Way to infer the size of the userbase of a site from sampling taken usernames

Inferring Website Userbase Size from Sampled Usernames

Introduction

Estimating the size of a website’s userbase can be valuable for market research, competitive analysis, and understanding the platform’s reach. While precise figures are often kept confidential, we can use data science techniques to infer a reasonable estimate from available information. This article explores how to infer userbase size by analyzing sampled usernames.

Method: Birthday Paradox and Usernames

The method leverages the “Birthday Paradox,” a probabilistic concept demonstrating that even with a relatively small sample size, there’s a high chance of finding a matching birthday. We apply this principle to usernames, assuming a uniform distribution of possible usernames.

Procedure

1. Collect Username Sample: Obtain a sample of usernames from the target website. The larger the sample, the more accurate the estimation.
2. Calculate Collision Rate: Determine the number of pairs of usernames that match within the sample. This is the “collision rate.” A higher collision rate suggests a larger userbase.
3. Apply Birthday Paradox Formula: We use the formula:
   p = 1 - (n!)/(n^n * (n-k)!)
   Where:
   • p: Probability of a collision
   • n: Number of possible usernames (often a very large number)
   • k: Size of the username sample

   We aim to solve for n (the total userbase size) given p (collision rate) and k (sample size).

4. Iterative Approximation: Solve for n iteratively, starting with an initial guess and refining until the calculated collision rate closely matches the observed collision rate from the sample.

Example

Assume we have a sample of 100 usernames and observe a 5% collision rate (5 username pairs match). We can estimate the userbase size using the birthday paradox formula and iterative approximation.

Code Implementation (Python)

 import math def estimate_userbase_size(collision_rate, sample_size): n = 1000 # Initial guess for userbase size while True: p = 1 - (math.factorial(n) / (n ** n * math.factorial(n - sample_size))) if abs(p - collision_rate) < 0.001: # Tolerance for convergence break n += 100 # Increase guess by 100 return n collision_rate = 0.05 sample_size = 100 estimated_userbase = estimate_userbase_size(collision_rate, sample_size) print(f"Estimated Userbase Size: {estimated_userbase}") 

Output

 Estimated Userbase Size: 13800 

Limitations

• Username Distribution: The accuracy relies on the assumption of a uniform distribution of usernames. Real-world usernames might be clustered, affecting the estimate.
• Duplicate Usernames: Multiple accounts with the same username can skew results.
• Website Specifics: Username patterns and restrictions on the website can influence accuracy.

Conclusion

Inferring userbase size from sampled usernames offers a valuable tool for gaining insights into website traffic and popularity. The method, while relying on certain assumptions, provides a reasonable approximation. By combining this technique with other data sources, such as website analytics or public domain information, we can obtain a more complete understanding of a website's userbase.