monar Labs

Monar Labs · Field note SYS-CTR

Your click-throughrate is a mathproblem you can'tsee.

Most teams treat Google Ads CTR like a copywriting exercise. It is actually a constrained optimization over hundreds of variables — and the ones that move it most are the ones nobody looks at. Here is the whole picture, made visible.

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Searching for maximum CTR An illustrative response curve with observations and a marked optimum. R&D · SEARCHING FOR MAX ƒ(x) max ƒ(x) x*

SYS · 01 — What we measure

It starts with one honest fraction.

The entire game reduces to a ratio: the clicks you win divided by the impressions you're shown. There are only two levers — earn more clicks on top, or stop paying for impressions that will never click on the bottom.

Most teams pour everything into the numerator. The quiet killer is the denominator: irrelevant impressions that inflate the bottom of the fraction and drag your whole rate down.

The objective function

CTR=ClicksImpressions

In plain terms: of everyone who saw your ad, what share actually clicked. Google constrains it — CTR = Clicks / Impressions, always between 0 and 1, and it feeds back into everything downstream.

In practice≈ 1 in 12 clicks
Watch the denominator do the damageDrag the slider

Hold clicks fixed. As more of your impressions become irrelevant, your CTR falls — even though the ad never changed.

4.6%resulting CTR

Relevant impressionsIrrelevant · 42%

SYS · 02 — Quality Score

Google grades your ad before it ever ranks it.

Quality Score is a 1–10 grade built from three signals. It multiplies your bid to decide rank — so a great score lets a smaller budget beat a bigger one. Set each signal and watch the grade move.

QS = 1 + eCTR + relevance + landing-page ∈ [1,10]
Expected CTR
Expected CTRWill people click this, historically?
Ad relevance
Ad relevanceDoes the ad match the search intent?
Landing page
Landing pageIs the destination fast and relevant?
6/10
Quality Score

SYS · 03 — The hidden auction

Every impression is an auction you never see.

Your bid alone decides nothing. Google multiplies it by the Quality Score you just built to get Ad Rank — then ranks you against everyone else competing for the same query. Position determines CTR. And you pay based on the ad beneath you divided by your own quality. Move the controls; watch the whole system respond.

Your max CPC bid$4.20
Quality Score (from the gauge above)6/10

Ad Rank = bid × QS = $4.20 × 6 = 25.2

#4SERP position
1.9%Est. CTR
$2.51Actual cost per click= rank below you ÷ your QS + $0.01
The auction boardRanked by Ad Rank

A higher Quality Score lets you outrank a bigger bid — and pay less for the same click. Illustrative auction; competitor ranks held fixed.

SYS · 05 — The full picture

Six groups of variables. Only five you control.

This is the full taxonomy of what feeds your CTR. Notice the last group: the levers that constrain you hardest — competitors, intent, seasonality — are the ones you cannot touch. Click through each group.

Bid & budget

The money levers that set your Ad Rank ceiling.

Max CPC bid (per keyword)b_k · Continuous
You control this
Daily / monthly budgetB · Continuous
You control this
Bid adjustments (device, location, time, audience)δ · Continuous
You control this
Bid strategy type— · Categorical
You control this

SYS · 06 — Why it's hard

This is not a checklist. It's a moving target.

Even with every variable named, the problem resists brute force. Five properties make it a genuinely difficult optimization — the kind that beats spreadsheets and gut feel alike.

01

Mixed-integer nonlinearity

Bids are continuous, match types and asset flags are discrete, and CTR is non-convex across them. There is no clean gradient to follow downhill.

02

Endogeneity

CTR is both what you maximize and an input to Quality Score. The objective feeds itself — the feedback loop, formalized.

03

Partial observability

Competitor Ad Ranks are never visible. You optimize against opponents you can only infer from proxy signals like impression share.

04

Non-stationarity

Seasonality, competitor moves, and algorithm updates shift the landscape under you. Yesterday's optimum is today's average.

Optimum drifts —
your setting holds
05

Latent quality signals

Google never exposes the exact weights inside Quality Score or the full Ad Rank formula. You are optimizing a function you can't fully read.

Named, connected, and constantly moving. That's why guessing loses.

It needs a System

Illustrative model

What happens when you optimize the System, not the ad.

Illustrative data · not client results
+58%Click-through ratevs. campaign baseline
−41%Cost per clicksame budget, better rank
8/10Quality Scorelifted from 4 to 8
−33%Wasted impressionstighter negative keywords

How to read this

A modeled turnaround, not a published case study.

These figures demonstrate how the connected variables can move together. They are illustrative placeholders until a documented field result replaces them.

Read the technical appendix

Fix the workflow. Not the tools.

Stop guessing at your CTR. Optimize the System behind it.

Monar builds a personalized System around the one workflow costing you clicks — connecting bids, quality, targeting, and measurement into a single operating flow you can actually steer.

See how Monar solves this