Bitcoin Wealth Distribution: Utopian vision of anarcho-capitalism

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Critiques the concentration of Bitcoin wealth, exploring how its distribution aligns with ideals of anarcho-capitalism, where economic power is concentrated among a few, often bypassing traditional systems.
Published

Mar 4, 2025

Keywords

Bitcoin

Summary

A plot that shows the distribution wealth of Bitcoin among the wallets with a balance greater than $5,000 USD.

Code 
# Libraries
# ===================================================
import pandas as pd
import numpy as np
from bs4 import BeautifulSoup
import requests
from io import StringIO
import matplotlib.pyplot as plt
from matplotlib.ticker import FuncFormatter
import matplotlib.patches as patches

# Bitcoin Price
# ===================================================
url = "https://min-api.cryptocompare.com/data/price?fsym=BTC&tsyms=USD"
response = requests.get(url)
data = response.json()
btcprice = data.get("USD")

# Bitcoin Supply
# ===================================================
def get_btc_supply():
    response = requests.get("https://blockchain.info/q/totalbc")
    satoshi = int(response.text)
    btcsupply = satoshi / 100000000
    return btcsupply
btcsupply = get_btc_supply()

# Data Extraction
# ===================================================
url = "https://bitinfocharts.com/top-100-richest-bitcoin-addresses.html"
soup = BeautifulSoup(requests.get(url).text, "html.parser")
table = soup.find("table", {"class": "table table-condensed bb"})
df = pd.read_html(StringIO(str(table)))[0]

# Data Transformation
# ===================================================
# Select columns
df = df[['Balance, BTC', 'Addresses', 'BTC']]

# Rename columns and add average
df.rename(columns={'Addresses': 'rows', 'BTC': 'btc'}, inplace=True)

# Extract start and end range
df['start'] = df['Balance, BTC'].str.extract(r'[\[\(](\d[\d,\.]*)')
df['end'] = df['Balance, BTC'].str.extract(r'-\s([\d,\.]+)\)')
df['btc'] = df['btc'].str.extract('([0-9.]+)')

# Convert to values
df['rows'] = df['rows'].replace({',': ''}, regex=True).astype(int)
df['start'] = df['start'].replace({',': ''}, regex=True).astype(float)
df['end'] = df['end'].replace({',': ''}, regex=True).astype(float)
df['btc'] = df['btc'].replace({',': ''}, regex=True).astype(float)

# Add average price
df['average'] = df['btc'] / df['rows']

# Select columns
df = df[['rows', 'start', 'end', 'btc', 'average']]

# Change first and last value
df.loc[df.index[0], 'start'] = 0.000001
df.loc[df.index[-1], 'end'] = 250000

# Create a list
result = []

# Iterate over each row 
for index, row in df.iterrows():
    n = int(row['rows'])
    start = row['start']
    end = row['end']
    average = row['average']
    
    # Generate a distribution
    valores = np.logspace(np.log(start) / np.log(12), np.log(end) / np.log(12), n)
        
   # Calcular el factor de escala para ajustar el promedio
    current_average = np.mean(valores)
    scale_factor = average / current_average
    adjusted_values = valores * scale_factor

    # Add values to result list
    result.extend(valores)

# Crear a dataframe with all values
df = pd.DataFrame(result, columns=['btc'])

# Calculate marketcap
marketcap = btcsupply * btcprice

# USD Value, Filter >5000 and count
df['usd'] = df['btc'] * btcprice
df = df[df['usd'] > 5000]
df['count'] = 1

# Grouping by 100 percentiles
df['percentile'] = pd.qcut(df['btc'], 100, labels=False) + 1

# Grouping by 10 percentiles
df['percentile2'] = pd.cut(
    df['percentile'], 
    bins=range(1, 111, 10), 
    right=False, 
    labels=[i + 9 for i in range(1, 101, 10)]
).astype(int)

# Calculate GINI Index
def gini(x):
    x = np.array(x)
    x = np.sort(x)
    n = len(x)
    gini_index = (2 * np.sum(np.arange(1, n + 1) * x) - (n + 1) * np.sum(x)) / (n * np.sum(x))
    return gini_index
gini_value = gini(df['usd'])

# Summarizing data 
df = df.groupby(['percentile', 'percentile2'])[['usd', 'btc', 'count']].sum().reset_index()

# Average price
df['average_usd'] = df['usd'] / df['count']
df['percentage'] = df['usd'] / df['usd'].sum()

# Select columns
df = df[['percentile', 'percentile2', 'usd', 'count', 'average_usd', 'percentage']]

# Define palette
color_palette = {
    10: "#050407",
    20: "#07111e",
    30: "#15334b",
    40: "#2b5778",
    50: "#417da1",
    60: "#5593bb",
    70: "#5a7aa3",
    80: "#6d5e86",
    90: "#a2425c",
    100: "#D21E00"
}

# Map palette color
df['color'] = df['percentile2'].map(color_palette)

# Percentiles dataframe 2
df2 = df.copy()
df2 = df2.groupby(['percentile2', 'color'], as_index=False)[['usd', 'count']].sum()
df2['average_usd'] = df2['usd'] / df2['count']
df2['percentage'] = df2['usd'] / (df2['usd']).sum()
df2['count'] = 10

print(df)

# Data Visualization
# ===================================================
# Font Style
plt.rcParams.update({'font.family': 'sans-serif', 'font.sans-serif': ['Open Sans'], 'font.size': 10})

