MRR / ARR movement bridge (the waterfall)

One-liner

The period-over-period bridge that reconciles beginning recurring revenue to ending recurring revenue through its movement terms: Beginning + New + Expansion - Contraction - Churn (and the open reactivation question) = Ending. This is the spine that NRR, GRR, and revenue churn all decompose from.

Why it diverges

The individual movement components are Board-defined (New Name ARR, Expansion CARR, Contraction or Down-Sell MRR, Churned MRR are the standards-board terms NRR and GRR are built on). What is consensus arithmetic, not a codified standard, is the bridge identity that sums them: no authority publishes “Beginning + New + Expansion - Contraction - Churn = Ending” as a named formula, but it is the accounting that every retention metric assumes. The divergence is therefore not in the spine but at its joints. It diverges on composition, the one free-computable axis: where the line falls between a contraction (a retained account that shrank) and a churn (a lost account), whether reactivation or resurrection is a fifth category or folded into New, and whether the bridge is run on revenue (dollar movement) or on logos (count movement), which are different waterfalls over the same book.

Legitimate convention families

Family	Axis	Method (short)	Representative source	Direction vs defensible
Four-term revenue bridge	composition	Beginning + New + Expansion - Contraction - Churn = Ending, on a recurring-revenue basis	standards-board components (New Name ARR, Expansion CARR, Contraction / Down-Sell MRR, Churned MRR) summed as consensus arithmetic	the defensible default
Five-term bridge with reactivation	composition	the four terms plus a separate Reactivation / Resurrection term for returning churned accounts	common operator practice (uncodified)	isolates win-back; raises Expansion or New if folded in instead
Logo movement bridge	composition	the same walk on customer counts, not dollars	inverse of standards-board logo retention	answers a different question; a count waterfall, not the revenue one
GRR-only sub-bridge	composition	Beginning - Contraction - Churn = retained base, expansion term dropped	standards-board GRR formula method	the no-expansion slice that GRR reads from

What the investor likely recomputes on

A reader recomputes the four-term revenue bridge on the same recurring-revenue basis used for NRR and GRR, reads NRR off (Beginning + Expansion - Contraction - Churn) / Beginning and GRR off (Beginning - Contraction - Churn) / Beginning, and is skeptical of a bridge that nets reactivation into Expansion or that cannot separate contraction from churn. The four-term identity is settled; the contraction-vs-churn split and the reactivation treatment are bounded by the bridge, not fixed by it. Name the terms and the split against real numbers rather than assume them.

The defensible read

Lead with the four-term bridge on the same basis as the paired NRR and GRR, and state the contraction-vs-churn rule and the reactivation treatment out loud rather than letting them sit inside an aggregate. The aggressive move to avoid is a bridge that folds reactivation or one-time revenue into Expansion, or that books a deep downgrade as contraction rather than churn, both of which flatter retention read off the bridge. Principle: defensibility, not optimization.

The three axes

The movement bridge diverges mainly on composition: the five-or-six movement buckets and what falls in each. New (new-logo recurring revenue), Expansion (upsell or cross-sell within retained accounts), Contraction or Down-Sell (a downgrade within a retained account), Churn (a fully lost account). The unsettled sub-questions: the contraction-vs-churn boundary (when a downgrade becomes a loss); whether reactivation (a previously churned account returning) is a distinct term or counted as New; and logo movement vs revenue movement, which are separate bridges. The settled part is that New, Expansion, Contraction, and Churn are the four Board-defined terms and that they sum to the net change. Basis is ARR vs MRR vs implied-monthly, the same recurring-vs-other question as NRR and GRR, inherited by whichever retention metric reads off the bridge. Timing is the period of the bridge (monthly walk vs quarterly vs annual cohort) and whether the terms are point-in-time deltas or averaged, again inherited by the retention metric built on it.

See the three axes for the shared model.

Classic errors touching the movement bridge

gross-vs-net churn confusion: the bridge is exactly where it lives; netting Expansion against Churn and Contraction before reporting hides the gross terms. The four-term bridge surfaces them. See classic-errors.md.
one-time-in-MRR: a setup or services fee booked into New or Expansion inflates the bridge and every retention metric read from it. See classic-errors.md.
a deep down-sell booked as contraction rather than churn (or vice versa): moves the Contraction and Churn terms without changing the total, but changes GRR and the contraction-vs-churn read.

Scope boundary

IN SCOPE (from the founder’s stated movement aggregates): naming the bridge terms, confirming the four-term identity reconciles, and reading NRR and GRR off the stated New, Expansion, Contraction, and Churn figures. The bridge is computable from the founder’s stated movement aggregates. OUT OF SCOPE (named but not computed): the true contraction-vs-churn split, the reactivation classification, and logo-vs-revenue movement, all of which need customer-level deltas, not the aggregates (the recognize-vs-reconstruct line per the README). The per-axis reconstruction from the client’s raw source systems is out of scope for this reference. Reconstructing it from raw source systems is a separate, multi-week effort the reference does not perform.

Citations

The Board-defined components (New Name ARR, Expansion CARR, Contraction / Down-Sell MRR, Churned MRR) and the NRR and GRR formula methods that sum them: see the New CAC Ratio (New Name ARR), Expansion CAC Ratio (Expansion CARR), and Gross Revenue Retention entries in the canonical definitions, and the NRR and GRR formula methods carried in the net revenue retention and gross revenue retention conventions.
The bridge identity itself is consensus arithmetic, not a codified standard: no authority publishes the summed “Beginning + New + Expansion - Contraction - Churn = Ending” formula; it is the accounting the Board components assume.
The retention metrics that decompose from the bridge: see nrr.md, grr.md, and churn.md.