The Scientific Method for AEO: How to Model, Test, & Win AI Search For Your Brand

If you've been in SEO long enough, you know Kyle Roof's name. The guy who scientifically decomposed Google's algorithm through single-variable testing - literally ranking lorem ipsum pages by isolating ranking factors one at a time. While everyone else was guessing, Kyle was running controlled experiments that would make a Stanford researcher jealous.

Now, as we shift from SEO to AEO (Answer Engine Optimization), we need that same scientific rigor - but the game is exponentially more complex. LLMs aren't just matching keywords; they're synthesizing information from millions of sources, and their outputs are probabilistic, not deterministic.

Combining statistical methods some of which are based on research from Anthropic, have given us the statistical framework to bring Kyle Roof-style scientific testing to the AI age. At Discovered Labs, we've operationalized this into a system that transforms AEO from educated guesswork into predictable, measurable wins.

Check out our interactive LLM Eval Calculator here - Built on the principles below.

The Uncomfortable Truth Expert Marketers Need to Face

Here's what keeps me up at night: almost all researchers and marketers testing AI mentions are doing it wrong. They're running tiny sample size prompts, getting a yes/no on brand mention, and calling it data. Unfortunately, this means that most of the research published currently isn't worth the paper it's printed on. That's like Kyle Roof testing one page and declaring he's cracked the Google algorithm.

The reality?

• LLMs generate different outputs for the same prompt (even at temperature 0)
• Your "80% brand mention rate" might actually be 60-100% with proper error bars
• Related prompts create statistical clusters that most evaluations ignore
• Without proper sample sizing, you're making million-dollar decisions on noise

Note: without naming the publications and recent papers have been published with sample sizes as small as 48 and claimed wild results as the headlines.

Part 1: The Kyle Roof Approach Applied to AEO - Single Variable Testing at Scale

Kyle's breakthrough was isolating variables. In AEO, this means:

The Variable Isolation Framework for AI Engines

1. Content Structure Variables
   • Test: Listicles vs. comparisons vs. technical documentation
   • Control: Same entity information, different formats
   • Measure: Brand mention rate per format across 100+ prompts
2. Authority Signal Variables
   • Test: Reddit mentions vs. industry publications vs. owned content
   • Control: Same messaging, different source types
   • Measure: Citation frequency and positioning
3. Entity Relationship Variables
   • Test: Direct competitor comparisons vs. category mentions vs. standalone content
   • Control: Same value props, different contextual framing
   • Measure: Recommendation strength scores

Real Testing Protocol Example:

Hypothesis: "Alternative to [competitor]" pages drive 3x more brand mentions than feature pages
Test Design:
- 50 "alternative to X" pages
- 50 feature-focused pages
- Each tested with 20 prompt variations
- 10 reruns per prompt (handling LLM wobble)
- Total: 20,000 LLM calls with clustered analysis
Result: Statistically significant lift of 2.7x (p<0.01)

Ideally we would also set this up an isolated environment but for most this isn't practical. Its often better to accept the risk of injecting noise into the experiment and getting real world feedback rather than spending 3 months just setting up the environments.

Part 2: The Evan Miller Statistical Framework - Making Your Tests Bulletproof

This is where most marketers' eyes glaze over, but stay with me, this is your edge. With this you'll be able to actually trust the feedback on your actions and know what works and what doesn't - simple.

The Three Pillars of Statistically Valid AEO Testing

Pillar 1: Variance Reduction Through Intelligent Resampling

The Problem Most Ignore:

• Ask ChatGPT "Best CRM for startups" 10 times
• You might get HubSpot mentioned 7 times, Salesforce 3 times
• Most marketers would test once and move on

The Scientific Approach:

# Pseudo-code for proper evaluation
for prompt in test_prompts:
    responses = []
    for i in range(10):  # K=10 resampling
        response = llm.generate(prompt, temperature=0.3)
        responses.append(check_brand_mention(response))
    
    prompt_score = mean(responses)  # Reduces conditional variance
    prompt_variance = variance(responses)  # Captures uncertainty

Why This Matters: A single test showing "not mentioned" might just be bad luck. Ten tests showing 70% mention rate? That's data you can bet your budget on.

Pillar 2: Clustered Standard Errors for Related Prompts

The Hidden Trap:

• You test 100 prompts about "project management software"
• They're all related (clustered)
• Standard statistics treat them as independent
• Your confidence intervals are fantasy

The Fix:

Prompt Clusters for SaaS AEO:
- Cluster 1: Feature comparisons (20 prompts)
- Cluster 2: Pricing questions (15 prompts)
- Cluster 3: Integration queries (25 prompts)
- Cluster 4: Use case scenarios (40 prompts)

Apply clustered standard errors → Real confidence intervals
Result: What looked like ±2% accuracy is actually ±5%

Pillar 3: Power Analysis for Right-Sized Testing

Stop guessing how many prompts to test. Calculate it:

The Formula That Changes Everything:

Required Sample Size = f(desired_precision, confidence_level, 
                        pilot_variance, resampling_count)

Example Calculation:
- Want: ±3% precision on brand mention rate
- Confidence: 95%
- Pilot shows: 15% variance between clusters
- Resampling: 10x per prompt

RESULT: Need 327 independent prompts (not 50, not 1000)

Part 3: The Practical Playbook - Your 30-Day AEO Domination Plan

Week 1: Baseline Reality Check

• Run 100-prompt pilot across your top 5 buyer journeys
• Use our calculator to determine full evaluation size
• Identify your current "share of voice" in AI responses
• Document which competitors appear alongside you

Week 2-3: Kyle Roof-Style Variable Testing

• Pick ONE variable (e.g., content depth)
• Create two content variants
• Test across 200+ statistically determined prompts
• Measure lift with proper confidence intervals

Week 4: Scale What Works

• Take your winning variable
• Apply across all content
• Re-test to confirm lift holds
• Calculate ROI: (Additional AI mentions × Conversion rate × LTV)

Part 4: The ROI Calculator - Let's talk money

Lets map out a sample scenario here to give you a sense of the magnitude of the opportunity AEO presents.

Traditional SEO:

• Rank #1 for "project management software"
• 10,000 searches/month
• 30% CTR = 3,000 visitors
• 2% conversion = 60 signups
• $500 LTV = $30,000/month

AEO with Proper Testing:

• 70% mention rate for "project management" queries
• 50,000 AI queries/month (and growing ~27% MoM)
• 15% click-through on AI recommendations
• 4.4x higher conversion (documented AI traffic conversion rates)
• Same $500 LTV = $165,000/month

The difference? $1.62M in annual revenue.

The numbers used here are figures we've seen internally from across our clients.

Your Next Steps (Stop Reading, Start Testing)

1. Today: Run our LLM Eval Calculator to figure out what testing volume you need
2. This Week: Design your first Kyle Roof-style single variable test
3. This Month: Implement full statistical evaluation framework
4. This Quarter: Own your category in AI search

The Bottom Line

Kyle Roof proved you could reverse-engineer Google through scientific testing. The latest AI Interpretability research and Anthropic's work gave us the statistical framework to do the same with LLMs. We've combined both approaches into a systematic methodology that turns AEO from art into science.

The marketers who win the next decade won't be the ones with the biggest budgets or the most content. They'll be the ones who understand that AI optimization is a data science problem, not a content problem.

And now you have the framework. The only question is: Will you use it before your competitors do?

Ready to implement scientific AEO testing?

Use our LLM Eval Calculator

Sources

• Anthropic Research
• LLM Interpretability Research