# Create the figure and suplots
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 8), gridspec_kw={'height_ratios': [10, 0.5]})

# First Plot
# ==================
# Plot Bars
bars = ax1.bar(df['percentile'], df['average_usd'], color=df['color'], edgecolor='darkgrey', linewidth=0.5, zorder=2)

# Title and labels
ax1.text(0, 1.1, 'Bitcoin Wealth Distribution', fontsize=13, fontweight='bold', ha='left', transform=ax1.transAxes)
ax1.text(0, 1.06, 'Intrapercentile Analysis of Wealth Concentration (excluding < 5000$ wallets)', fontsize=9, color='#262626', ha='left', transform=ax1.transAxes)
ax1.set_xlabel('% Wallets', fontsize=10, weight='bold')
ax1.set_ylabel('Wealth ($)', fontsize=10, weight='bold')

# Configuration
ax1.grid(axis='x', linestyle='-', alpha=0.5, zorder=1)
ax1.set_xlim(0, 101)
ax1.set_ylim(0, 2000000)
ax1.set_xticks(np.arange(0, 101, step=10))
ax1.set_yticks(np.arange(0, 2000001, step=250000))
ax1.tick_params(axis='x', labelsize=10)
ax1.tick_params(axis='y', labelsize=10)
ax1.spines['top'].set_visible(False)
ax1.spines['right'].set_visible(False)

# Function to format Y axis
def format_func(value, tick_number):
    if value >= 1e6:
        return '{:,.1f}M'.format(value / 1e6)
    else:
        return '{:,.0f}K'.format(value / 1e3)

# Formatting x and y axis
ax1.xaxis.set_major_formatter(FuncFormatter(lambda x, _: f'{x:.0f}%'))
ax1.yaxis.set_major_formatter(FuncFormatter(format_func))

# Lines and area to separate outliers
ax1.axhline(y=1850000, color='black', linestyle='--', linewidth=0.5, zorder=4)
ax1.axhline(y=1800000, color='black', linestyle='--', linewidth=0.5, zorder=4)
ax1.add_patch(patches.Rectangle((0, 1800000), 105, 50000, linewidth=0, edgecolor='none', facecolor='white', zorder=3))

# Y Axis modify the outlier value
labels = [item.get_text() for item in ax1.get_yticklabels()]
labels[-1] = '17M'
ax1.set_yticklabels(labels)

# Show labels each 10 percentile
for i, (bar, value) in enumerate(zip(bars, df['average_usd'])):
    value_rounded = round(value / 5000) * 5000
    if i % 10 == 0:
        ax1.text(bar.get_x() + bar.get_width() / 2, 
                 abs(bar.get_height()) * 1.4 + 50000,
                 f'{value_rounded:,.0f}',
                 ha='center', 
                 va='bottom', 
                 fontsize=8.5,
                 color='#2c2c2c', 
                 rotation=90)

# Show GINI Index
ax1.text(
    0.09, 0.97, f"Gini Index: {gini_value:.2f}", 
    transform=ax1.transAxes,
    fontsize=8.5,
    color='black',
    ha='right',
    va='top', 
    bbox=dict(boxstyle="round,pad=0.3", edgecolor='gray', facecolor='white')
)

# Show MarketCap
ax1.text(
    0.05, 0.88, 
    f"Price: ${btcprice / 1e3:.0f} k\nMCap: ${marketcap / 1e12:.2f} Bn", 
    transform=ax1.transAxes,
    fontsize=8.5,
    color='black',
    ha='center',
    va='top'
)

# Second Plot
# ==================
# Plot Bars
ax2.barh([0] * len(df2), df2['count'], left=df2['percentile2'] - df2['count'], color=df2['color'])

# Configuration
ax2.grid(axis='x', linestyle='-', color='white', alpha=1, linewidth=0.5)
ax2.tick_params(axis='x', which='both', bottom=False, top=False, labelbottom=False)
ax2.tick_params(axis='y', which='both', left=False, right=False, labelleft=False)
ax2.spines['top'].set_visible(False)
ax2.spines['right'].set_visible(False)
ax2.spines['left'].set_visible(False)
ax2.spines['bottom'].set_visible(False)
x_ticks = np.linspace(df2['percentile2'].min(), df2['percentile2'].max(), 10)
ax2.set_xticks(x_ticks)
ax2.set_xlim(0, 101)

# Add label values
for i, row in df2.iterrows():
    plt.text(row['percentile2'] - row['count'] + row['count'] / 2, 0, 
             f'{row["percentage"] * 100:.2f}%', ha='center', va='center', color='white', fontweight='bold')
    
 # Add Year label
formatted_date = 2024 
ax1.text(1, 1.1, f'{formatted_date}',
    transform=ax1.transAxes,
    fontsize=22, ha='right', va='top',
    fontweight='bold', color='#D3D3D3')

# Add Data Source
ax2.text(0, -0.5, 'Data Source: BitInfoCharts. "Top 100 Richest Bitcoin Addresses."',
         transform=ax2.transAxes,
         fontsize=8,
         color='#2c2c2c')

# Adjust layout
plt.tight_layout()

# Save it...
plt.savefig("C:/Users/guill/Downloads/FIG_BITINFO_Bitcoin_Wealth_Distribution.png", dpi=300, bbox_inches='tight') 

# Plot it!
plt.show()

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