Ok, So I'm trying to get percentage estimate of how many impressions are at the top of a search page between the hour. Based on the metrics: $Impressions,\,Previous\,Impressions,\,Top\,Impression\,\%\,\&\,Previous\,Top\,Impressions\,\%$.
For ease we can put these as the following variables:
$x = Total\,Impressions\,(for\,the\,day\,so\,far)$
$y = Previous\,Impressions\,(Total\,Impressions\,for\,the\,day\,an\,hour\,ago)$
$a = Top\,Impression\,\%\,(for\,the\,day\,so\,far)$
$b = Previous\,Top\,Impression\,\%\,(Total\,from\,an\,hour\,ago)$
From this, I want to estimate what percentage of the impressions over the past hour were at the top position. To do this I'm using the following:
$( x(a) - b(y) ) / ( x - y ) = EST.$
So to put this into action if the following is true:
$x = 250$
$y = 213$
$a = 67\%$
$b = 66\%$
Based on the above math that would mean the estimation percentage would be $72\%$.
So the maths reckons from the $37$ new impressions $72\%$ of them were possibly at the top of the page. This seems reasonable but in some cases, it totally breaks down. E.g. if there is less than ten of a difference the estimation becomes wild. Which is to be expected. But I also get issues like in the following case:
$x = 250$
$y = 240$
$a = 70\%$
$b = 66\%$
The estimation would be $166\%$. Which for our estimation purpose cant be true. I could always condition this not to be allowed to go above $100\%$, But I feel there is probably a better way to go about this.
What I wanted to know is, if anyone had any thoughts on what would be a more accurate way to try and get the estimate? If not, is there any particular issues with the current math that might cause more upset like it is useless with a difference less than ten?