# Application of Bayesian Averaging for Ranking

I have a sample with two metrics and one ratio per attribute. I am trying to rank the attributes based on the ratio and variable amounts and from my research I have found that most people find Bayesian Averaging as the best formula to create a ranking system. I'm trying to apply this methodology using this practice and an example from this question, but I'm getting tripped up on where the inputs should go in the answer provided.

Here are my variables/ratio:

• Subscriptions

Here is example data:

Facebook: 20 | 10 | .5

TV: 4000 | 2000 | .5

LinkedIn: 2000 | 900 | .45

My assumption here is that "TV" is the strongest driver of conversion followed by "LinkedIn" due to the larger variable sizes creating a stronger indicator of performance than "Facebook" which might convert higher, but the variable size is small.

From the answer in the linked question, I'm a bit confused as to the inputs being used in the formula provided and how I can translate my metrics into the equation. Should "P" = Lead to Subscription %, with an unknown "nr" and "n" = Leads ?

It is also advised to add a dummy value to each calculation to have a larger impact on the smaller variable sizes and almost none on the larger. Does this approach sound correct?

You can simply calculate conversion (i.e. LtS),

$$C = {n_l \over n_s}.$$

In "Bayesian averaging" you need a correction for total number of leads, adding "dummy" leads (e.g. $200$), so

$$C' = {n_l \over n_s + 200 }.$$

Attributes with a large number of leads see their modified conversion alter very little from their real one, while attributes with relatively few leads will see their modified conversion move considerably toward low values.

In effect, the attributes with many leads will rank higher than attributes with the same LtS but fewer leads.

My assumption here is that "TV" is the strongest driver of conversion followed by "LinkedIn" due to the larger variable sizes creating a stronger indicator of performance than "Facebook" which might convert higher, but the variable size is small.

• $C_1 = 0.05$
• $C_2 = 0.48$
• $C_3 = 0.41$