Math Never Lies, But it Often Misleads

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I'm often fond of saying that:

Math Never Lies, But It Does Often Mislead

Let me give you an example to illustrate this point.

Let's say you use math to analyze a client and discover they generate $100 million in profit.

Is this good or bad?

It's a simple question.

From a math perspective, all we know is that $100 million in profit is true.

But math alone can not tell us if the $100 million is good or bad.

For this we need context.

Let me explain.

Assume we take this same example, and introduce the fact that the client generated $1 billion in sales in order to produce the $100 million in profit.

Math tells us their profit "margin" (a margin is some financial metric expressed as a percentage of sales, or in this case $100M/$1B) is 10%. Once again, math tells us the 10% profit margin is true.

But, with this additional math "fact", do we know if $100 million in profit or 10% profit margin is good? Or is it bad?

Once again, we still do not know.

And once again, we need more context.

Now let's say that all of our client's competitors had a profit margin % of only 5%.

Since profit is good, more is better. So math can tell us that 10% profit margin > 5% profit margin. Once again, math tell us this greater than expression is true.

Okay, Pop Quiz:

In this instance, is a 10% profit margin good?

What do you think?

[Please form an opinion before you continue reading.]

(Scroll down for my "answer.")

 

 

... no peeking 🙂

 

 

 

Now the temptation is to say that based on industry performance, a 10% profit margin is pretty good, considering everyone else is generating only 5% profit margin.

BUT, from my point of view, we still don't know if a 10% profit margin is good or bad.

Here's why.

What if I tell you that the client's profit margin last year was 15%?

Now what does that say?

It suggests the client is better than the rest of the industry but substantially worse than itself from the prior year. So arguable this is "bad," but perhaps not as bad as everyone else.

But wait... there's more! (I know I sound like an infomercial on TV.)

What if we then discover that profit margins for competitors last year was also 15%.

Clearly the whole industry is on the decline (though math tells us what changed, it does not tell us whyit changed). And everybody is worse off.

So in this context, is 10% profit margin good or bad?

I would say 10% profit margin stinks, but it stinks less than the rest of the industry. And the drop to 10% profit margin shows margins are getting stinkier but at a slower
rate than the rest of the industry.

But wait... that's not all!

(Can you tell I'm writing this late at night?)

What if you knew what profit margins were 2 years ago or 5 years ago?

That might change the picture too.

So what is my point in all of this?

Important: Never rely only on math to draw conclusions.

Math is always true, but by itself is not always insightful.

By the way, this is sometimes a challenge for PhDs and engineers transitioning to consulting. CIBs with these backgrounds won't grasp why, with a perfect GRE math score, they weren't able to pass a case.

Math is necessary, but not sufficient --- and the example above illustrates why.

(Incidentally the same issue is true of first year consultants that are overly reliant on math. If consulting were just one big math test, there would be absolutely no need to make candidates jump through so many hoops with the case interview. No, consulting requires you to think extremely critically.)

Equally important as the computations you might make during a case (or engagement) is the quality of the questions you ask once you see the quantitative data.

Hence demonstrating your ability to "ask good questions" in a case interview or of a senior client gets you noticed in this business.

Do you want to know the #1 question you should be asking in your cases and your engagements?

It is a very simple question that has served me extremely well in my consulting career.

It is the question: Why?

Example:

Profit margins declined from 15% to 10% this year.

Why?

Profit margins for the client declined to 10% this year, but competitor profit margins declined to 5%.

Why?

In many ways, the sole purpose of math is to give you the opportunity to ask the optimal why question and to find the answer.

The only time you ever want to make a firm conclusion is when:

1) You know the math is correct.

2) You know why the math is what it is (e.g., you know the underlying cause behind the metrics).

Never conclude until you are 100% sure about both!

If you have a suspicion for why something is happening (we call this a hypothesis), you do the math to see if you get the result you would have expected given your rationale.

If you have a numerical indicator suggesting something is true, do not conclude it is true until you investigate and understand why something is happening.

Whether you start with the math or start with the "why" question, you're never done until you've done both. This is as true for case interviews as for client work.

The challenging part for client work is the time when you ask "why" is often late at night, you're tired, and the last thing in the world you want to do is ask "why."

You can either force yourself to do it then and there or leave a note on your desk reminding yourself to ask yourself this question in the morning.

It is the consultant that asks a few more "why" questions than his or her colleagues (and clients) each week that quite often rises to the top in terms of performance.

This is as true for aspiring management consultants as it is for working ones.

P.S. I hope I did my math above correctly. You never want to do math at midnight, but hey, -- it happens. If you saw a glaring math error like 5 + 5 = 15 and you think it is incorrect, most likely you are right! 🙂

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