Price Is Not Right

Please stop quoting Price's Law. Price's law or Price's square root law states that square root of the number of people involved contributes to more than half the output. Well, that's not exactly what he says but that's what people take price's law to be.

For example, if you have small startup of 25 people, 5 (=√25) people will deliver more than half of the results.

I have heard it in multiple podcasts and discussions now. Very popular and prominent figures are promoting this idea. I feel that it is not a good lens to look at the world with. Here is why:

Context is wrong

The original context of this study looked at scientific publications. Price found that a small proportion of researchers were producing the majority of the papers.

Another way to see this is perhaps Lotka's law. It says the same thing in a different way. If we looked at a sample of 100 authors, a vast number researchers will only have one paper. Only about a quarter of them will have two papers. Only ten of them will have three papers.

This makes sense: most researchers publish at least one paper, often as a requirement of their doctorate.

However, most of those people would not continue working as researchers. They would not be in a role in their field expanding the boundary of the field. Tens of thousands of new doctorates graduate every year in different fields. Not discounting true genius or momentum but there aren't enough opportunities for them to be in positions where they continue writing paper after paper. Maybe they change their jobs or fields. Maybe they aren't as lucky with research topics. Maybe they aren't really that smart or are lazy. Maybe they stop working. There could be a thousand other reasons you will find that explain this distribution if you dig deep enough. There is nothing unbelievable about this statistic. I don't have actual data but I would expect real numbers to be far worse.

However, this does not support the hypothesis people try to insinuate when they quote Price's law. It does not in any way imply that those other people are not as good. Or that they are not making equally valuable contributions elsewhere or in other ways. I haven't been able to get my hands on an affordable copy of the book but at least the wikipedia page on this does not in any way insinuate anything to that effect.

It does not apply to labour

Let's look at what the insinuated implications of price's law is for different scale:

• If we had only one person, that person (√1=1) will be doing more than 50% of the work. You would hope so and that's perfectly fine.
• If we had 4 people, 50% (√4=2) of the people will do more than 50% of the work. That's also perfectly fine. It's probably the ideal scenario. It starts to be less ideal after this.
• If we had 25 people, 20% (√25=5) of the people will do more than 50% of the work. Now it is starting to become noticeable.
• If we had 100 people, 10% (√100=10) of employees will do more than 50% of the work. Maybe it is starting to be a problem.
• If we had 1000 people, 3% (√1024=32) of employees will do more than 50% of the work. Now it is a big problem.

Many people like to refer to Elon Musk's Twitter as an example. He fired almost 50% of the staff and the company was still fine. To me, this screams extreme ignorance about how software works.

To explain this, imagine twitter before Musk. Imagine they had a thousand software engineers hired at the time. They probably did not have a thousand software engineers but bear with me for a second. What were they actually doing? Twitter is an established (i assume cloud based) software service company. You don't have engineers manually sorting tweets and physically delivering them from one person to others. That all is automated, part of twitter's programmed business logic. So what were these thousand engineers doing in the company?

They were most likely working on either improving their existing product or developing new products and features. I am not saying companies don't have inefficiencies. If you compare your product development teams today to even 20 years ago, it will look vastly more inefficient. But these 1000 engineers were probably working on at least a 100 different initiatives to improve twitter's value proposition in one way or another. You of course will need some staff to keep the lights on. If you have good engineers writing good software, that overhead will be minimal. Maybe 1% of their staff at the time. Even if you fired all of the employees, unless they stopped paying the cloud bills, I would expect twitter to be continue to be up and running for a long time. It may not stay relevant and people may switch to other services - but that's a different point. So it is not surprising at all that twitter did not collapse.

To drive the point home, contrast this to your physical mail delivery service. If they had a thousand people, and you fired half the staff, you would notice a significant drop in performance. Your mail delivery will probably be exponentially delayed relative to the drop on staff volume. It may even start a negative feedback loop, leading to speedy collapse of the service. You would not expect the same thing of a saas company.

It is both true and false at the same time

If you looked at the nature of success in the globalised world, you would find this pattern everywhere. For example, a small number of music artists account for a large percentage of the hits. A small number of individuals hold a large proportion of wealth in the world. It's called pareto principle.

