Logistic Decay Function to Estimate the Lagged Seasonal Impact of Google Ads

I'm going to try to connect Star Wars with using a logistic decay function to estimate the lagged seasonal impact of Google Ads performance. Haha here we go! (Cue Force theme)

Example:
Let’s say your peak month drives $100 in sales. You apply a logistic decay curve:
👉 Month 1: $75
👉 Month 2: $50
👉 Month 3: $25
👉 Month n: $0

This mimics ad stock logic, like Obi-Wan’s voice echoing after death, the ad’s influence lingers long after the spend.

Cool analogy. Flawed logic.

Here’s the problem: This is curve-fitting, not causality. There’s a difference between:
👉 Trying to understand how ad impact lingers in aggregate (like building a Rebel base model), and
👉 Trying to optimize performance campaigns in real time (like targeting the exhaust port on the Death Star).


But here’s the issue: this is curve-fitting, not causality. There’s a difference between:
👉 Trying to understand how ad impact lingers in aggregate.
👉 Trying to optimize a performance campaign in real-time (Google Ads).

Problems with this approach in Google Ads context:
👉 No grounding in actual lagged conversions.
👉 Assumes every conversion in Month 0 has equal spillover.
👉 Violates incrementality: you can’t assign impact just because the math looks good.
👉 Inflates ROAS without control groups or counterfactuals.

If you want to stay on the light side of measurement, try this instead:
👉 Use Conversion Lag Data
→ GA4 path: Explore → Funnel → Time Lag Breakdown
→ Google Ads: Tools → Attribution → Conversion Lag Report

👉 Analyze Seasonality With Holdout Periods
→ Use historical analogs + pause campaigns to measure true drop-off

👉 Run Geo-Experiments or PSA Tests
→ Real-world lift beats spreadsheet simulations every time

👉 Apply Ad Stock Only in MMM Contexts
→ Don’t wield Jedi tools in the wrong battle

👉 Build Planning Buffers, Not Theories
→ “Spillover” is a planning assumption, not a causal truth
→ It's fine to say: “January’s spike often carries into February and March” just don’t claim it’s due to logistic decay unless proven

Bottom Line:
The Force might linger, but ad impact should be measured, not imagined.
Don’t Jedi-handwave your way into fake ROAS. Simulate effect. Then test it.
Your optimization strategy deserves something more powerful than...a logistic curve and a dream.