Formulas

Notes

• Search Lost IS (budget) is a single metric, do not multiply Budget by Search Lost IS.

Ecommerce

• ATC Rate: Adds to cart / Link Clicks

Google & Bing

• Total Impressions Eligible For (Search): Impressions / Search IS
• Daily Budget Needed to Minimize Search Lost IS (budget): (Total Impressions Eligible For * Search Lost IS (budget) * CTR * CPC) / days in period
• Last X Days ROAS
  • Last 30 Days ROAS: Conversion_value_per_cost.date_range(last_30_days)
  • Last 14 Days ROAS: Conversion_value_per_cost.date_range(last_14_days)
• Last C Days Cost/Conv
  • Last 30 Days Cost/Conv: Cost_per_conv.date_range(last_30_days)
  • Last 14 Days Cost/Conv: Cost_per_conv.date_range(last_14_days)

Universal

• Hook rate: 3 Second Video Plays / Impressions
• Hold Rate: 95% Video Plays / 3 Second Video Plays
• 25% Video Play Rate: 25% Video Plays / Impressions
• 50% Video Play Rate: 50% Video Plays / Impressions
• 75% Video Play Rate: 75% Video Plays / Impressions
• 95% Video Play Rate: 95% Video Plays / Impressions
• 100% Video Play Rate: 100% Video Plays / Impressions
• CRSS Rate: (Post Comments + Post Reactions + Post Saves + Post Shares) ÷ Impressions
• Repeat Play Rate: 50% Video Plays / Reach

Ad Culling

Statistical cull rule for underperforming ads. Answers the question: if this ad's true CPA were exactly at goal, how unlikely is the result we're actually seeing? If the answer is "unlikely enough," the ad is probably not at goal and can be cut.

Uses the Garwood exact Poisson upper bound at 2k+2 degrees of freedom, where k = observed conversions. This is the standard exact interval and guarantees at least the stated coverage.

The rule

Cull if:  {Actual CPA} > {Goal CPA} × {Multiplier}

At 0 conversions CPA is undefined, so the same multiplier is compared against spend instead:

Cull if:  {Spend} > {Goal CPA} × {Multiplier}

Underlying formula

λ_upper    = ½ · χ²(1−α, 2k+2)
Multiplier = λ_upper / k

Where α is the false-positive tolerance (α = 0.05 for the 95% table, 0.20 for the 80% table, etc.).

At k=0 the chi-square term collapses to a closed form — no lookup needed:

Multiplier (k=0) = ln(1/α)

Example: goal CPA $80 at 95% → cull a zero-conversion ad once it passes $240 spend.

95% confidence

Cull ads with a 95% chance of not hitting goal CPA. Most conservative — longest leash before cutting.

Conversions	Multiplier
0 †	3.00
1	4.74
2	3.15
5	2.10
10	1.70
15	1.54
20	1.45
30	1.36
50	1.27
75	1.21
100	1.18
125	1.16
150	1.15

† Compared against spend, not CPA — CPA is undefined at zero conversions.

90% confidence

Conversions	Multiplier
0 †	2.30
1	3.89
2	2.66
5	1.85
10	1.54
15	1.42
20	1.35
30	1.28
50	1.21
75	1.16
100	1.14
125	1.12
150	1.11

† Compared against spend, not CPA — CPA is undefined at zero conversions.

85% confidence

Conversions	Multiplier
0 †	1.90
1	3.37
2	2.36
5	1.70
10	1.44
15	1.34
20	1.29
30	1.23
50	1.17
75	1.13
100	1.11
125	1.10
150	1.09

† Compared against spend, not CPA — CPA is undefined at zero conversions.

80% confidence

Most aggressive — cuts fastest, highest false-positive rate. Roughly 1 in 5 culled ads would have hit goal given more data.

Conversions	Multiplier
0 †	1.61
1	2.99
2	2.14
5	1.58
10	1.37
15	1.28
20	1.24
30	1.19
50	1.14
75	1.11
100	1.09
125	1.08
150	1.07

† Compared against spend, not CPA — CPA is undefined at zero conversions.

Worked example

Goal CPA = $80, ad has spent $520 with 5 conversions → actual CPA $104.

