Why rounding errors lose tenders

A rounding error in TV costing is any small imprecision that survives into the final plan — a truncated CPP, a budget carried as 100 instead of 100.3. It matters because a media plan is a chain of calculations, and every link feeds the next. The instant someone pastes a number into a proposal, it stops being an estimate. Before that it was a working hypothesis you could refine. After, it is an obligation: the budget, the TRP volume, and the discount tier declared to the seller are all signed up to it. Clients read a proposal as a promise, not as a record of your thinking.

That line separates two modes of work. Rough arithmetic earns its keep on a first pass, when you want the order of magnitude and need to kill the scenarios that were never viable. The same arithmetic fails in a tender, where the calculation becomes a document with consequences.

Why does a 0.3% difference change the whole plan?

The gap between 100 and 100.3 looks cosmetic until it meets the first discount tier. The budget you declare to the seller — the Shop List figure — decides which discount you get, and that relationship is a staircase, not a smooth curve. Fall a fraction short and you land a step lower.

A dropped step doesn't move one row in the table. Discount size sets how much inventory is available to you; inventory sets the achievable TRP and the whole media logic of the campaign. Two proposals whose inputs differ by a rounding error can describe genuinely different campaigns.

Multiplication accumulates error; it does not cancel it

Past the tier, the error stops being local. The CPP chain multiplies:

In a sum, deviations in opposite directions sometimes cancel. In a product they compound. A small inaccuracy in the base rides through every later factor and surfaces at the end. The practical damage is worse than the error itself: you end up defending a number you cannot decompose. And "show us how you got that figure" comes up in almost every defense.

What that means for how we build

So in TV Budgeting we don't aim to roughly agree with the reference. We hold parity below 0.01% against an agency's reference Excel — a pinned state, re-checked on every code change: roughly 750 tests on the calculation core and roughly 2,100 tests on the interface.

The boundary of responsibility deserves its own sentence. CPP in our engine stays a proxy. We answer for the arithmetic of the plan — that the chain of multipliers runs without loss, that the result reproduces. We don't answer for the market price, which lives in negotiation with the seller. Where measurement data enters the calculation, we reproduce Nielsen's numbers; we don't substitute our own interpretation of them.

Two smaller decisions come out of the same logic:

• Behavior at a tier boundary. The budget → discount → budget loop is iterative by nature, and it sometimes oscillates between two adjacent steps. The system takes the larger budget, a deliberately conservative choice in the buyer's favor. Better a figure with headroom than one you cannot cover in front of client and seller.
• No silent defaults. If an input value is missing, the calculation fails with the field name instead of quietly slotting in something "typical." A silent default looks convenient until you find half the plan resting on a number nobody entered. An explicit error costs a minute; an undetected default costs the tender.

Is this a tools argument?

One clarification, so nobody takes away a false picture of the market. This isn't manual Excel versus software. In mature markets like Kazakhstan and Russia the processes have been tool-driven for years, and the live question is which class of tool takes on which share of responsibility for the number. We work through that fork in Alternatives to Enterprise Media Planning Platforms

Tenders are rarely lost on presentation design. They are lost on the request to break the number down step by step. So treat reproducibility as part of the commercial offer, not a technical detail: it decides whether you can defend your figures in a room where they are checked out loud.