Waking up early in the morning
Formal shirt and trousers, neatly pressed
An hour’s commute each way
Conversations by the water cooler
Team lunches; Expense accounts
Hourly coffee breaks
Meetings. Conference calls. Presentations
Studs. Fighters. Free-riders.
Reviews. Deadlines. Status reports.
Salary credit!
It’s been a long time since I wrote about the Studs and Fighters framework. I had overdosed on it a few months back, when I’d put some 3 posts in 4 days or something, but that was when I was hajaar enthu about corporate affairs.
It’s been almost two months since I quit my last job, and in this period, among other things I’ve lost all enthu for anything corporate. I don’t find Dilbert funny anymore. I usually just put well left to the office-politics posts that some of my friends on Google Reader share. And since the S&F theory was mainly meant to deal with corporate situations, that too has gone to the backburner.
I was thinking about Mitchell Johnson’s inclusion in the Aussie team in the Third Test. Given how badly he has been bowling all tour, and given that Stuart Clark hasn’t been bowling badly at all, it seems like a surprising selection. But dig deeper, and employ my favourite framework, and you’ll know why he’s still in the team.
It seems like Johnson is a stud bowler (as I’d remarked earlier, Test match bowling in general is stud). And the theory goes that form matters so much less for the stud. This is mainly because studs are significantly more inconsistent than fighters, which makes forecasting one data point based on historical data a nightmare. This also means that the last few data points say much less about a stud’s next data point than they do for a fighter’s case.
All that a stud needs to do to make amends for his hitherto bad form is to come up with one, or maybe a handful of moments of inspiration/insight. And that can happen any time. In fact, theory says that it is more likely to happen when the stud is defocussed on what needs to be done.
So even in the first couple of Tests, you could see Johnson occasionally coming up with the totally awesome delivery, which would produce wickets. Most of the time he was crap, but the occasional moments of brilliance were enough for him to make an impact. So the thinking in persisting with him is that sooner or later, he will produce enough moments of brilliance in a game that no one will look at all the crap he has bowled, and even that the moments of brilliance can push up his confidence which can lead to less crap.
This kind of thinking doesn’t apply to a traditional fighter, who isn’t capable of that “moment of brilliance”. He usually relies on consistency, and accuracy, and process to do what he needs to do. For the fighter, it has to be a steady rise from one “form situation” to another. And so persisting with the fighter doesn’t make sense. So for example, if Mike Hussey continues batting in the same way as he has been this series, there is a case of sending him to domestic cricket.
The problem with a lot of fighters is that they refuse to acknowledge the existence of studs and treat them too as fighters (on the other hand, most studs understand the existence of fighters). And this treatment of studs (assuming they are fighters) can have disastrous effects.
Earlier today, while contributing to a spectacular discussion about ambition on a mailing list that I’m part of, I realized that my CV basically translates to spectacular performance in entrance exams and certain other competitive exams, and not much otherwise. This made me think of the concept of a “discrete job” – where you are evaluated based on work that you do at certain discrete points in time, as opposed to a continuous job where you are evaluated based on all the work that you do all the time.
A good example of a discrete job is that of a sportsman. Yes, a sportsman needs to work hard all the time and train well and all that, but the point is that his performance is essentially evaluated based on his performance on the day of the game. His performance on these “big days” matter significantly more than his performance on non-match days. So you can have people like Ledley King who are unable to train (because of weak knees) but are still highly valued because they can play a damn good game when it matters.
In fact any performing artist does a “discrete” job. If you are an actor, you need to do well on the day of your play, and off-days during non-performing days can be easily forgiven. Similarly for a musician and so forth.
Now the advantage of a “discrete” job is that you can conserve your energies for the big occasion. You can afford the occasional slip-up during non-performing days but as long as you do a good job on the performing days you are fine. On the other hand, if you are in a continuous job, off-days cost so much more, and you will need to divide your energies across each day.
If you are of the types that builds up a frenzy and thulps for short period of time and then goes back to “sleep” (I think I fall under this category), doing a continuous job is extremely difficult. The only way that it can be managed is through aggregation – never giving close deadlines so that you can compensate for the off-day by having a high-work day somewhere close to it. But not every job allows you the luxury of aggregation, so problem are there.
Now, my challenge is to find a discrete job in the kind of stuff that I want to do (broadly quant analysis). And maybe give that a shot. So far I’ve been mostly involved in continuous jobs, and am clearly not doing very well in that. And given my track record in important examinaitons, it is likely I’ll do better in a discrete job. Now to find one of those..