At 95%: $80 × 2.10 = $168. Actual CPA of $104 is below it → keep. At 80%: $80 × 1.58 = $126. Actual CPA of $104 is still below it → keep.

Same ad at 5 conversions on $900 spend → actual CPA $180, above both → cull.

Notes and guardrails

• Interpolate conservatively. For conversion counts between table rows, round down to the nearest listed row (e.g. k=7 uses the k=5 multiplier). This errs toward keeping ads.

• Attribution lag. The zero- and low-conversion cases are the most exposed to conversions that haven't landed yet. Gate the rule behind a minimum ad age (7–14 days depending on the account's click window) or exclude the most recent N days of spend from the calculation. Without this, the rule will cull ads whose conversions are still in flight.

• Learning phase. On Meta, a $80 goal CPA triggers a cull at $240 spend under the 95% zero-conversion rule — which can land inside or barely past learning. Consider pinning the zero-conversion rule at 95% even when running 80% or 85% elsewhere, since a false positive costs the most when there's no signal at all.

• This is a one-sided test. It only asks whether the ad is worse than goal. It says nothing about whether one ad beats another — for that, use a proper two-sample comparison.

• The rule tests the entity as configured — not the goal. A failed test says the composite (this creative, audience, placement, bid, offer, landing page) is not at goal. It does not apportion blame among those parts, and it cannot tell you whether the goal is reachable by some other configuration, because it holds no data on ads that were never run. "Cull this ad" is supported by the math; "the goal is unrealistic" is not.

• Run it on the entity you would actually cull. Applied to an ad set or campaign, the rule tests a spend-weighted blend, and a blend can fail while an ad inside it succeeds. An ad-set-level failure is a prompt to decompose to the ad level, not a verdict on the ads.

• Past roughly k=150 the rule stops adding information. The multiplier is asymptotic to ~1.15 at 95%, so a high-volume entity that fails is failing by a margin more data will not overturn. At that point the decision is a business one — reallocate, rebuild, or reset the goal — not a statistical one.

• To estimate the true CPA rather than test it, invert the same Poisson for a two-sided interval: Spend / λ_hi to Spend / λ_lo, where λ_hi solves P(K ≤ k | λ) = α/2 and λ_lo solves P(K ≥ k | λ) = α/2. This returns the range the entity is plausibly operating in, which is more actionable than pass/fail once k is large. Note the interval describes performance already observed — it is not a forecast, and its optimistic end is not a target the entity can be expected to reach.

• Interval convention. These tables use 2k+2 degrees of freedom. This is a deliberate choice tied to how evaluation is triggered — see Why 2k+2 below before changing it or porting it to code.

Why 2k+2

2k and 2k+2 are not competing approximations of the same quantity. Each is the exact answer to a different sampling design, and the right one depends entirely on what triggers the evaluation.

Fixed-window sampling — an ad is inspected at an arbitrary moment (a scheduled script reading current cost and conversions). Spend is fixed by the calendar; conversion count is the random variable. This is Poisson, and the exact bound is 2k+2.

Inverse sampling — evaluation fires the instant an ad records its k-th conversion, and the question is how much spend it took to get there. Conversion count is fixed by the trigger; spend is the random variable. This is Gamma/Erlang, and the exact bound is 2k.

This reference uses 2k+2 because evaluation is scheduled, not tier-triggered: the Google Ads Script runs on a cadence and reads whatever cost and conversions each entity currently has. If the trigger is ever changed so that evaluation fires only on tier crossings, 2k becomes the correct convention and these tables should be regenerated.

The zero-conversion rule is necessarily fixed-window regardless — there is no "0th conversion" to wait for — which is why it is always ln(1/α). An earlier version of this framework used 2k for the conversion tiers while pairing it with the fixed-window zero rule; the resulting k=0 / k=1 threshold collision was a symptom of mixing two sampling frames in one table, not an error in the 2k math itself.

