Applied mathematics in business consulting

May 12th, 2010

As a part of my continuous moral degradation and the resulting increasing alignment with the forces of Evil, I'm sharing an apartment with a gal who used to work in HR assessment. She recently got me acquainted to a friend of hers, BC, who works as a business consultant (names have been changed to protect the guilty).

BC's primary educational background is in applied mathematics. Having put the math they teach in CS departments to relatively few uses as a working programmer, I asked her about the uses of applied mathematics in business consulting. BC cited the following two examples.

The first example involves compensation and its dependence on key performance indicators, affectionately known as KPI and estimated by HR assessors. One way of looking at this dependence is to consider how it affects compensation over time as an employee's competence increases.

A psychological discussion is then possible on the relative merits of the different graphs plotting the compensation functions f(KPI). If f is linear (has a constant derivative), we make people struggle equally hard at every step. If f's derivative increases over time (for instance, when f is exponential), we make elevation hard at first and then increasingly easy. If f's derivative decreases over time (for example, if f is logarithmic), we make the last mile the hardest. And so on.

Through a psychological discussion of this sort, someone in the consulting company decided that what was really needed in some case or other was an S-shaped curve. The problem was that you couldn't just draw an S-shaped curve – the plotting had to be done in Excel according to a formula; an S-shaped curve which just blithely goes through arbitrary points doesn't cut it when you deliver a Compensation Model. But how do you make a formula to go up slowly, than fast, than slowly again? Exponents don't work. Logarithms don't work. A sine does look like an S, but it's a wrong kind of S, somehow. What to do?

An S-shaped curve

Enter BC with 6 years of math studies under her belt. A compact yet impressive formula is spelled out, and – presto! – Excel renders an S-shaped curve. (I guess she used the sigmoid function but I didn't check.) The formula brought delight to management and fame to BC, and compensation payments issued according to its verdict keep adding up to scary numbers (BC's agency works with some really big companies).

The second example involves the compensation of managers. Naturally, a good manager near the bottom is worth less to the firm than a bad manager near the top, and therefore the compensation function should now depend on the manager's level in the hierarchy as well as his KPI (or better). Equally naturally, the numbers coming out of the compensation spreadsheet will under no circumstances arise through an externally conducted study of their psychological implications or any similarly unpredictable device. The numbers will result from nothing but the deep understanding of the organization possessed by the top management.

The development process of the managerial compensation function is thus complementary to that of the employee compensation function. Instead of producing numbers from a beautiful spreadsheet, what is needed here is to produce a beautiful spreadsheet from the numbers specified by the top management. The spreadsheet then promptly generates back these exact numbers from the input parameters.

The purpose of the spreadsheet is to relieve the top managers from the need to justify the numbers to their underlings. In order to guarantee that they are relieved from this need, the formula should not contain terms such as 1/(level^2), which could raise questions such as why not use 1/level, why not use 1/log(level) and other questions along these lines. Rather, the formula should contain terms which could raise no questions at all simply due to their size and shape.

BC faced this problem at an early stage of her career, and despite the natural stress, came up with an interesting Compensation Model, its key term being e raised to the power of something unspeakably grand, combining the trademark Gaussian look and feel with an obvious ability to deter the skeptics from asking questions. The only problem with that term was the very source of its utility, namely, the fact that it evaluated to 0 for all values of KPI and hierarchy level.

The deadline being close, BC told the manager of the consulting project in question about the status of her work and expressed her doubts regarding the delivery of the Computational Model. The manager told her that she just doesn't get it, does she, it's great, the right numbers come out and that's all there is to it and we should send it right away. And so they did, to everyone's complete satisfaction.

Her command of applied mathematics aside, BC is generally quite powerful.

For instance, she once got invited to consult some government agency about a project of theirs, while being on vacation and without it being explained to her that she was about to attend a formal meeting with the whole team. In order to maintain the reputation of the guy who somewhat clumsily brought her in, she had to improvise.

The project, worthy of a government agency, was related to some sort of war on corruption, the unusual thing being that they wanted to fight the corruption of other governments. Their weapon of choice was the training of representatives of another government, financed by the other government, in their supposedly superior methods of governance. While the general concept was impressive on many levels, the details were unclear.

BC had to speak, and she spoke based on a principle appearing in a book by some McKinsey alumni (she didn't tell its name nor generally recommended it): whatever you tell people, it should contain 3 main points. Possibly 4. But preferably 3. More is overwhelming and less is boring. So she said: "At its core, your project is about teaching people. It is therefore essential to clearly understand three things:

And they started writing it down.

I asked BC whether there was some way to unleash her on the company employing me so that she grinds a few bullet points into them (a handsome Compensation Model being as good a place to start as any). She said something to the effect of "it only works on the weak-minded"; it was apparent, she said, that the government agency in question had little previous exposure to consulting.