I first got this idea during some assignment submission at IIT. One guy in our class, known to be a perfectionist is supposed to have put in 250 hours of effort into a certain course project. He is known to have got 20 out of 20 in this project. I put in about 25 hours of effort into the same project and got 17. Reasonable value for effort, I thought. And that was when I realized the law of diminishing returns to effort. And that was the philosophy I carried along for the rest of my academic life (the following four years).
The problem with working life as opposed to academic life is that the eighty-twenty formula doesn’t work. The biggest problem here is that you are working for someone else, while you were essentially working for yourself while you wree a student. Eighty was acceptable back then, it is not acceptable now. Even if you are working for yourself, the problem is that the completion-rewards curve is completely diffferent now.
Imagine a curve with the percentage of work done the X axis and the “reward” on the Y axis. In an academic setting, it is usually linear. Doing 80% of the work means that you are likely to get 80%. Fantastic. The problem wiht work is that the straight line gets replaced by a convex curve. So even to get an 80% reward, you will need to maybe do 99% of the work. The curve moves up sharply towards the end so as to give 100% reward for 100% work (note that I’m talking about work done here, not effort. Effort is irrelevant)
Now, why did I cap reward at 100% in the previous paragraph? Why did I assume that there is a “maximum” amount of wokr that can be done? Note that if there is a ceiling to the amount of work to be done, and to the reward, then you are looking at a payoff like a bond – the upside is limited – 100% but the downside is unlimited (yeah I know it’s limited at 0, but it is so far away from 100% that it can be assumed to be infinitely far away). Trying hard, doing your best each time, the best you do is 100%. But slip up a bit, and you will get big deficits. It is like the issuer of the bond defaulting.
Almost thirty years back, Michael Milken noticed this skewed payoff structure for bonds, and this led him to invent “junk bonds”, which are now more politely known as “high yield debt”. Now, these bonds were structured (basically high leverage) such that a reasonably high rate of default was built in. In an ordinary bond the “default expectation” is that the bond won’t default at all. For a high-yield bond, the “default expectation of default” is much higher than 0 – so there is a definite upside if the bond doesn’t default. So that balances the payoffs.
So how does that translate to work situations? You need to basically get yourself a job where there is significant scope for doing “something extra”. So that if you take into account the “something extra”, the “expectation” will be say something like 90% of the work. So by doing only a bit more than your old 80-20 rule from college, you can fulfil expectations. And occasionally even beat them, resulting in a major positive payoff (either in terms of money or reputation or power etc.).
The deal is that when the expectation is lower than 100%, the reward-work curve changes. It remains heavily convex for the duration within the expectation (so if expectation is 90% of work for 80% of profit, the curve will be highly convex in the {(0,90),(0,80)} area). And beyond this, it gets less convex and closer to linearity, and so gives you a bit more freedom.
I’m too lazy to draw the curves so you’ll have to imagine them in your heads. And you can find some info on convex curves here: http://en.wikipedia.org/wiki/Convex_function
For a change I’m keeping up a promise that I’ve made on my blog – I’m actually writing a follow-up post that I’d promised. In the past, I’ve guilty several times of promising to continue something in a follow-up post and then conveniently forgetting about it.
So I had mentioned in my last post that the word “compensation” as used to describe salary is not really misplaced. There has been a lot of debate on this topic. The opponents of the word have said that you aren’t losing an arm or a leg in order to be “compensated”. They say that you are only getting paid for the value you add, and so the use of the word “compensation” is plain wrong. I must admit I haven’t really bothered to read the arguments of the people who support the use of the word.
The basic fact: you work because you need the cash flow to fund the rest of your life.
I know a lot of career-minded folks among you will jump on me for this, but I stand by this. Just get down a little deeper, and ask yourself why you are doing what you are doing. Maybe you don’t get the kind of questions in your head that I normally do, and described in my previous post. Maybe your jobs have put you in the kind of comfort zone where you don’t really need to ask yourself such questions (I was in a similar state not too long back, I must admit). But I encourage you to make that effort and ask yourself this uncomfortable question. And it will be down to the money.
You might say that you are doing some stuff “for the sake of career development”. Rephrase that and you will find that you are doing that in expectation of higher future earnnigs. You might say that you are doing something because you want to “achieve something”. Dig deeper and you may find that you define the fruit of your achievement in monetary terms.
