Online Analytics: Monte Carlo Simulation

Do your eyes glaze over when ever you hear the words simulation ? Simulation refers to trying to predict actual events , usually in a controlled atmosphere. Monte Carlo simulation is a type of simulation that draws on repeated random sampling to hit the result, and it is usually computed using computers (unless you are Enrico Fermi who did it in 1942.)

The classical definition as per the most peer reviewed online statistical journal (called )

“the term describes a large and widely-used class of approaches. However, these approaches tend to follow a particular pattern:

  1. Define a domain of possible inputs.
  2. Generate inputs randomly from the domain, and perform a deterministic computation on them.
  3. Aggregate the results of the individual computations into the final result.”

and ”

Monte Carlo simulation methods are especially useful in studying systems with a large number of coupled degrees of freedom, such as liquids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model). More broadly, Monte Carlo methods are useful for modeling phenomena with significant uncertainty in inputs, such as the calculation of risk in business (for its use in the insurance industry, see stochastic modelling). A classic use is for the evaluation of definite integrals, particularly multidimensional integrals with complicated boundary conditions.

Monte Carlo methods in finance are often used to calculate the value of companies, to evaluate investments in projects at corporate level or to evaluate financial derivatives. The Monte Carlo method is intended for financial analysts who want to construct stochastic or probabilistic financial models as opposed to the traditional static and deterministic models.”

Here is a very good example of using the simulation to calculate distribution of leads to a website and the resultant conversion rate and probabilities. The down loadable excel sheet is great for learning both this class of simulation as well , maybe adding more robust mathematics in your online estimation efforts. The site is also great for excel related 

Use it if you think estimating Online Profitabilty is more complex than :

conversion ratio *number of leads *profit per conversion-number of leads*cost per lead.