User:Adamw/CentralNotice

Independent variables
$$v$$ - number of unique visitors to the site, since an arbitrary reference time

$$p$$ - number of pageviews

$$p_v$$ - pageviews coming from "known" visitors

$$p_\bar{v}$$ - pageviews by "new" visitors

$$S$$ - a visitor's view score, their non-normalized chance of seeing a banner.

Dependent variables
$$I$$ - number of banner impressions

$$P_p$$ - probability of seeing a banner, per pageview

$$P_v$$ - probability of seeing a banner, per visitor

Scratch
$$\frac{dv}{dt} = \frac{dp}{dt} \times \frac {p_v}{p_\bar{v}}$$

= Scenarios =

5% of visitors
Limit a test to some percentage of visitors.

We set $$P$$, the probability that any visitor sees a fundraising banner. Each visitor is assigned a score $$S$$, which is sticky until $$P < S$$, a banner is displayed and new $$S$$ is assigned. Verify that $$\lim_{v \to \infty} \frac{I}{v} = P$$, or $$P_v$$, the chosen constant.

1,000 impressions, now
A short burst of traffic is needed to test something quickly.

5% of full rate
Whatever the experiment hide algorithm might be, it is cut by 95%. "Ramp up"

5% of pageviews receive a banner
This might not be a scenario.