Organizational Complexity Index
D ≈ log(N) / log(L) measures structural complexity. D ≈ 3-4 is efficient; D > 5 suggests over-branching; D < 2 suggests under-branching.
Your lungs have a fractal dimension of approximately 2.88—complexity that fits 70-140 m² of gas exchange surface into your chest. Oak trees, blood vessels, and river networks all exhibit similar fractal properties: self-similar branching structures that efficiently distribute resources across scales. Organizations exhibit fractal structure too: hierarchies branch from CEO through levels to individual contributors. The Organizational Complexity Index borrows from fractal geometry to diagnose whether your structure is pathologically complex or pathologically simple. McKinsey (2012) found knowledge workers spend 28% of their workweek on email alone, plus nearly 20% searching for information. Harvard Business Review (2017) found executives now spend 23 hours per week in meetings, up from under 10 hours in the 1960s—complexity's coordination cost. Amazon addresses this with the 'six-page memo' rule, forcing clear thinking before meetings. The index formula D ≈ log(N) / log(L) relates organization size (N employees) to hierarchy depth (L levels). A 10,000-person company with 5 levels has D ≈ 5.7; one with 7 levels has D ≈ 4.6. Efficient structures cluster around D ≈ 3-4. Higher D suggests excessive hierarchy; lower D suggests insufficient management span.
When to Use Organizational Complexity Index
Use as a quick diagnostic when evaluating organizational structure—after acquisitions, before reorganizations, or when comparing divisions. Apply when decision-making feels slow but you can't pinpoint why. Deploy when headcount grows but productivity doesn't scale. The index provides objective benchmarking: are you more complex than peers? More complex than you were five years ago?
How to Apply
Map Hierarchy
Document the organizational hierarchy from CEO through all branches to individual contributors. This creates the raw material for measurement. Include all formal reporting relationships; informal structures matter but aren't captured by this index.
Questions to Ask
- Do you have an accurate, current org chart?
- Are all reporting relationships documented?
- Are there hidden levels (assistant-to, chief-of-staff) not shown?
- Are matrix reporting relationships creating unmeasured complexity?
Outputs
- Complete organizational chart
- Documentation of reporting relationships
Count Parameters
Count two numbers: L (total hierarchical levels from CEO to frontline) and N (total employees). For L, count the longest path from CEO to individual contributor. For N, use total headcount including contractors if they're in the reporting structure.
Questions to Ask
- How many levels exist on the longest path from CEO to IC?
- What is total headcount in the reporting structure?
- Are contractors included in the count?
- Does the organization have consistent depth across divisions?
Outputs
- L (hierarchical levels)
- N (total employees)
Calculate Index
Compute complexity index: D ≈ log(N) / log(L). This formula borrows from fractal dimension mathematics. Example calculations: 10,000 employees with 5 levels gives D ≈ log(10,000)/log(5) ≈ 5.7. Same 10,000 employees with 7 levels gives D ≈ log(10,000)/log(7) ≈ 4.7. The index captures how 'efficiently' hierarchy converts levels into capacity.
Questions to Ask
- What is log(N) / log(L) for your organization?
- How does this compare to the same calculation a year ago?
- How does this compare across divisions?
- What would D be if you added/removed one level?
Outputs
- Complexity index D
- Historical comparison if available
Interpret Results
Compare to benchmarks grounded in fractal efficiency: D ≈ 3-4 suggests efficient structure optimized for coordination and span. D > 5 suggests overly complex hierarchy (too many layers, narrow spans, coordination costs dominate). D < 2 suggests excessive flatness (too wide span, insufficient management oversight, chaos risk). Note: optimal D varies by work type—creative work tolerates lower D; operational work may require higher D.
Questions to Ask
- Is D in the 3-4 efficient range?
- If D > 5, which layers add no value?
- If D < 2, do managers have realistic spans of control?
- What D would you expect given your work complexity?
Outputs
- Structural diagnosis (efficient / over-branched / under-branched)
- Recommended structural investigation