw Ulam** in 1940 for Project Manhattan. Its name derives from the casino in Monte Carlo, where Stanislaw Ulam’s uncle used to play often.

This quantitative risk analysis technique is used to identify the level of risk in achieving objectives, determining the impact of the identified risks by running multiple simulations and finding a range of results.

It is possible to run this simulation to analyze the impact of the risks on the costs of the activities, duration estimation, etc.

Every decision has a certain degree of uncertainty and the **Monte Carlo** simulation helps in such situations, avoiding nasty surprises later on.

This technique offers a range of possible outcomes and the probabilities with which they will occur for any choice of action.

According to the number of uncertainties and intervals specified, a Monte Carlo simulation can involve **countless recalculations** before it is completed, which is why it is a very complex technique.

## Example of how the Monte Carlo method works

Let’s say we’re in the Monte Carlo casino and we’re playing Blackjack.

If we wanted to find the odds of getting Blackjack, we could simply count the number of possible hands in this case and divide by the total number of possible card combinations to get the chance – which is about 1/21.

Now, let’s imagine that our sample space is much more difficult to calculate, for example considering that our deck contains thousands of cards instead of only the classic 52, or, even more difficult, we don’t even know how many cards there are.

There is another way to find this probability.

We could play a hundred games and record the results while we play; we could get a Blackjack 20, 40 or even 50 times and assign the probability using one of these values; anything is possible but these are certainly uncomfortable techniques.

If we think about playing a total number of times, the Law of Large Numbers states:

*“As the number of identically distributed, randomly generated variables increases, their sample average is close to their theoretical average.”*

Besides being easily one of the most important laws of statistics, this **is the foundation for the Monte Carlo simulation** that allows you to build a stochastic model with the method of statistical tests.

## Monte Carlo simulation in project planning

Let’s suppose we have three assets with the following estimates (in months):

Activities |
Optimistic |
Most likely |
Pessimistic |
PERT estimation |

A |
5 | 4 | 6 | 4.5 |

B |
5 | 6 | 7 | 6 |

C |
6 | 7 | 8 | 7 |

Total |
16 | 17 | 21 | 17.5 |

From the table above it can be concluded that according to the PERT estimation, these three activities could be completed in 17.5 months.

However, in the best case scenario, according to the most optimistic estimation, they will be completed in 16 months and in the worst case, in 21 months.

If we run the **Monte Carlo simulation** for these activities five hundred times, we will get the following results:

Duration (months) |
Likelihood of completion |

16 | 4% |

17 | 8% |

18 | 60% |

19 | 75% |

20 | 95% |

21 | 100% |

From the table above we can see that there is a:

- 4% chance of completing the project within 16 months
- 8% chance of completing the project within 17 months
- 60% chance of completing the project within 18 months
- 75% chance of completing the project within 19 months
- 95% probability of completing the project within 20 months
- 100% chance of completing the project within 21 months

The Monte Carlo method therefore provides a more in-depth analysis of the data and helps to make a more educated decision.

## Modelling uncertainty and risk with the Monte Carlo method

In short, the following statements apply to the Monte Carlo simulation:

- If the asset is risk-free, a single point estimate from expert judgement can be trusted. Then, the activity and project schedule can be modelled according to the most likely estimate.
- If the asset carries a low risk, the estimate is fairly accurate, except for unforeseen changes due to random factors. Therefore, a Beta or triangular distribution can be used.
- If the activity carries a known risk, the causes of the variance are known and the project team knows that the activity will be earlier or later if these risks occur. It is therefore advisable to use a Beta or triangular distribution.
- If the task presents an unknown risk and therefore the project manager does not have the right expertise to produce a reliable estimate, one can set a range of possible values and model the task according to a uniform continuous distribution.
- If the activity falls within the so-called “black swan theory“, in which a major unexpected event can happen with great consequences, it is possible to manage these risks as a hypothesis and, according to the
**Monte Carlo strategy**, to model it all as a risk-free activity.

To factor in risk, assets are usually based on three points (as seen in the table above): optimistic, pessimistic and more likely.

In order to choose the type of statistical distribution, it is worth considering qualitative risk analysis for the activity:

- Triangular symmetrical or Beta if the activity has a low probability,
- Triangular asymmetric or Beta if the activity has an average probability,
- Consistent if the activity has a high probability.

The advantages of using** Monte Carlo analysis** on projects are many:

- It helps to assess the risk of the project.
- Converts risks into numbers.
- Provides early identification of probabilities.
- Create a more realistic budget and program.
- It helps to predict the probability of failure or exceeding time and cost.
- Quantifies risks to better estimate impacts.
- Provides objective data for decision making.
- Helps obtaining management support for risk management.
- Helps in the decision-making process with objective evidence.
- Helps finding opportunities to achieve project goals or milestones.

Bottom line, Monte Carlo simulation is a key technique in risk analysis that allows decisions to be made under uncertain conditions.

Although this technique is not commonly used in projects, when taken into account it significantly increases the chances of achieving a successful project within the approved baselines.