BC says she (still) believes that business consulting is meaningful and valuable, which sounds paradoxically at this point. But, looked at from another angle, it really isn't. Don't view her stories as ones undermining the credibility of business consulting but rather as ones building her own credibility as a person aware of the actual meaning of things and willing to sincerely share that understanding (how many people would instead say that they Developed Cutting-Edge Compensation Models?) If she says there's meaning to it, perhaps there is.

1. Frank AdrianMay 12, 2010

"Don’t view her stories as ones undermining the credibility of business consulting..."

Yes, for that, read "The Management Myth" by Matthew Stewart, which completely immolates the practice. The basic point is that the models that are preached by the consultants are completely without empirical merit. Ask a consultant where are the studies that show that his model works, and the best you'll ever get is either a series of anecdotal data points or a logical argument as to why this "makes sense" without mentioning the axioms from which the argument is derived. In short, business consulting is a mountain of horsecrap built from the fevered imagination of what the consultants think they can sell. Plus, a ripping good read...

2. Yossi KreininMay 12, 2010

People do keep buying. As to empirical evidence and scientific studies – a whole lot of good things in life are close to impossible to scientifically prove or analyze. (Of course I'm the last person to seriously defend consulting or any other practice where people supposedly having general economical and/or psychological knowledge tell people with actually relevant knowledge what to do, although I did see such people being right about things which shouldn't be obvious to an outsider a couple of times.)

3. MarcusMay 13, 2010

A formula for making something arbitrary appear scientific, yep that's management consulting ;-)

4. Yossi KreininMay 13, 2010

Um, are you by any chance the Marcus of "Humus is the bridge to piece"?

5. Julia Edwards - HR ConsultingMay 14, 2010

Recruitment is very important in an organization. Its complexities are very much more to be handled with care. Services regarding human resources needs expertise and most likely experience in decision -making. So innovative Software tools are highly needed in their field, Integrated with those HR consulting technique for better organizational productivity such as hiring new competent candidates for the desired job.

6. Yossi KreininMay 14, 2010

Wow, this HR spam comment is so impressive in both its contents and its quick arrival right after the publication that I don't even want to delete it.

7. MoeMay 14, 2010

It's too bad they don't know that any proxy you measure for attainment of a goal quickly becomes worthless when people learn to cheat it.

But what can we expect when so many organizations punish honesty? Their response when they find cheating is to raise their standards.

Over time, their standards become high enough that *only* cheaters can meet them and they end up selecting only the best cheaters for their organization.

Sadly, this can still work. Usually because they also find ways to cheat that benefit the business, being good at it.

8. Yossi KreininMay 14, 2010

Cheating – you mean KPI measurements? That's a whole different topic. One way they use to measure KPI is an interview with an HR assessor who then writes down numbers quantifying your leadership skills, social skills, systemic thinking and the like. Cheating is relatively hard, at the expense of the "measurement" being somewhat irreproducible. It's a trade-off.

9. TommyMay 15, 2010

I'd rather not know about the layer of slime that greases the gears of our world. There is the illusion that an intelligent and decent human being can be a lotus, blossoming amidst the muck, but in reality, some jerk will show up and stomp on all of the flowers before they get a chance to be pollinated.

I'd watch the company you keep, Yossi. ; )

10. Yossi KreininMay 15, 2010

"I’d rather not know about the layer of slime that greases the gears of our world" – That's what BC said when I volunteered to tell her a few stories about the inner workings of the automotive industry to reciprocate for hers.

11. jujhyMay 15, 2010

The formula referenced in the beginning looks like f(x) = tanh(x)/2 +1/2

12. YonatanMay 15, 2010

I'd think that KPI is probably as useful as gamma radiation or the sound of sea waves for generating random numbers – and important task in computer science.
But that is besides the point. You wrote these 20 paragraphs about a girl you were set up with and no mention of what she looked like?

13. Yossi KreininMay 16, 2010

You underestimate the power of the KPI. Their numbers aren't perfectly random, rather, they have biases – correlations with reality, some positive, some negative, with the positive ones convincing to accept the negative ones as positive.
As to your question – if you're the Yonatan I think you are, I'm surprised.

14. TillJul 21, 2010

looks exacly like a error function.

15. patriciaDec 4, 2010

it is not totaly wrong to post her story as one undermining the creatability of buisness consulting

16. asteriaMar 10, 2014

damn!!! i love this thing

17. kApr 9, 2017

Just give us the formula oh wise one! Is it mere hyperbole off on some tangent? Doubtful. Does it enable deep, and artificial thought? Perhaps. Is its derivative a thing of beauty? Absolutely.

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