Triangulate on answers

Triangulate on answers

Mar 22, 2011

You can approach most complex problems from various angles. Each one might give you an approximate answer; by comparing these you can estimate the overall answer.

Approach your problem from different angles

When I interviewed to join Accenture, I went through a series of case interviews. If you’ve heard of strategy consulting, you’ve most certainly have heard of these: The interviewer asks you a seemingly complicated question and wants you to show him/her how you get to the answer. Traditional case questions include: How many golf balls can you fit in a Volkswagen? How many gallons of white paint are sold yearly in the US to paint residential houses? How much does it cost to run a (successful) presidential campaign? Etc.

Perhaps the most interesting such interview I went through started with small talk: My interviewer wanted to know what I was doing. At the time, I was finishing my dissertation on the vibrations of oilwell-drilling tools to help prevent failure of the tools. “Excellent”, he said, “we’ll use that. Imagine that over the next three months you wrap up your findings into a software that is now ready for sale and that is likely to reduce drilling tools failures by at least 50%. How much should you sell it for?”

That’s a revenue question. You generate revenue by either having a high volume of sales or by making a lot of money on each sale. So one way to answer is to pick the direction in which you want to go. Say that you are looking at selling lots of these applications. Then to be attractive, you might want to charge as low a price as possible. A brute force approach to decide this price tag is to go with a {cost + margin} approach (I know, I know, pricing strategists hold this approach in contempt because it “leaves value on the table” but remember, here, we’re not trying to find an optimal price yet, just trying to find a good-enough one). The cost might be that of my time for three years of work, plus equipment, advising, tuition, university admin charges and so on. If you go into details—for instance by identifying a monthly cost and adding it all up—you might find that the overall cost might be, say, $1M. Now, for the sake of argument, assume we want a margin of 50% on top of that and that we plan on selling at least 15 licenses. So my {cost + margin} tag is $1.5M and I need to charge to 15 clients, therefore I should sell each license for $100k.

Ok, that’s a quick and dirty number. We can make it less quick and dirty by probing further into each of the hypotheses we’ve made. “That’s all fine”, says my interviewer, “but let’s triangulate this answer: How do you answer that question from a different angle?”

Well, you can answer that in terms of the client’s perspective: How much is it worth to them to halve their drilling failures? Assume that a typical failure requires an average of three days to be fixed, that during that time you can’t drill, and that a typical drilling day costs $500k. So each failure costs $1.5M in down time. Furthermore, a big petrochemical company expects an average of 10 failures every year. That’s $15M lost every year due to drill-string failures. If they can eliminate half these failures, they’d save $7.5M a year. So I can charge any of them anywhere up to  $7.4M for my little software and it would still make economic sense for these companies to buy it.

So let’s summarize the story so far. In one approach, we can charge some $100k per license. In another, we can charge all the way up to $7.4M. That’s quite a variance! And you can generate other answers if you keep looking at your problem from other angles. For instance, how much do similar packages cost today? Or, how much do alternatives—such as adopting an overly conservative drilling strategy—cost?

[IMAGE MISSING: Screen-shot-2011-03-14-at-11.53.11-AM-e1300121711974.png]
Triangulate estimates to get the answer of complex problems

Look for common ground

Here is a little experiment that I run sometimes when I teach. I have a photos of various transparent recipients—a glass, a jar, etc.—filled with M&Ms. I project one of those to my group of students and I ask them to estimate the number of M&Ms they see by writing down that number on a piece of paper. Then we collect the pieces of paper, and I read them out loud while someone captures each estimate in an Excel spreadsheet. At the end of the exercise, we calculate the average of all estimates and it is almost always closer to the actual number of M&Ms than 95% of the estimates of the group. It’s a nice trick that I picked up from James Surowiecki’s Wisdom of Crowds to show that groups are usually smarter than individuals. But today, the point isn’t so much that crowds are smart but that everyone
writes down their estimates. This is to avoid anchoring.

[IMAGE MISSING: Screen-Shot-2019-12-20-at-13.21.25.png]
Harnessing the wisdom of crowds, find a way to get independent viewpoints.When you project the picture of a jar filled with 2,500 M&Ms, it is common to have estimates ranging from the 100s to over 10,000. Whoever tells to the classroom their answer first will act as an anchor for the rest of the people: If my friend goes first and says “300,” I might get concerned about how foolish my 6,000 is going to look like; maybe she knows something I don’t, maybe I should cut my estimate to, say, 600. But the point of the exercise is to have widely diverging estimates. It is because extremes cancel each other out that the whole thing works. If, on the other hand, we use 300 as an anchor, we’re going to zero-in on that number, not the actual quantity of M&Ms. So, in this case, anchoring is bad.Going back to the problem of estimating how much a drilling software capable of halving the failures of drill-strings should cost, the point of adopting different approaches is to generate several anchors. Don’t get stuck with the $100k price tag. Don’t get stuck with the $7.4M one either. Just use different and, as much as possible, independent approaches to define the universe of possibilities and realize that a good price tag is somewhere in between the anchors.


Chevallier, A. (2016). Strategic Thinking in Complex Problem Solving. Oxford, UK, Oxford University Press, pp. 35–38.

Surowiecki, J. (2005). The wisdom of crowds, Random House LLC.