Alternatives considered and rejected:

• Wald normal approximation (Multiplier = 1 + z/√k). Rejected. Returns 0 at k=0, so it culls zero-conversion ads at any spend, and it undercovers badly at low k — precisely where the decision is hardest. Do not use, even though the closed form is tempting for scripting.
• Jeffreys / gamma credible interval (2k+1). Rejected on cost-benefit, not correctness. It has the best average coverage of the three, but differs from 2k+2 by less than 0.05 at k≥10, and being a credible rather than confidence interval it carries an interpretation burden every time the number has to be explained.

Porting note: the Gamma(k, 1/k) relative-CPL formulation used in the CPL Reliability Suite and cull-rule generator is the 2k convention. Any tooling built on that formulation predates this decision and will produce different multipliers than the tables above.

Zero-Conversion Click Threshold

Companion to the zero-conversion spend rule. Same statistics, same multiplier table — clicks as the exposure unit instead of dollars.

When to Use This Instead of Spend

The spend rule ({Spend} > {Goal CPA} × {Multiplier}) is the default and should stay the default on most accounts.

Reach for the click version when:

• CPCs vary widely between ads in the same ad set, and you want to judge traffic/offer quality independent of what the auction charged
• An ad is accumulating cheap clicks and no conversions — spend crawls toward the threshold slowly while the traffic evidence piles up fast
• You are evaluating landing page or offer performance rather than a budget decision

The Rule

Cull if:  {Clicks} > {Multiplier} ÷ {Goal CVR}

Where {Goal CVR} is the click-to-conversion rate as a decimal (3% = 0.03).

Multiplier

The multiplier is fixed at the 0-conversion row and does not move.

This test only ever asks one question — "zero conversions, is that too unlikely?" — so the observed conversion count is pinned at 0. Clicks are exposure, not conversions; they no more move the multiplier than spend does in the dollar version. Confidence level is the only input that changes it.

Confidence	Multiplier
95%	3.00
90%	2.30
85%	1.90
80%	1.61

These are −ln(1 − confidence), the expected-conversion count at which observing zero becomes unlikely enough to act on.

Precomputed Thresholds

Clicks at which a zero-conversion ad gets turned off:

Goal CVR	95%	90%	85%	80%
20%	15	12	10	9
10%	30	23	19	17
5%	60	46	38	33
3%	100	77	64	54
2%	150	115	95	81
1%	300	230	190	161
0.5%	600	460	380	322

Each cell is Multiplier ÷ Goal CVR, rounded up.

Why Division, Not Multiplication

The multiplier is a count of conversions, not a rate. Goal CVR is conversions per click, which puts the unit in the denominator:

clicks = conversions ÷ (conversions per click)
       = 3.00 ÷ 0.20
       = 15

Sanity check by multiplying back — every cell in a confidence column returns that column's multiplier:

• 15 clicks × 20% = 3.0
• 100 clicks × 3% = 3.0
• 300 clicks × 1% = 3.0

The spend rule reads as multiplication because Goal CPA is dollars per conversion, putting dollars in the numerator. Same test, inverted unit.

Sourcing Goal CVR

Do not use the ad's own CPC to back into a CVR. CVR = CPC ÷ CPA makes Clicks × CVR collapse to Spend ÷ Goal CPA, and the click rule becomes the spend rule wearing a different hat.

The click rule only carries new information when Goal CVR comes from outside the ad being tested:

• Trailing account or campaign click-to-conversion rate over a stable window (90 days is usually enough; exclude any period with tracking gaps)
• A documented client benchmark where one exists
• The landing page's historical CVR when the same page serves multiple ads

Round the benchmark down. A conservative CVR raises the click threshold and favors keeping ads, consistent with the interpolation guardrail.

Exact Form

The precomputed table uses a Poisson approximation. The exact binomial form is:

Cull if:  {Clicks} > ln(1 − {Confidence}) ÷ ln(1 − {Goal CVR})

The two diverge only above ~10% CVR — at 10% the exact form gives 29 clicks against the table's 30. The approximation errs toward keeping the ad, so the table is safe to use as-is. Reach for the exact form only on high-CVR lead forms where the difference is material.

Beyond Zero Conversions

At k ≥ 1, prefer the CPA form. Once an ad has conversions, actual CPA is defined and the main Ad Culling rule answers the same question using a metric most people read natively. This subsection exists so the click form is written down correctly rather than re-derived, and for accounts where CVR — not CPA — is the native reporting metric.

