Does your resource have a brand?

By «Brand» — hereinafter we will understand the presence of a resource with an accumulated permanent audience. You can rephrase the question:

– Does your resource have a regular (branded) audience?  

Reach in marketing (Reach) — is the proportion (or number) of people from the selected audience who completed the target action
For online we define:
The selected audience is users who visited the resource for the first time (New Users, NU)
Target action (conversion to a brand) – return to the resource after the first day of visiting (New brand, NB)
The question needs to be answered:

– What is the share of New users who visited the resource for 2 or more days?

Obviously, if all NU visit the resource for 2 days or more, then Reach brand =100%

Brand reach: α₀ = NB/NU (1)

α₀ – can also be determined as the conversion rate of new users to brand

The actual answer to the question (see title) lies in estimating the error measuring the share (α). More precisely, we will be interested in the measurement error α over a time interval of 1 day. Next, we will use the well-known random sampling formula for the “share” (not to be confused with the error formula for the “average”). Google to help you.

Let us recall that the sampling method is based on the concepts of general and selective populations.
The set of units from which the selection is made is usually called the general population — these are NB and NU over an unlimited time interval.
A collection of selected units from a population is called a sample population. Let us denote by V₀ and V the daily values of NB and NU, respectively. For daily sampling, we rewrite (1) as:

Brand reach: α = V₀/V   (2)

The values of α₀ (general) and α (selective) may differ by the amount of measurement error: α₀ = α ± ∆

The formula for the measurement error of a simple random sample is:

∆ = t ·   (3)

t is the value of the Laplace integral, which are tabulated and contained in reference books. For example, if when calculating the error we use the value t=2, then with a probability of 0.954 we can say that the true (general) value is in the interval:

α₀ = α ± 2 ·    (4)

From (4) we find the condition when the measurement is equal to the error. Let us substitute α = ∆ into the equality, and write expressions (2) and (3):

V₀/V =2 ·

and after abbreviations we get the condition when the measurement error is equal to the measured value:

V₀ = ≈ 4    (5)    для V >>1

The condition α = ∆ led us to the unexpectedly simple conclusion that the daily number NB: V₀ ≈ 4

Let’s formulate a rule:
The measurement is considered valid if the measurement error is no more than 1/2 of the measured value: ∆ = α/2 then expression (5) will look like:

V₀ = ≈ 16    (6)    для V >>1

Mnemonic rule:
– Your resource has a Brand (α) if the daily number is new brand: V0 ≥16  

Typically, the values of α are in the interval [5%÷10%], then using formulas (2) and (6) we find that the min number of daily allowances for new users is in the interval [320 ÷ 160], respectively.

Example of traffic from V₀ =16:
Every day a resource with NU = 200 generates NB=16. Brand reach, α =16/200=8%
During the lifetime T₁ = 90 days, the user visits the resource with a frequency of ω = 10 days.

1. Brand reach, α = V₀ · T1 = 16 90 = 1440 accumulated brand audience
2. Day: Brand users = V₀ · ω = 16·10=160
3. Total traffic= 200 New + 160 Brand = 360
4. Visiting period: T₂ = T₁/ω = 90/10= 9дн

Let’s imagine that we magically managed to achieve daily visits to the site: T₂ =1. Then the retention rate on the resource is ω = T₁/ T₂ =90 days.
In this case, the brand’s daily traffic will be:

Brand users = V₀ · ω = 16 · 90=1440 (!)

Thus, the entire audience accumulated by the brand will visit the site daily. This will be the maximum possible brand traffic for the conditions: V₀ =16, T₁ = 90 days, T₂ =1

The article will primarily be useful to owners of small websites. It is important to understand that even a small daily traffic of new users ~160 can form a significant permanent audience on your resource.

The Brancounter service, if condition (6) is met, will show web analytics of your brand.