So where does “quality of work”, “impact on society”, “value add”, etc. all fit in? I know that in the not-so-distant past, I’ve also talked a lot about these things. I have rejected a number of potential job offers because I don’t like the “quality of work”. This definitely needs to be incorporated into the model, right?
The next basic fact: work is inherently unpleasant.
I don’t think I’ll spend too much time elaborating this here. Maybe I’ll explain this in the comments if you want. So this is where things like “quality of work”, “value add” etc. all fit in – they make work so much less unpleasant. For example, I enjoy spreadsheet modeling. So if my work involves a lot of spreadsheet modeling, I’ll feel so much less unpleasant doing it. Of course, what I am doing remains “work” and it has to be done, in a certain way by a certain day, and so it remains unpleasant. But the fact that I enjoy the core activity makes it less unpleasant.
Similarly, if you think that the work that you are doing gives you a sense of achievement, then it is as if you are doing a part of the work for yourself, and not for someone else, and thus need to be compensated less. “Compensated less”. So this is where it fits in. You get “compensated” because work is inherently unpleasant. You need some incentive to do the stuff that is inherently unpleasant. So you get compensated.
You may have to live in a city that is not your preferred choice – you need to get compensated for that. You may face an extremely long commute where you waste your time – you need to get compensated for that. You might have to work long hours which can intrude on your personal time – you need to get compensated for that. You may have to deal with lousy colleagues or customers, you need to get compensated for that. The list goes on. And if you think about it, a large part of the money that you get out of your work is just that – compensation. Compensation for your time, your effort, your mindspace, your willpower, etc.
So why work at all, you might ask. Go to basic fact one. You work because you need the money. You are in a certain job because you believe that after compensating for all your “sacrifices” for the job, it will leave you with some more money to fund your life. If you think that the money your job leaves you if you take out the “compensation” part of it is lower than what you need to sustain life, you need to question why you are doing that job.
Investment bankers (the inside the wall type) usually end up spending a lot of their time at work, and despite the reasonable bonuses they get, they might feel they are not being compensated enough. They are doing it because they expect that when they ultimately get promoted they will make enough and more to cover for all this unpleasantness. It is basically an “investment”. If, however, you think you are in a job where you are inadequately compensated but don’t see any hopes of significantly higher compensation in the future, you are cheating yourself by not looking for another job.
This also explains why it is a bad thing to compare your salary with your peers and your old classmates and then feel good or bad about it. No two people have the same needs. No two people find the same things unpleasant to the same degree. No two people make the same trade-offs. Comparing your salary with you peer gives little information.
On a closing note (I know it’s already monstrously long) I find the phrase “work-life balance” amusing. I think it is a construct brought about by the pigs so as to con the sheep into workign harder for them. There is no “balance” between life and work. Life is the master and work is the slave.
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There are these days when you wake up and start wondering what the fuck you are upto. You start asking yourself why you are where you are, doing what you are doing. You ask yourself why you are not on that monthlong roadtrip of rural Karnataka, with the hope of maybe producing a shelf of books at the end of it. You ask yourself why you haven’t been doing stuff that you had promised yourself that you would do.
That new guitar has already started rusting, and the left index finger that you had cut the last time you played has long healed. The car mileage grows only in small increments – which approximately represents the distance you go to work. Half the days you cook rice, and mix it with copious quantities of Mother Dairy Dahi, and some pickle that has been sent from home. The other days you go to the same restaurant, sit at the same table and order the same set of items.
You are doing it for the sake of your career, you tell yourself. Career. Tha FUBAR thing. Which you are trying to marginally resurrect and repair by doing what you are doing, and trying to bring back to it some vague sense of recognition. You meet your friends. You hear them shag about their jobs. You hear about all the cool things that they are doing, and about how they are fast moving up the corporate ladder. About how you are a failure in life if you don’t work hard at this stage of life, and if you can’t win the rat race.
You meet friends’ friends. The first thing they ask you is what you do – and you are likely to get judged on that. So you need to make sure that you have a good story to tell about your job, which makes you sound cool. Coming up with formulae to price the movement of sacks of rice is not cool, as I found out. Financial services is usually met with a question asking you to predict the direction of the index. Sales is usually met with “the sun is very hot nowadays, no?”. And IT is met with “are you a Java coder or a C# coder?”.