The zero-conversion rule reads as Multiplier ÷ Goal CVR only because at k=0 the multiplier is the Poisson bound. In general the bound is λ_upper(k) = k × Multiplier(k), the expected-conversion count that would make the observed k look too low:

Cull if:  {Clicks} > {k} × {Multiplier(k)} ÷ {Goal CVR}

Equivalently, stated as a rate:

Cull if:  {Actual CVR} < {Goal CVR} ÷ {Multiplier(k)}

The two are the same inequality, since Actual CVR = k ÷ Clicks. Set k=0 and the first collapses back to the zero-conversion rule above.

Note the multiplier divides here where the CPA rule multiplies. CPA is lower-is-better and CVR is higher-is-better, so the tolerance band opens in the opposite direction — the same reason the k=0 rule divides.

{Multiplier(k)} is the ordinary multiplier from the Ad Culling confidence tables. Multiplied through, it gives:

Conversions	95%	90%	85%	80%
0	3.00	2.30	1.90	1.61
1	4.74	3.89	3.37	2.99
2	6.30	5.32	4.72	4.28
5	10.50	9.25	8.50	7.90
10	17.00	15.40	14.40	13.70
15	23.10	21.30	20.10	19.20
20	29.00	27.00	25.80	24.80
30	40.80	38.40	36.90	35.70
50	63.50	60.50	58.50	57.00
75	90.75	87.00	84.75	83.25
100	118.00	114.00	111.00	109.00
125	145.00	140.00	137.50	135.00
150	172.50	166.50	163.50	160.50

Divide the cell by Goal CVR to get the click threshold. The k=0 row is the multiplier table from above, unchanged.

Worked example

Goal CVR 3%, 95% confidence, ad has 420 link clicks and 5 conversions → actual CVR 1.19%.

Exposure form: 5 × 2.10 ÷ 0.03 = 350 clicks. 420 is above it → cull. Rate form: 3% ÷ 2.10 = 1.43%. Actual CVR of 1.19% is below it → cull.

Same ad at 300 clicks → actual CVR 1.67%, and 300 is under the 350 threshold → keep, both ways.

Notes

• Interpolate with actual k. Round k down to the nearest listed row to pick the multiplier, as always — but keep your real k in the k × Multiplier term. At k=7 that is 7 × 2.10 = 14.7 against a true bound of 13.15, a higher click threshold, which errs toward keeping the ad. Substituting the row's k for your own inverts that and culls early.
• No k=0 / k=1 collision. 4.74 sits above 3.00, so at 3% goal CVR one conversion moves the threshold from 100 clicks to 158 — a conversion correctly buys the ad more runway, never less.
• The exact binomial form does not generalize. ln(1 − C) ÷ ln(1 − CVR) is a k=0 closed form. At k ≥ 1 the exact analogue is a Clopper–Pearson beta bound, which needs a solver; the Poisson table is the practical answer and stays conservative.
• Still one primary unit per account. Having both a CPA form and a CVR form at k ≥ 1 does not license running them together and culling on whichever trips first. See the guardrail below.

Guardrails

All guardrails from the spend-based culling framework carry over unchanged. Additionally:

• Do not run both rules loosely. Clicks and spend are correlated but not identical, so culling on "whichever trips first" inflates the false-cull rate. Pick one primary unit per account and document it.
• Lock zero-conversion click tests at 95%, same as the spend rule, even on accounts running 80–85% elsewhere. In practice the 95% column is the only one most accounts should use.
• Clicks must be link clicks, not all clicks. On Meta, clicks (all) includes engagement that never reached the landing page and will fire this rule early.
• Attribution lag applies to the click counter too. Clicks post immediately; conversions do not. The 7–14 day window is still required before the click count means anything.

When the Rules Disagree

Two rules on the same ad can return opposite verdicts — the click rule says cull, the spend/CPL rule says keep. Before reading that as a signal about the ad, work through it in this order. The first step alone resolves most cases.

First: are the two rules testing the same goal?

