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Decentralization Metrics

Quantifying mining pool concentration and network security

Contents

Why Measure Decentralization?

Bitcoin's security model relies on the assumption that no single entity (or small group) controls more than 50% of the network's hashpower. Decentralization metrics help us:

  • Detect concentration risks — Early warning of potential 51% attack vectors
  • Track trends over time — Is mining becoming more or less distributed?
  • Compare across periods — How does current concentration compare to historical?
  • Assess protocol health — Fundamental metric for network resilience
Important Caveat

Pool hashrate ≠ entity control. A pool with 30% hashrate doesn't mean one entity controls 30% of mining. Pools are collections of independent miners who can switch pools at any time. However, pool operators do control block template construction.

Herfindahl-Hirschman Index (HHI)

HHI — Market Concentration Index

The HHI is a standard economic measure of market concentration, calculated as the sum of squared market shares.

Herfindahl-Hirschman Index $$\text{HHI} = \sum_{i=1}^{n} s_i^2$$
Where
$s_i$
Market share of pool $i$ (as percentage, 0-100)
$n$
Number of pools

HHI Scale

HHI Range Interpretation Example Scenario
< 1,500 Low concentration (competitive) 10+ pools with similar shares
1,500 - 2,500 Moderate concentration Few dominant pools, several small
> 2,500 High concentration 1-2 pools dominating
10,000 Monopoly Single pool with 100%

HHI Properties

  • Range: 0 to 10,000 (when using percentages)
  • Minimum: Approaches 0 as shares become infinitesimally small and equal
  • Maximum: 10,000 (single entity with 100%)
  • Squaring effect: Larger shares contribute disproportionately more
Example Calculation

If 3 pools have shares of 40%, 35%, and 25%:
$\text{HHI} = 40^2 + 35^2 + 25^2 = 1600 + 1225 + 625 = 3450$ (high concentration)

Normalized Herfindahl Index (NHI)

NHI — Comparable Concentration

The NHI adjusts for the number of participants, making it comparable across markets with different numbers of players.

Normalized Herfindahl Index $$\text{NHI} = \frac{\text{HHI} - \frac{1}{n}}{1 - \frac{1}{n}}$$

When using percentages (HHI from 0-10,000):

NHI (Percentage Form) $$\text{NHI} = \frac{\text{HHI} - \frac{10000}{n}}{10000 - \frac{10000}{n}}$$
Where
$n$
Number of pools (participants)
$\frac{10000}{n}$
Minimum possible HHI (perfect equality among $n$ pools)

NHI Scale

NHI Range Interpretation
0.0 - 0.1 Very low concentration (highly competitive)
0.1 - 0.25 Low concentration
0.25 - 0.4 Moderate concentration
0.4 - 0.6 High concentration
0.6 - 1.0 Very high / near-monopoly

Why Use NHI?

Raw HHI depends on the number of participants. A market with 3 equal players has HHI = 3,333, while 10 equal players has HHI = 1,000. NHI normalizes both to 0 (perfect competition given the number of players).

Nakamoto Coefficient

Nakamoto Coefficient — 51% Threshold

The minimum number of entities needed to collectively control more than 50% of the network. Named after Satoshi Nakamoto.

Nakamoto Coefficient $$N = \min\left\{k : \sum_{i=1}^{k} s_{(i)} > 50\%\right\}$$
Where
$s_{(i)}$
Market share of the $i$-th largest pool (sorted descending)
$k$
Number of pools in the coalition

Algorithm

  1. Sort pools by market share (descending)
  2. Sum shares starting from largest
  3. Count how many pools until sum exceeds 50%
  4. That count is the Nakamoto coefficient

Nakamoto Interpretation

Nakamoto Interpretation Security Implication
1 Single entity dominance Critical — 51% attack trivial
2 Duopoly Severe — Two-party collusion risk
3-4 Oligopoly Concerning — Small cartel possible
5-10 Moderate distribution Better — Collusion requires coordination
>10 Well distributed Healthy — Attack requires many colluding parties
Historical Context

Bitcoin's Nakamoto coefficient has typically ranged from 3-5 over the past decade. Brief periods have seen it drop to 2 (during GHash.io's peak in 2014).

Top-N Share Metrics

Simple but intuitive metrics showing the combined market share of the largest pools:

Top-N Share $$\text{Top-}N = \sum_{i=1}^{N} s_{(i)}$$

Common Benchmarks

Metric Typical Range Concern Threshold
Top-1 (Largest pool) 15-30% > 40% (approaching dominance)
Top-3 40-55% > 60% (significant concentration)
Top-5 55-70% > 75% (high concentration)

Interpreting the Metrics Together

Each metric captures different aspects of concentration. Use them together:

Metric What It Captures Limitation
HHI Overall market concentration Depends on number of pools
NHI Concentration relative to perfect distribution Less intuitive to interpret
Nakamoto 51% attack threshold Binary — doesn't show "closeness"
Top-N Share of largest players Doesn't account for tail distribution

Healthy Network Characteristics

  • Nakamoto coefficient ≥ 4
  • No single pool > 25%
  • Top-3 pools < 50%
  • NHI < 0.3
  • Stable or improving trend over time
Real-World Complexity

These metrics measure pool concentration, not actual entity concentration. Some entities operate multiple pools, some pools have the same ownership, and some "unknown" blocks may belong to known pools. Treat metrics as indicators, not absolute truth.