Occasionally you want to get away from all this. These are the times when you accept that you are doing what you are doing because of the increments it produces in your bank balance. Sometimes you realize that the monthly increments in your bank balance are not enough; and some of those times you console yourself saying that you are doing this in expectation of larger inflows in the future. You consider your job to be an investment – that the dough you are not getting now will get more than compensated for later in your life.
So when on certain days you wake up and ask yourself why the fuck you are where you are and doing what you are doing, you usually don’t have an answer. In those states of mind, “career”, “development”, “investment”, “corporate” etc. all don’t matter at all. Neither does “net present value of expected future earnings”. Your total costs look inflated. Your benefits look deflated. Every line of thought that runs in your head then tells you that you should go off into the Himalayas. You go to office instead.
I’ll stop this essay here. In a forthcoming essay I’ll explain about how a job is essentially about costs and benefits, and why they use the word “compensation” to describe your salary. I have occasionally argued in the other direction, but thinking about it again, I think the word “compensation” with reference to salary package does make a lot of sense.
Suppose you and me together have to do two tasks A and B. We need to decide who does what (let’s assume that we need to pick one task each). Now I’m a stud and you are a chutiya so I’m better than you at both A and B. So how do we split? It all comes down to the degree to which I’m better than you in each of these tasks. Suppose I’m marginally better than you at A, but significantly better than you at B. Theory of comparative advantage (commonly used to describe international trade) says that I should do B and you should do A – this way, total productivity is maximized. I suppose this makes intuitive sense.
You have a number of people cribbing about what is popularly knonw as “chutiya kaam” – approximately translates to bullshit work. Work that is uninspiring for them, but which they need to do because it needs to be done. Sometimes you have otherwise fairly intelligent and efficient people assigned to chutiya kaam – with the explanation that there is no one else who is well-enough equipped to do it. And these people find that less intelligent nad less efficient people are being given better work.
The reason the more intelligent and efficient person might get the chutiya kaam is that he is better at that than his colleagues, even if he is better than his colleagues in the more intelligent stuff. So I suppose if you want to avoid chutiya kaam altogether, one of the ways of doing it is to prove yourself to be a chutiya at that. To be inefficient and incapable of doing that, and in the hope that it will then get palmed off to someone else who is perceived to be better.
But then this is a double edged sword. There are people who believe that all kinds of “chutiya kaam” are inferior to all non-chutiya kaam. And that if you are not good at chutiya kaam you cannot be good at everything else. I’m reminded of this guy in my class who was captaining the class team for a day and who refused to let me open the bowling because I’d dropped a catch. “You can’t even catch properly, and how can you expect to bowl?” he had asked.
The unfortunate thing is that a large number of people are like this. They refuse to accept that chutiya and non-chutiya kaam are not comparable, and require different skill sets, and that they will neeed to apply trade theory to figure out who does what. They look at your skills in one and use that to judge you in another. And allocate resources suboptimally. And when faced with this kind of people, the strategy of trying to be chutiya at chutiya kaam may not work.
So I suppose the key is to figure out what kind of person your boss is. Whether he appreciates that different jobs can take different skills, and no one job “dominates” another. And whether he applies trade theory when it comes to work allocation. If the former, you can’t really do anything. If the latter, you can try being chutiya at chutiya kaam.
Postscripts
“chutiiya kaam” is not a homogeneous term. Some jobs are chutiya for some people but non-chutiya for others. It varies from person to person.
I have grouped all “chutiya kaam” together just for the sake of convenience. There are differnet kidns of chutiya kaams and all of them require different skill sets.
Each non-chutiya kaam also requires its own skill set. I’ve again grouped them together for the sake of convenience of argument
I firmly believe that principles of economics that can be useful in real life (such as demand and supply, trade theory, game theory, etc.) should be part of the 10th standard economics syllabus, rather than teaching kids to mug up GDP growth rates for different states for different decades
I have resisted the temptation to bring in the studs and fighters theory into this analysis
When people crib to other people that their job is not too exciting and that it’s too process-oriented and that there’s not muc scope for independend thinking, the usual response is that no job is inherently process-oriented or thinking-oriented, and that what matters is the way in which one perceives his job. People usually say that it doesn’t matter if a job is stud or fighter, and you can choose to do it the way you want to. This is wrong.
So there are two kinds of jobs – stud (i.e. insight-oriented) and fighter (i.e. process oriented). And you can do the job in either a stud manner (trying to “solve a problem” and looking for insights) or in a fighter manner (logically breaking down the problem, structuring it according to known formula and then applying known processes to each sub-problem). So this gives scope for a 2 by 2. I don’t want this to look like a BCG paper so I’m not actually drawing a 2 by 2.
