Monte Carlo Decisions: Which Cell Phone Plan is Really the Most Cost Effective?

By Michael Lieberman 

Monte Carlo simulations are used to make informed decisions based on predict probability distributions. As a basic example, if you roll three dice, you can get a total outcome from 3 to 18 with varying degrees of likelihood. Monte Carlo simulations can throw three dice one million times and tell you how likely you are to get a number higher than 10. And what if two of the dice were twelve sided? Or what if the dice were loaded? Monte Carlo simulations can incorporate different probability distributions and give you the skinny about the current situation.

A perusal through websites of some of the leading market research firms confirmed the lack of awareness of Monte Carlo simulations and its usefulness in common research applications, such as ROI, loyalty, product development, customer satisfaction, and regression modeling— the bread and butter of our industry.

In this blog, we are going to illustrate a simple example. We are going to use the monthly cell phone usage of a regular customer and use a Monte Carlo simulation to help him decide which plan is best.

Let’s call our customer Lenny. Lenny is faced with an important decision: which monthly cell phone plan to subscribe to.

Lenny has to choose one of two plans; one from Cellular One and one from Western Wireless. Each offers different benefits. Which is better for Lenny?

We are going to explore a decision process based on models of cellphone usage. The model is helpful as a basic example of defining assumptions, defining outcomes, and using forecasting methodology. Basically, we are going to take Lenny’s cellphone usage, run his habits many times, and give him, in percentiles, which plan would be more cost effective in the long run. The process is called Sensitivity Analysis.

Below are the particulars of the two plans Lenny is exploring:

Cellular One

Pro: 400 minutes per month, no extra charges for long distance calls

Con: Every minute over 400 is an extra $0.40

Western Wireless

Pro: Unlimited minutes

Con: Long distance charges are $0.08 per minute

In our first month of data, Lenny used 400 minutes a month, of which 30% are long distance calls. In that case, Cellular One’s plan will save him $4.61. But how likely is this scenario? If Lenny better off in the long run going with Cellular One?

As the months pass, though, Lenny’s cell phone usage varies. Through his phone records we know that he uses on average 400 minutes a month—but with a standard deviation of that usage of 20 minutes. Also, Lenny’s long distance percentages vary. The most likely is 30%. Lenny’s minimum, though, is 10% and his maximum is 40%.

If Lenny only changes the percentage of long distance minutes, Lenny will see that, as the percentage increases, the Western Wireless plan costs more and the Cellular One plan looks better and better. Changing only the minutes used produces the opposite effect. Changing both variables at once results in a more complicated relationship.

Instead, what I did was the run 100,000 simulated months of Lenny’s cellphone usage (about 8333 years) and came up with the distribution below:

I highlighted at which point Lenny is better off with Cellular One. Here would be the recommendation I would give him.

  • Given your cell phone usage, there is a 65% chance that Cellular One equal or better than Western Wireless.
  • On average (50%) you will save $1.61 a month with Cellular One.
  • The chances of you saving $4.61 in a given month, as in the first month data you gave us, is about 15%, so don’t expect to save that much money unless you have a month where you make a large number of long distance calls.

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