B2B SaaS Net Revenue Retention: Cohort Expansion Modeling, Churn Contagion, and Usage-Based Pricing

## Mathematical Foundations of Net Revenue Retention

In enterprise software economics, Net Revenue Retention (NRR) is the single most predictive metric of long-term enterprise valuation multiples. NRR isolates the compounding expansion capacity of an established customer cohort without conflating new logo acquisition.

### 1. Cohort Decomposition Formula

For a designated customer cohort originating at time $t_0$, the Net Revenue Retention at time $t$ is expressed as:

$$\text{NRR}(t) = \frac{\text{ARR}_{\text{base}}(t) + \text{ARR}_{\text{expansion}}(t) - \text{ARR}_{\text{contraction}}(t) - \text{ARR}_{\text{churn}}(t)}{\text{ARR}_{\text{base}}(t_0)}$$

| Pricing Architecture | Median GRR | Median NRR | Expansion Velocity (YoY) | Churn Half-Life |
|:---------------------|:----------:|:----------:|:------------------------:|:---------------:|
| Per-Seat Flat Rate | 88.4% | 104.2% | +15.8% | 5.2 Years |
| Pure Consumption (Metered) | 82.1% | 124.6% | +42.5% | 3.8 Years |
| Hybrid (Base Platform + Metered)| 91.2% | 119.8% | +28.6% | 7.1 Years |
| Tiered Feature Gate | 86.5% | 108.1% | +21.6% | 4.9 Years |

### 2. Churn Contagion Mitigation

Contraction often precedes outright cancellation by 90 to 180 days. Implementing automated usage anomaly detection allows account management teams to intervene when active weekly user seats decline by more than 15% across two consecutive billing cycles.