How to replace estimations and guesses with a Monte Carlo simulation

> Before claiming that the simulation above is reliable, I must expose a few things you’ll need to pay attention to when using a Monte Carlo Simulation to make forecasts:

> (A) The quality of the inputs upon which your simulations depend.

> (B) The consistency and predictability of your team.

> (C) The need to re-forecast.

> (D) The size of your work packages.

Among those, I am not exactly sure what the author is referring to with (C). However, problems arise most often when none of A, B, and D is controlled by the person being asked to estimate.

Now, if you can control A, B, and D, YOU DO NOT NEED TO RUN MONTE CARLO. You'll be able to split the work and guess within 10 - 20% just by using rules of thumb.

If you cannot control A, B, and D, running Monte Carlo will not help you.

I say this as a person who's been doing Monte Carlo since the late 80s.

By definition, "uncertainty" is the thing that does not have a PDF ... You can quantify risk based on assumptions you make about underlying probability distributions from which you are drawing. Far too often, even in Monte Carlo, people decide to work with the easy distributions instead of the most appropriate distributions.

The "easy" distributions tend to admit actual mathematical solutions which means Monte Carlo is helpful if you can't do the math but not strictly necessary.

Monte Carlo shines when you cannot get nice solution and there is your opportunity to not be constrained by the need to do so: Draw from appropriate distributions.

Also, know the difference between LLN and CLT and when to appeal to which to justify your methods.

Not in some way -- literally. The samples are averaged, and as the number of samples goes to infinity, the average converges to some true value. In the case of one of the histograms you plot, you are averaging an indicator function .

> I thought of this differentiation because I consider the MC approach to yield a forecast, while an "estimation" is the typical term used in agile settings for "guessing how long/much work it will take.". I'll think of ways of making this distinction clearer.

It seems to me the distinction you care for is to provide not a single value ("estimate"), but a distribution of values. That's not specific to Monte Carlo.

> As for the misused mathematical terminology I guess you're referring to "confidence intervals"

That's certainly one of them. I even misunderstood what you were doing and said you don't need confidence intervals, but in the way you're using them those again can be obtained by quadrature.

My main gripe remains the language, and the presentation of the method. You could most likely obtain your results by hand, i.e. with pen and paper, and you would still get a distribution at the end of the day. The advantage of running Monte Carlo is that it simplifies this process. You could illustrate this by getting the distribution of the sum of two independent uniform random variables in two different ways: by doing a convolution, and by MC. Wow, MC was so much easier, anyone can do it, and it can handle arbitrarily complicated distributions (in principle).

Perfection may be impossible, but Brooks' Law being a harsh mistress, and scope creep being a very real thing, having a serious think about how big you intend the project to be to be before you start can make the difference between finishing it in months, and having it turn into a years-long death march project.

You break down the tasks, the dependencies, the risks, complications, places where there are options that need more research or comparison…and you’ll see the volume involved and have an idea of the size in the terms you mean. All without numerically estimating a single task in the plan.