Counterfactual Savings and the Productivity Denominator

A rate fifty percent lower, taking a quarter more hours, nets thirty-seven and a half: the saving is on hours multiplied by rate, never on rate alone.

Counterfactual savings and the productivity denominator concerns the arithmetic by which sourcing and location savings are overstated. A node that is fifty percent cheaper per hour and takes twenty-five percent more hours to do the same work delivers a saving of thirty-seven and a half percent, not fifty; the saving is on cost, which is rate multiplied by hours, and quoting it on rate alone silently assumes the hours are equal. The overstatement compounds when the comparison is against a counterfactual — an "equivalent in-house cost" that prices today's volume at the established node's rate while assuming the established node's headcount, productivity and overhead structure would have been identical — and it is compounded again when a program carries several savings figures produced on different bases and none is reconciled with the others. The quality-adjusted cost framework that quantifies the productivity denominator by node is owned by Labor Arbitrage and Global Workforce Optimization; the per-head cost stack by Workforce Cost Modeling; the cost-per-outcome denominators by Unit Economics of Workforce Operations; the credible estimation of a counterfactual generally by Counterfactual Reasoning in WFM. This page takes the arithmetic as given and addresses what happens after it — the construction of the baseline, and the reconciliation of several savings figures against one another.

The arithmetic, in one line

Cost is rate multiplied by hours, so a comparison on rate alone is valid only where hours per unit are equal — a rate lower by a fraction r against hours higher by a fraction h saves 1 − (1 − r)(1 + h), not r. At one half and one quarter that is thirty-seven and a half percent; at a two-thirds hours penalty a forty-percent rate saving is gone entirely. Labor Arbitrage and Global Workforce Optimization quantifies the same adjustment by node and shows how far below the headline a quality-adjusted saving typically lands; the productivity denominator is where the honest figure lives, and a saving quoted without it has not been computed.

The reconciliation discipline

1. State every savings figure with its basis. Counterfactual or observed; gross or net of transition; annualized or in-year; against which volume; on which productivity assumption.
2. Reconcile before presenting. Where several figures circulate, publish the bridge between them — what each includes that the others exclude — or withdraw all but one.
3. Carry the productivity denominator explicitly. Hours per unit by node is a measured attribute, not an assumption, and the saving is recomputed when it moves.
4. Separate the transition from the run-rate. The one-off cost of getting there and the recurring saving once there are different quantities with different owners; netting them into one figure hides whichever is inconvenient.
5. Prefer substitution at natural break points. Because transition cost is the binding variable, moving work at renewal, attrition or contract expiry preserves most of the gross saving; relocating an existing team consumes it.

Building a comparable pair

The commonest sourcing saving is a counterfactual: the cost the estate would bear if the work now done at a lower-cost node were done at the established one. The counterfactual is not an observed cost and cannot be audited against one, so its construction decides the answer. A defensible comparison adjusts both sides: the counterfactual for what the established node would actually have done, and the actual for the costs the lower-cost node carries that its rate does not show.

Adjustments required before a counterfactual and an actual can be compared

Item	Why it matters	Applies to
Productivity difference	The established node would not have taken the lower-cost node's hours; pricing the lower-cost node's hours at the established rate overstates the counterfactual by the productivity gap	Counterfactual
Management and governance overhead	A distant or outsourced node carries oversight, quality, vendor-management and coordination cost that the established node's rate does not include and that sits in other budgets	Actual
Ramp and rehire	Higher attrition and longer time to proficiency at the lower-cost node are recurring costs, not one-off transition items	Actual
Transition cost	Severance, parallel running, knowledge transfer and migration are real and can exceed the first year's gross saving; the outsourcing literature treats these alongside vendor search, ongoing management and eventual reversion as a single class of costs omitted from the headline rate	Actual
Rate structure	A supplier's rate is a price, not a cost: it contains the supplier's margin, and supplier rates can run above a captive center's cost at comparable scale in the same market, though a subscale captive frequently loses the comparison — the supplier is then the fast option, not the cheap one	Actual
Scope basis	Whether the figure is annualized, current-year, or run-rate, and what volume base it assumes; two true figures on different bases are not comparable	Both

The last row is the one most often left implicit. Three figures produced on different bases — an annualized run-rate saving, a current-year addressable saving, a counterfactual gross saving — circulating with no stated relation between them constitute three answers to one question, and the relation between them cannot be recovered by a reader.

Why suppliers are the fast option

In a market where the estate also runs a captive center, the supplier's rate is a price containing someone else's margin, overhead and risk premium, and whether it exceeds a captive's cost in the same market turns on the captive's scale. What the premium buys is not a lower cost but speed to seat — capacity in weeks rather than the months a captive build takes — and, sometimes, an exit right the captive does not have. Whether the exit right is real is a contract question; where notice periods and minimums make a supplier as slow to exit as a captive, the premium has bought speed of entry only. Labor Arbitrage and Global Workforce Optimization carries the location-comparison framework and BPO and Vendor Management for WFM the contract dimension; the point here is that a supplier rate belongs in the cost term of a placement model as a price with a margin, not as a cost.

Failure modes

• Quoting the rate saving. The hours difference is assumed away and the saving is overstated by the productivity gap.
• Auditing a counterfactual against nothing. The "equivalent in-house cost" is presented as if observed and cannot be checked.
• Netting transition into run-rate. A large one-off cost disappears into a multi-year saving.
• Carrying three figures. Annualized, in-year and gross savings circulate unreconciled, and the first challenge discredits all of them.
• Treating the supplier rate as a cost. The margin is invisible, and a supplier is assumed cheaper than a captive whose cost at comparable scale may be lower.

Maturity Model Position

Costing sourcing decisions on the productivity denominator is a Level 3 discipline on the WFM Labs Maturity Model™: it requires hours per unit to be measured comparably by node, which is the same instrument discipline that Level 3 quality comparison requires. It is a companion to the Level 3 instrumenting rule at Instrumenting the Objective Before Building the Model — the cost term of a placement model is only as honest as the denominator under it.

See Also

• Workforce Cost Modeling — the per-FTE cost stack
• Unit Economics of Workforce Operations — cost per outcome
• Labor Arbitrage and Global Workforce Optimization — cross-location comparison
• BPO and Vendor Management for WFM — the contract dimension of supplier cost
• Instrumenting the Objective Before Building the Model — the cost term as one of several
• Placement Rules and the Tenure Contract — why speed to seat is purchasable and proficiency is not
• Counterfactual Reasoning in WFM — estimating a counterfactual credibly
• Sourcing Strategy Under Cost Pressure — transition cost as a first-class objective term