Example Scenario: BrandX & "Best Smartphones" Tag

Let's assume we are tracking "BrandX" for the tag "Best Smartphones" across 4 queries, with 2 AI models (ChatGPT + Perplexity) running for each query. The results are:

  • Query: "top smartphones 2024"
    • BrandX found at positions 2, 7 (best: 2)
    • BrandX found at positions 4, 9 (best: 4)
  • Query: "best android phone"
    • BrandX found at positions 5 (best: 5)
    • BrandX found at positions 3 (best: 3), domain found in position 5
  • Query: "iphone vs samsung"
    • BrandX Not Found
    • BrandX domain found in 6
  • Query: "latest google pixel review"
    • BrandX Not Found
    • BrandX Not Found

Total Queries: 4, Total Responses: 8

Responses with BrandX: 4, Queries with BrandX: 2

Key Distinction: Responses vs Queries

Most metrics (Score, Position, Total Mentions, etc.) are based on RESPONSES:

  • Each AI model's response to a query counts separately
  • 1 query × 2 models = 2 responses
  • If BrandX appears multiple times in a response, only the best (lowest) position is used for Score, Position, etc.

Example: If you track 1 query across 2 models (ChatGPT + Perplexity), and your brand appears in both responses, then Distinct Mentions (Responses) = 2, but Distinct Mentions (Queries) = 1.

Only "Distinct Queries" metrics (see below) count unique queries: 1 query × 2 models = 1 distinct query

Score (0-100)

The Score metric converts the raw position of your brand (and competitors) in search results into a normalized value from 0 to 100. Higher scores are better.

How it's calculated:

Let N be the total number of responses, Pi be the position in response i (1 to M), and M be the max position considered (e.g., 30).

1. Calculate a Normalized Value (NVi) for each response based on its position Pi:

  • If Pi = 1, then NVi = 1.
  • If Pi >= M or the brand is not found, then NVi = 0.
  • Otherwise (1 < Pi < M), NVi = 1 - (Pi - 1) / (M - 1).

2. Sum the Normalized Values (NVi) for all N responses.

3. Divide the Sum by the total number of responses (N) to get the average normalized value.

4. Multiply the average by 100 to get the final Score.

Example: BrandX Score

Calculate NV for each response (assuming M=30):

  • Query 1, ChatGPT (Position=2): NV = 1 - ((2 - 1) / (30 - 1)) = 0.97
  • Query 1, Perplexity (Position=4): NV = 1 - ((4 - 1) / (30 - 1)) = 0.90
  • Query 2, ChatGPT (Position=5): NV = 1 - ((5 - 1) / (30 - 1)) = 0.86
  • Query 2, Perplexity (Position=3, Domain=5, Best=3): NV = 1 - ((3 - 1) / (30 - 1)) = 0.93
  • Query 3, ChatGPT (Not Found): NV = 0.00
  • Query 3, Perplexity (Domain=6): NV = 1 - ((6 - 1) / (30 - 1)) = 0.83
  • Query 4, ChatGPT (Not Found): NV = 0.00
  • Query 4, Perplexity (Not Found): NV = 0.00

Sum of NV = 0.97 + 0.90 + 0.86 + 0.93 + 0 + 0.83 + 0 + 0 = 4.48

Average NV = Sum / Total Responses = 4.48 / 8 = 0.560

Final Score = Average NV * 100 = 0.560 * 100 = 56.0

(Formula)

Score = ( (1/N) * Sum(NVi) ) * 100

(Where NVi is defined as)

NVi = 1 - (Pi - 1) / (M - 1)  (if 1 <= Pi < M), else 0

Why use Score?

It provides a consistent way to compare performance even when the raw position numbers might fluctuate. A higher score reliably indicates better visibility relative to the top position, considering both position when found and frequency of being found.

Visibility (0-100%)

The Visibility metric represents the percentage of AI model responses where your brand (or a competitor) was mentioned. Higher percentages are better.

How it's calculated:

Count all AI model responses where your brand was mentioned, then divide by the total number of responses across all queries and models.
Note: we count the responses, not the mentions (distinct mentions). 

Visibility = ( Distinct Mentions (Responses) / Total responses ) * 100%

Example: BrandX Visibility

From our scenario: BrandX appears in 5 responses out of 8 total responses.

Visibility = ( 5 / 8 ) * 100% = 63%

Position (1-30)

The Position metric shows the average ranking position of your brand (or a competitor) across responses where it was mentioned. Lower numbers are better (Position 1 is the highest).

How it's calculated:

Let Pi be the position in response i where the brand was mentioned, and let Ii be 1 if mentioned, 0 otherwise. MentionCount = Sum(Ii).

The formula is:

Position = ( Sum of Pi for all responses where mentioned ) / MentionCount

(Formula)

Position = Sum(Pi * Ii) / Sum(Ii)

If MentionCount is 0 (Sum(Ii) = 0), the position is N/A.

Example: BrandX Position

From our scenario: BrandX appears at best positions 2, 4, 5, 3, and 6 across all responses.

Sum of Best Positions = 2 + 4 + 5 + 3 + 6 = 20

Number of Responses with Mentions = 5

Average Position = 20 / 5 = 4.0