mathbabe

Crossposted on nakedcapitalism.com.

There is a study out, entitled The Best and The Rest: Revisiting the Norm of Normality of Individual Performance, written by two business school professors, that has been bothering me recently. I’ll explain why soon, but first a thought experiment.

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Imagine a group of people competing for something. They’re all driven, talented people, who have put serious resources into getting good at this particular thing. They’ve also all had help of some form, and encouragement from their community to compete in this arena. At the very least they have to have deep confidence in their own abilities to even compete in this particular area.

At the end of the competition, that particular one, these people are ranked according to how they’ve done. By luck, by skill, depending on previous practice, resources, or direct support from external advisors, some of them have achieved impressively high rankings, while others, in spite of their hard work and efforts, are falling behind.

Next, there’s a community feedback element. This group of people are not done – they’re hoping to become famous worldwide, or at least in this arena, for being highly ranked, maybe even the best. And the community has direct influence on what happens next, in future rounds of competition. So, individuals can vote for certain people to win, or directly give them more time or resources to do so, or even help them in their next round.

In subsequent rounds, the ranking gets more defined and the community becomes increasingly certain that the winners deserve to be there and that they are truly fabulous at this particular skill, even though the original native differences in talent are not enormous. Luck, resources, and self-confidence were all important indicators of success in that first round, some just as important as native skill.

This continues for years. At retirement, the highly ranked individuals have produced a massive amount compared to the ones that did poorly in the early rounds. In fact, the distribution is highly skewed, and seems to serve as proof that the original ranking was warranted.

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I didn’t specify what field the above story took place in, so let me suggest a few that might work. First, there’s the music industry. Lots of would-be rock stars vie to be the next Taylor Swift. Heck, even Taylor Swift vied, once upon a time, to become herself. Of course, it helped that she was able to persuade her wealthy parents to move to Nashville when she was 14 to pursue her career. And – not to say she isn’t talented, because she most definitely is – we all know that once you have a hit, your career is much more likely to go well after that, with contracts, money, support, and great musicians flocking to you.

Or, it could be academics. If you stand out as an undergrad, especially at the right college, you get into a good grad school, and if you have enough confidence, determination, and the good luck to get a nice thesis problem, you might have a thesis that stands out, which leads to NSF grants, reduced teaching loads, opportunities to speak at conferences, semesters off of teaching to pursue research, and a host of co-authors who are increasingly willing to do the work to write up joint results. Again, none of this happens without determination, drive, and talent, but it definitely happens more and faster with the help of a supportive community. It’s all about the feedback loop of success.

Or, here’s another arena: sales. If you are known as a successful salesman, if you have a slightly better reputation than the next salesperson, then you’ll get the dibs on the jobs in a typical organization. That means you can be choosy, and take the easy pickings, and pass over the harder jobs. Over time your likability and personal network grows, and you become the go-to person in the organization for success, partly because of your hard work ethic, but partly because of the way success breeds success.

Or how about basketball? All professional basketball players are amazingly good at what they do. How much better does one have to be to get more playing time? Which leads, of course, to more points, more double doubles, or what have you.

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Now to the paper. It talks about the distribution of performance, and notes that in arenas above, performance, which they equate with output of songs for musicians, or papers for academics, or sales figures for salesmen, are distributed more as a power law probability distribution than as a bell curve. Of course, that is true, and I think we know why, from above. It even has a name: the Matthew Effect, which is even referred to in the paper, on page 112.

The primary goal of the paper is to make the case that “performance” is not normally distributed. It is distributed with a much fatter tail. They suggest using the Pareto distribution:

Before I go on, let me mention that their examples are restricted to researchers, entertainers, politicians, and amateur and professional athletes. They never mention secretaries, computer programmers, marketers, cashiers, or data analysts. In fact most of the people who work at regular jobs are completely excluded from this study.

So it’s really more accurate to say that the primary goal of the paper is to redefine the word “performance”. They switch from one definition to the other without explanation, so their studies on pro athletes somehow magically refer to average workers.

That brings us to the second goal of this paper. Namely, the conclusion that we should use this “performance isn’t normally distributed” rule to focus even more on elite actors.

Here’s one version of the elitism argument (page 108):

Leadership theories that avoid how best to manage elite workers will likely fail to influence the total productivity of the followers in a meaningful way. Thus, greater attention should be paid to the tremendous impact of the few vital individuals. Despite their small numbers, slight percentage increases in the output of top performers far outweigh moderate increases of the many. New theory is needed to address the identification and motivation of elite performers.

What’s particularly irksome is this kind of logic (page 112):

For selection, this means that there are real and important differences between the best candidate and the second best candidate. Superstars make or break an organization, and the ability to identify these elite performers will become even more of a necessity as the nature of work changes in the 21st century (Cascio & Aguinis, 2008b)

If you think back to our original thought experiment, there is actually very little difference between good candidates at the beginning. Second, this “we absolutely need to keep our talent” mentality is exactly the argument we see time and time again excusing pay raises for CEO’s. And now there’s a “mathematical” reason for it.

That brings us to the third and final goal of the paper, the “CEO pay is not exorbitant” argument, (page 112):

Likewise, compensation systems such as pay for performance and CEO compensation are an especially divisive issue, with many claiming that disproportionate pay is an indicator of unfair practices (Walsh, 2008). Such differences are seen as unfair because if performance is normally distributed then pay should be normally distributed as well.

Let me rephrase: since “performance” isn’t normally distributed, there’s no way pay should be either, when we define it for everyone. So let’s just go ahead and overpay CEO’s.

It might be a good moment to remind people that even in academics, the top performers don’t make 100 times what the lower performers get. Compare that to McDonalds, where the burger flippers would have to work 1 million hours to get one year of CEO pay.

In pop music and pro sports, there is a crazy pay differential, but that’s not something to be proud of or something we want to replicate.