CPL = CPC ÷ CVR, so a Goal CPL and a Goal CVR jointly imply a CPC:

Implied Goal CPC = {Goal CPL} × {Goal CVR}

An $80 CPL goal at a 3% CVR goal implies $2.40. An ad buying clicks below that is held to a stricter standard by the click rule than by the CPL rule, and will trip it first — systematically, on every cheap-click ad in the account.

Check it directly:

CVR this ad needs = {its CPC} ÷ {Goal CPL}

At $1.20 CPC against an $80 CPL goal, the ad needs 1.5%, not 3%. The thresholds bear this out — the click rule fires at 3.00 ÷ 0.03 = 100 clicks against the benchmark, but at 3.00 ÷ 0.015 = 200 clicks against what the ad actually needs, and the spend rule agrees: $80 × 3.00 = $240, which at $1.20 CPC is the same 200 clicks.

The two rules can only disagree because they were given different goals. Set Goal CVR = CPC ÷ Goal CPL and they collapse into one rule that cannot contradict itself — which is the same identity the Sourcing Goal CVR section warns about, seen from the other side. There it is a reason not to source Goal CVR from CPC; here it is the diagnostic for why two goals conflict.

If the goals are inconsistent, the CPL goal is the business goal. Trust it, and fix the Goal CVR for this ad.

Second: a shorter window is not a second opinion

If the goals are consistent and a short recent window still disagrees with a longer one, note what the short window actually is: a subset of the long one. Those clicks and that drought are already inside the long-window test, and that test — with more data — is saying the drought does not overturn the earlier evidence. Re-slicing to isolate the bad stretch and re-testing it is not new evidence; it is the same evidence with the inconvenient part removed.

Two questions settle whether the short window is admissible at all:

• Is it older than the attribution window? Clicks post immediately and conversions do not, so a recent window is the single worst place to trust a zero. If the window is younger than the click window plus processing, discard the result — it is not a signal.
• Was the window chosen in advance? A standing "trailing 14 days, every Monday" applied uniformly to every ad is a test. A window picked after noticing the ad looked bad is not.

Ruling out a tracking break comes first regardless. Zero conversions on real traffic is indistinguishable from a broken tag; check other ads on the same landing page before concluding anything about this one.

Third: test against the ad's own history, not the goal

An ad that passes on the full window and fails on a recent one is not necessarily failing its goal — it may have changed. That is a different question, and neither cull rule answers it: as noted in the Ad Culling guardrails, the test is one-sided and compares an entity to a goal, not to anything else, itself included.

Same machinery, with the rate swapped from goal to observed:

Recent decay is real (95%) if:  {Recent clicks} > 3.00 ÷ {this ad's historical CVR}

Use the multiplier column for other confidence levels, and compute the historical CVR excluding the window under test. An ad converting at 2.5% historically needs 120 recent clicks with nothing to clear the bar; at 150 clicks the expected count is 3.75 and P(0) = e^−3.75 ≈ 2.4%.

Note this cuts the opposite way from a goal test: an ad beating its goal makes a drought more surprising, not less. A strong performer going quiet trips this sooner than a marginal one.

A pass here reads as "this ad changed," not "this ad failed" — which points at creative fatigue, audience saturation, a broken landing page, or a seasonal shift. Those are diagnoses to investigate, not a cull.

Guardrails

• Every extra look raises the real false-cull rate. The stated confidence is per test. Two units × two windows × a check on every script run is a family of tests, and the lifecycle probability of culling an at-goal ad is meaningfully above the nominal 5%. The exact figure is not worth computing — the tests are heavily correlated — but the direction is certain.
• The zero-conversion spend rule is the exception. Spend crosses Goal CPA × Multiplier exactly once, so checking daily does not grant repeated attempts at that threshold. The conversion tiers above it are a sequence of tests and do.
• Do not resolve a disagreement by taking the verdict you prefer. Pick the primary unit and window in advance, per the click-threshold guardrails, and let the other rule inform diagnosis rather than the decision.
• To make the system respond to decay, change the standing rule — a uniform rolling window applied to every ad. Adding a second opportunistic test on top of the first raises the false-cull rate invisibly.