But let me also highlight the fact that it reflects very narrow one dimensional thinking. Not everyone contributes or contributes the same way or to the same extent. You can call it talent, luck, connection, work ethic or whatever else. To reinforce my earlier point, what are these other researchers doing with majority of their career if they are only publishing one paper? Probably something else of value.

It has no practical implications

Let's assume that price's law as they insinuate is true. Majority of the people are not as good as a small percentage of "high performers" as determined by the sample size. For example, in a sample of a thousand researchers, 32 would be considered these "high performers". What are you going to do with this information?

Imagine a scenario where you had a large research house with these 1000 researchers. You, empowered with price's law have been asked to cut down your operational budget by 20%. That's easy right? You can identify your high performing researchers using the same metric like number of published papers and reduce your staff down to 800. Maybe you found a way to eliminate length of career as a factor to produce a truly unbiased evaluation.

What does that actually do?

Firstly, is your research house producing the same same amount of output after the lay offs? Of course not. It will reduce your output. If you inverted this law and reduced the number of total people, the end total will be less. You will have less number of researchers working on projects or less number of projects, which means less number of papers will be generated in the same amount of time.

Secondly, the price's law will apply to the remaining 800. Efficiency has jumped from 3% to 3.5% of researchers producing 50% of the output. If you had another round of lay offs, it will jump to 4% of staff doing 50% of work in remaining group of 640 staff. You can continue laying off people in the name of efficiency until your research house shuts down. But it won't change the fact that you will continue producing less and less until you produce nothing.

Price's law does not say that if you managed to identity and keep the top 32 people that was producing 50% of the output in the 1000 person company firing every else, you will be able to retain that 50% output. All it says is that in that remaining group of 32 high performers, 6 (√36=5.7) people will produce more than half the output. But that's not what people realise or assume when they quote Price's law. This sounds plausible unless you have thought about it this deeply and is absurd.

This also contradicts economies of scale. The natural implication of this law is that your team will be most efficient when it's 4 or less people. These four will will likely need to wear multiple hats and take on various roles to keep the operation running smoothly. This is in contrast to bigger teams, where individuals may become more specialized and may be able to do certain tasks more efficiently or their costs may go down if you do more of the same task.

Then how do we reconcile the fact that the output won't scale proportionally with the number of people? What this simplistic view does not capture is the fact that the nature of the activity itself is not scalable.

With research and other creative fields, there is a element of chance. For example, imagine that with 1 skilled researcher, there is a 80% chance that they will produce produce a paper in a year. That is 4/5. If we had two researchers with the same probability, what is the chance that they will both produce a paper this year? The answer is 4/5 * 4/5 = 16 / 25 = 64%. Ok, this line of thinking is not 100% accurate because their performance is not perfectly independent. Why not? If you had 10,000 researchers with the optimum level intelligence and work ethic with perfect conditions working in a field, they will not be able produce 10,000 new unique papers. Any data behind Price's law would prove that. That is the nature of research and creative endeavours. It's a reality of life and logic. Only a small percentage of researchers would have everything lined up to have the most publications.

Another way to look at this is perhaps a soccer team. In a soccer team, you have a few "star" players who score most of the goals, while others may contribute in less visible ways. If you judged players by their goal-scoring alone, you can fill up a team with these "star" players who are typically strikers / forward position players. This formula might even give you a losing team as not all strikers will be the best at all the other positions that matter such as defence or midfield.

It's a horrible mindset

It's just a horrible thing to do to go around thinking that way.

It feels true because we are naturally biased to have high opinions of ourselves and lower opinions of others. It seems plausible that other people don't work as hard as us. That's our self-serving ego. Even when we try to think about it, we are most familiar with what we are contributing. Our life is especially hard. We are special. Bla bla bla. Other people's contributions and problems will feel less significant simply because we are less familiar. This is the availability heuristic at play.

If you let it dominate your thinking, it will make you an toxic and resentful person. If you are a leader in your company, it might even make your workplace toxic. You are more likely to drive good people away.

Conclusion

In conclusion, while Price's Law is a nice little phenomenon to observe, it does not practically mean what most people think it means. To mean that, it does not accurately reflect the complexities of human behaviour, the nature of creative work, or the dynamics of team performance. And thinking that most people are not doing their best does more harm than good.