How to Size Your Pooled Plans Using Variance (A Simple Risk Frames)

Akira Oyama
Feb 26
3 min read

In Part 1 Mobility Rate Plan Optimization Is Risk Management (Not Just Cost Cutting)

I argued that mobility rate plan optimization is not just a cost-cutting exercise. It is a risk management problem. In this post, I'll walk through a practical framework for doing that.

If your unbilled report is imperfect, pooled plan optimization is a forecasting problem. The goal is to decide how much pooled capacity buffer to buy (via higher pooled tiers or unlimited) to reduce overage risk.

This post shows a simple framework.

Plan menu (simplified)

Unlimited: $30/line
1GB pooled: $10/line
5GB pooled: $20/line
Overage: $10 per GB

What you are "buying" when you move a line from 1GB → 5GB

Moving one line from 1GB to 5GB:

Adds +$10 fixed monthly cost
Adds +$4 GB pooled capacity

So you're paying $10/4GB = $2.50 per GB of buffer.

Overage cost $10 per GB.

That's the core decision:

Is buying buffer at $2.50/GB worth it to reduce overage priced at $10/GB?

Step 1: Define pooled usage as forecast + error

Let:

F = forecast pooled usage (from unbilled)
A = actual pooled usage (billed)
E = A - F = forecast error
K = pooled allowance

Overage occurs when:

A > K

Overage GB:

max(A - K, 0)

Overage $:

10 x max(A - K, 0)

Total pooled cost:

Fixed cost + 10 x max(F + E - K, 0)

The whole point is: E is uncertain, so cost is uncertain.

Step 2: Build an error history from your own data

For each past month:

Forecast pooled usage (from unbilled)
Actual billed pooled usage
Error: E_month = Actual - Forecast

Now you have a distribution of forecast errors.

From that, compute:

average error (bias)
standard deviation (volatility)
95th percentile error (bad month)
99th percentile error (ugly month)

Percentiles are usually more actionable than standard deviation for business decisions.

Step 3: Choose a risk target (your "confidence level")

pick one rule:

90% confidence: overage should happen in < 10% of months
95% confidence: overage should be rare
99% confidence: near-zero surprise tolerance

This is your policy decision. Everything else is math.

Step 4: Translate the target into required pool headroom

If you target 95% confidence:

You want:

K ≥ F + E95

Where E95 is the 95th percentile forecast error.

That means required headroom is:

Headroom ≥ E95

Step 5: Decide how many lines to move to 5GB

Example scenario:

500 lines are pooled
Forecast pooled usage F = 475 GB
If all are on 1GB: allowance K0 = 500 GB
Current headroom = 25 GB

If you move m lines to 5GB:

K(m) = 500 + 4m
Headroom(m) = K(m) - F = (500 + 4m) - 475 = 25 + 4m
Extra fixed cost = 10m

To meet 95% confidence:

25 + 4m ≥ E95

So:

m ≥ (E95 − 25)/4

Example:

If E95 = 120 GB:

m ≥ (120 − 25)/4 = 95/4 = 23.75 → 24 lines

Cost:

Extra fixed = 24 x $10 = $240/month
Added buffer = 24 x 4GB = 96 GB

That's your risk premium for 95% confidence.

Step 6: Validate with a quick backtest (recommended)

For each historical month:

Compute A (actual pooled usage)
Compute overage under each candidate m:
- K(m) = 500 + 4m
- Over GB = max(A - K(m), 0)
- Over $ = 10 x Over GB
Add fixed premium 10m