📈 Pareto Salary: Price’s Law and Compensation 🔗

If the square root of people produce half the value, how many times higher than the average salary should the salary of top performers be?

Price’s Law suggests that in a given domain, the square root of the number of people involved produces 50% of the output. This is a specific application of the Pareto Principle (often known as the 80/20 rule).

If we apply this mathematical model to calculate the hypothetical value generated by the top tier of employees, the gap between top performers and the average grows exponentially as the company scales.

📑 Table of Contents 🔗

⚖️ The Scale of Asymmetry 🔗

Here is the ratio of a top performer’s productivity compared to the company average, based on the total number of people in the system.

(Note: The “Productivity of Top Performers” column reflects the individual contribution of someone in the absolute highest tier calculated by recursively applying the square root rule until the group size is small enough to evaluate.)

🧮 Example Calculation: A 10,000-Person Company 🔗

To understand how the math works, let’s break down a company of 10,000 people. If we repeatedly apply Price’s Law (the square root of the group produces half the remaining value), we get the following tiers:

In this scenario, a single person in that elite group of ~3 people is producing 3.95% of the entire company’s value. The average employee is producing 0.01%.

According to this model, the top performer is generating 395 times more value than the average employee.

💻 The Code 🔗

This Python script generates the data for the tables above.

import math

def calculate_top_productivity(number_of_people, total_value_percent):
    """
    Recursively calculates the productivity of an individual in the top tier 
    based on Price's Law (square root of N produces 50% of the value).
    """
    next_tier_size = math.sqrt(number_of_people)
    
    # Base case: if the next tier is more than half the current group, 
    # we've drilled down as far as the math allows. Return the average of this tier.
    if 2 * next_tier_size > number_of_people:
        return total_value_percent / number_of_people
        
    return calculate_top_productivity(next_tier_size, total_value_percent / 2.0)

# Generate table data for company sizes from 10 to 100,000
for exp in range(5):
    total_people = math.pow(10, exp + 1)
    
    top_performer_value = calculate_top_productivity(total_people, 100.0)
    average_value = 100.0 / total_people
    ratio = top_performer_value / average_value
    
    print('| %6.0f | %5.2f%% | %6.3f%% | %7.2fx |' % (total_people, top_performer_value, average_value, ratio))

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