How much is a random person worth to your business? The answer changes dramatically as you gather more information. Let’s explore how customer value assessments evolve with data, using examples from probability theory to illuminate the powerful impact of information on business decisions.

## Assessing value with limited information

Imagine I called you out of the blue. Against your better judgment, you answer the call. I say, “Hi! I am standing next to someone. What do you think they are worth to your company?”

Assuming you don’t just hang up on the random madman I represent, how would you answer? Knowing nothing else, how would you place a value on this random individual?

You would have to be very generic — and probably throw in several caveats. You might say, “Assuming they are an adult in the U.S., then…” and quickly do the calculation for a truly unqualified individual.

The next thing you would probably do is play a quick game of 20 questions with me:

- “How old are they?”
- “What is their gender (if relevant to your product)?”
- “What region do they live in?”
- “Are they users of my product category?”
- “Are they currently in the market?”

With this information, you could give a more nuanced and accurate assessment of their value .

The things you care about depend on your specific business, but the key thing to notice here is the “value” of the person isn’t changing. I am still standing next to the same individual. What changed is your assessment based on the information you received.

While this may seem obvious, it is rarely properly understood. The true business value of the individual, in this case, remains the same. What changed is the accuracy of your assessment.

## The Monty Hall problem: The surprising value of new information

One math/logic problem probably sparked more internet debates than any other. Known as the Monty Hall problem, it goes like this:

- A contestant on a game show is shown three doors. Behind two of them, there are goats, and behind one is a brand-new car. If a contestant picks the right door, they win the car, otherwise it’s goats for them.
- The contestant, knowing only this, chooses a door at random. However, before that door is opened, the game show host opens one of the others, revealing a goat.
- The contestant is then given the choice to either stick with their original choice or switch to the other door. What should they do?

Mathematics proves there is one clear and correct answer — the contestant should switch.

If they switch, the probability of getting the car is 2/3. If they stick, the probability is 1/3. This seems counter-intuitive, as nothing changed with the car or goats. So, how did the probability change?

It didn’t. The probability of getting the car behind the initially chosen door was 1/3 before the door was opened and stayed at 1/3 after. What changed is the information we have about the other two doors: that one door now has a probability of zero, and so the other must now have a probability of 2/3. The contestant should switch.

(By the way, if you are not convinced and believe it shouldn’t matter whether the contestant switches, I recommend a quick Internet search — but be prepared for an avalanche of results!)

*Dig deeper: How to categorize customer data for actionable insights*

## The power of information in measuring customer value

The Monty Hall problem is an excellent example of how the assessed value of something depends heavily on available information. If the car is worth $60,000, then the expected “value” of playing the game (to the contestant) is originally $20,000. Once the host opens another door and the contestant switches, the value doubles to $40,000.

This also demonstrates the mathematics behind even a simple case is complex and non-intuitive. It involves conditional probabilities and Bayesian statistics. Unlike frequentist statistics, which you might know from high school, Bayesian statistics uses prior knowledge and updates estimates with new data to find a “posterior” probability. What was once a controversial approach to statistics is nowadays at the core of how the web and ecommerce function.

Returning to your business case, what can you know about people who are potential customers of yours? How does their (assessed) value change as you have more information about them? We usually think about the “path to purchase” or “customer journey,” but we don’t always calculate the expected value of customers at each stage. Once you start thinking this way, you might consider:

- How does the value change as we know more about our potential customers?
- Are there actions or interventions that can increase (or diminish) their real value?
- How do we determine how much we should invest to help move someone from one part of the path to another? (Not that anyone ever had arguments about marketing spend.)

The reason fully quantified customer journeys are not more commonly utilized is simple — the mathematics is hard, sometimes really hard.

However, with modern Bayesian techniques and with readily available software (i.e., PyMC, Stan and BUGS), there is no excuse for organizations not to know the true value of customers at any part of their journey.

This is especially true online, where analytics lets us gather information more easily. However, this should also be extended to the “real” offline world.

The next time I call you with a prospect, remember that with the *right* information, you can assign value to this potential customer, which informs stakeholders and drives customer-centered strategies.

*Dig deeper: Beyond the tech: Mastering customer data with a modern approach*

*Contributing authors are invited to create content for MarTech and are chosen for their expertise and contribution to the martech community. Our contributors work under the oversight of the editorial staff and contributions are checked for quality and relevance to our readers. The opinions they express are their own.*