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The same calculation drives three surfaces, the Headcount calculator, the capacity strip on Horizon, and the Capacity headroom derived signal on the Watchlist. This document is the maths.

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The core formula

Given your inputs:
  • V: weekly ticket volume (current)
  • g: weekly growth rate (% per week)
  • d: AI deflection rate (% of tickets resolved without humans)
  • N: number of agents
  • u: target utilisation cap (%)
Forepost computes: 
human_now    = V × (1 − d/100)
max_per_agent = human_now / N / 0.84
team_cap     = max_per_agent × N × (u/100)
week_growth  = V × (g/100) × (1 − d/100)
breach_week  = max(0, ceil((team_cap − human_now) / week_growth))
If week_growth = 0 (no volume growth) breach is treated as stable (returned as 99 internally; rendered as “no breach”).

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Why 0.84

The constant 0.84 is the implicit headroom inferred from your current state. It says: whatever utilisation you’re at right now, that corresponds to 84% of an agent’s true ceiling. So human_now / N / 0.84 is the per-agent throughput at full theoretical capacity. This is a heuristic. It assumes you’re not currently working agents past their cliff. If your team is at 95% utilisation today and CSAT is already crumbling, the model will overestimate ceiling. We chose this constant after testing against five reference workspaces; it works well in the 60-85% utilisation range that healthy teams operate in.

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Hire-by date

hire_by_week = max(0, breach_week − 8)
Eight weeks is the assumed lead time to source, sign, and ramp a support hire. It’s a sensible default for most support roles in 2026; teams scaling fast might want to widen it to 10-12.

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Cost model

monthly_cost = round(salary × 1.25 / 12)
annual_cost  = round(salary × 1.25)
The 1.25 multiplier covers benefits, payroll tax, tooling, and onboarding overhead. UK payroll-loaded; US figures may need a higher multiplier (typically 1.3-1.4 with healthcare).

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What the chart shows

A 28-week projection drawn from these inputs:
  • Volume line (blue): V × (1+g/100)^w projected forward, deflection-adjusted to humans-only.
  • Current capacity line (red dashed): flat at team_cap.
  • +1 hire capacity line (green dashed): flat at max_per_agent × (N+1) × (u/100).
  • Hire-by marker: vertical at hire_by_week.
  • Breach marker: vertical at breach_week.
The instant the volume line crosses Breach, you’re past target utilisation. CSAT typically degrades 2-3 weeks after that point.

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Where it falls short

  • Doesn’t model seasonality. A January spike vs a steady base looks the same.
  • Assumes constant deflection. If your AI rate is climbing, real breach is later than the model suggests.
  • No agent skill mix. Two agents handling the same volume can have very different effective throughput.
  • Doesn’t account for backlog burn-down. Capacity is allocated to inbound only.
The model is intentionally simple. The point is to make capacity visible, not to predict it to the day.

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Where the model lives in code

Worker side: calcBreach(ws) in worker.js. SPA side: calcHC() in src/App.jsx. Both use identical maths.