Two of the four quadrants are “normal” and productive – doing stud jobs in a stud manner, and fighter jobs in a fighter manner. There is usually an expectancy match here in terms of the person doing the job and the “client” (client is defined loosely here as the person for whom this job is being done. in most cases it’s the boss). Both parties have a good idea about the time it will tak e for the job to be done, the quality of the solution, and so on. If you are in either of these two quadrants you are good.
You can’t do a stud job (something that inherently requires insight) using a fighter process. A fighter process, by definition, looks out for known kind of solutions. When the nature of the solution is completely unknown, or if the problem is completely unstructured, the fighter behaves like a headless chicken. It is only in very rare and lucky conditions that the fighter will be able to do the stud job. As for “fighterization”, about which I’ve been talking so much on this blog, the problem definition is usually tweaked slightly in order to convert the stud problem to a fighter problem. So in effect, you should not try to solve a “stud problem” using a fighter process. Also, as an employer, it is unfair to expect a mostly fighter employee to come up with a good solution for a stud problem.
The fourth quadrant is what I started off this blog post with – studs doing fighter jobs. The point here is that there is no real harm in doing a fighter job in a stud manner, and the stud should be able to come up wiht a pretty good solution. The problem is wiht expectations, and with efficiency. Doing a fighter job in a stud manner creates inefficiency, since a large part of the “solution” involves reinventing the wheel. Yes, the stud might be able to come up with enhanced solutions – maybe solve the problem for a general case, or make the solution more scalable or sustainable, but unless the “client” understands that the problem was a stud problem, he is unlikely to care for these enhancements (unless he asked for them of course), and is likely to get pained because of lack of efficiency.
Before doing something it is important to figure out if the client expects a stud solution or a fighter solution. And tailor your working style according to that. Else there could be serious expectation mismatch which can lead to some level of dissatisfaction.
And when you are distributing work to subordinates, it might also help to classify them using stud nad fighter scales and give them jobs that take advantage of their stronger suits. I know you can’t do this completely – since transaction costs of having more than one person working on a small piece of work can be high – but if you do this to the extent possible it is likely that you will get superior results out of everyone.
One of the topics that I’d introduced on my blog not so long ago was “fighterization“. The funda was basically about how professions that are inherently stud are “fighterzied” so that a larger number of people can participate in it, and a larger number of people can be served. In the original post, I had written about how strategy consulting has completely changed based on fighterization.
After that, I pointed out about how processes are set – my hypothesis being that the “process” is something that some stud would have followed, and which some people liked because of which it became a process. And more recently, I wrote about the fighterization of Carnatic music, which is an exception to the general rule. Classical music has not been fighterized so as to enable more people to participate, or to serve a larger market. It has naturally evolved this way.
And even more recently, I had talked about how “stud instructions” (which are looser, and more ‘principles based’) are inherently different from “fighter instructions” (which are basically a set of rules). Ravi, in a comment on Mohit‘s google reader shared items, said it’s like rule-based versus principles-based regulation.
Today I was reading this Vir Sanghvi piece on Lucknowi cuisine, which among other things talks about the fact that it is pulao that is made in Lucknow, and now biryani; and about the general declining standards at the Taj Lucknow. However, the part that caught my eye, which has resulted in this post with an ultra-long introduction was this statement:
The secret of good Lucknowi cooking, he said, is not the recipe. It is the hand. A chef has to know when to add what and depending on the water, the quality of the meat etc, it’s never exactly the same process. A great chef will have the confidence to improvise and to extract the maximum flavour from the ingredients.
This basically states that high-end cooking is basically a stud process. That the top chefs are studs, and can adapt their cooking and methods and styles to the ingredients and the atmosphere in order to churn out the best possible product.You might notice that most good cooks are this way. There is some bit of randomness or flexibility in the process that allows them to give out a superior product. And a possible reason why they may not be willing to give out their recipes even if they are not worried about their copyright is that the process of cooking is a stud process, and is hence not easily explained.
Publishing recipes is the attempt at fighterization of cooking. Each step is laid down in stone. Each ingredient needs to be exactly measured (apart from salt which is usually “to taste”). Each part of the process needs to be followed properly in the correct order. And if you do everything perfectly, you will get the perfect standardized product.
Confession time. I’ve been in Gurgaon for 8 months and have yet to go to Old Delhi to eat (maybe I should make amends this saturday. if you want to join me, or in fact lead me, leave a comment). The only choley-bhature that I’ve had has been at Haldiram’s. And however well they attempt to make it, all they can churn out is the standardized “perfect” product. The “magic” that is supposed to be there in the food of Old Delhi is nowhere to be seen.
Taking an example close to home, my mother’s cooking can be broadly classified into two. One is the stuff that she has learnt from watching her mother and sisters cook. And she is great at making all of these – Bisibelebhath and masala dosa being her trademark dishes (most guests usually ask her to make one of these whenever we invite them home for a meal). She has learnt to make these things by watching. By trying and erring. And putting her personal touch to it. And she makes them really well.
On the other hand, there are these things that she makes by looking at recipes published in Women’s Era. Usually she messes them up. When she doesn’t, it’s standardized fare. She has learnt to cook them by a fighter process. Though I must mention that the closer the “special dish” is to traditional Kannadiga cooking (which she specializes in), the better it turns out.
Another example close to home. My own cooking. Certain things I’ve learnt to make by watching my mother cook. Certain other things I’ve learnt from this cookbook that my parents wrote for me before I went to England four years ago. And the quality of the stuff that I make, the taste in either case, etc. is markedly different.
So much about food. Coming to work, my day job involves fighterization too. Stock trading is supposed to be a stud process. And by trying to implement algorithmic trading, my company is trying to fighterize it. The company is not willing to take any half-measures in fighterization, so it is recruiting the ultimate fighter of ’em all – the computer – and teaching it to trade.
Preliminary reading on studs and fighters theory:
Earlier today I was talking to Baada and to Aadisht (independently) about jobs, and fit, and utilization of various skills and option value of skills not utilized etc. So it is like this – you possess a variety of skills, and the job that you are going to do will not involve a large number of these. For the skills that you have that match the job’s requirements, you get paid in full. For the rest of the skills you possess, you only get paid the “option value” – i.e. your employer has the option to utilize these skills of yours and need not actually utilize them.
Hence in order to maximize your productivity and your pay, you need to maximize the cos theta.
Assume your skill set to be a vector in a N-dimensioanl hyperspace where N is the universe of orthogonal skills that people might possess. Now there are jobs which require a certain combination of skill sets, and can thus be seen as a vector. So it’s about maximizing the cos theta between your vector and your job’s vector.
So it’s something like this – you take your skills vector and project it on to the job requirement vector – your total skills will get multiplied now by the value of cos theta, where theta is the angle in the hyperspace between your skills vector and the job vector. For the projection of your skills on the requirement, you get paid in full. For the skills that you have that are orthogonal to the requirement, you get paid only in option value.
One option is to of course build skill set, and keep learning new tricks, and maybe even invent new skills. However, that is not a short-term plan. In the short to medium term, however, you need to maximize the cos theta in order to maximize the returns that your job provides. But as Baada put it, “But there is slisha too much information asymmetry to ensure that cos theta is maximised.”
There are two difficult steps, actually. First, you need to know your vector properly – most people don’t. Even if you assume that you can do a lot of “Ramnath” stuff and get to know yourself, there still lies the challenge of knowing the job’s vector. And the job’s requirement vector is typically more fluid than your skills vector. Hence you actually need to estimate the expected value of the job’s requirement vector before you take up the job.
The same applies when you are hiring. It is actually easier here since the variation in the hiree’s vector will not be as high as the variation in the job profile requirement vector, and you have a pretty good idea of the latter so it is easy to estimate the “projection”.
This perhaps explains why specialists have it easy. Typically, they have a major component of their skills vector along the axis of a fairly well-defined job profile (which is their specialization). And thus, since theta tends to 0, cos theta tends to 1, and they pretty much get full value for their skills.
At the other extreme, polymaths will find it tough to maximize their returns to skills out of a single job, since it is unlikely that there is any job that comes close to their skills vector. So whichever job they do, the small value of the resulting cos theta will cancel out the large magnitude of the skills vector. So for a polymath to maximize his/her skills, it is necessary to do more than one “job”. Unless he/she can define a job for himsel/herself which lies reasonably close to his/her skills vector.
(there is a small inaccuracy in this post. i’ve talked about the angle between two vectors, and taking the cosine of that. however, i’m not sure how it plays out in hyperspaces with a large number of dimensions. let us assume that it’s vaguely similar. people with more math fundaes on this please to be cantributing)