Calculating Stacked Bid Multipliers in Enhanced Campaigns

By Tinuiti Team

Sep 18 2015

Have you ever encountered the following scenario?

You create a new campaign in January with a mobile bid multiplier of 0% and let it run for a few months. In April, you do a mobile bid analysis and realize that you need to set your mobile bid multiplier to -75%. You do just that.

A few months later, it’s time for another mobile bid analysis. Now, in July, you pull a report from April (when you implemented the first mobile bid multiplier) through June and realize that you need to adjust your mobile bids +100%.

What do you do now?

You can’t set the mobile bid multiplier to +100%; that would disregard the fact that the data you looked at was based on an existing multiplier of -75%. You need to figure out a “stacked” mobile bid multiplier to implement. A “stacked” multiplier is a combination of the existing bid multiplier that was already in place and the new bid multiplier that will be stacked on top of it.

How do you figure out the stacked multiplier to implement?

You can use the following formula:

Stacked multiplier = (current multiplier * new multiplier) + current multiplier + new multiplier

For example:
Current multiplier: -75%
New multiplier: +100%
Stacked multiplier = (-75% * 100%) + -75% + 100%
Stacked multiplier = -50%

This also works for Geo, Time of Day/Day of Week, RLSA, Demographic, and Household Income bid multipliers. As time goes on, you can continue to use the above formula to stack new multipliers on top of the existing multiplier, as frequently as you wish, ad infinitum.

You can download this template to easily calculate your stacked multipliers in bulk. Simply input your data into columns A-D and column E will calculate the stacked multiplier to apply in the engine.

Before you use the above formula, you need to determine an initial bid multiplier to implement – and the new multipliers to stack on top of that as time goes on. To calculate this, I like to use the simple formula Google provides in the following article: http://adwords.blogspot.com/2013/05/bidding-best-practices-part-3.html

As we are now officially in the “Year of Mobile”, it is more important than ever that you regularly optimize your mobile bid adjustments to get the most efficient return on ad spend.

How did I arrive at this formula?

You don’t need to understand how the above formula works in order to use it successfully, so if you hate math, you can stop reading here. However, for all you math nerds out there who want to take a trip back to 7th grade algebra, keep reading.

Take the following scenario:
You have a beginning bid (BB) of $1.00 and a current multiplier (CM) of -75%. You would use the below formula to calculate your current bid (CB) of $0.25:

CB = BB * (CM + 1)
CB = $1.00 * (-75% + 1)
CB = $1.00 * .25
CB = $0.25

Now, you want to apply a new multiplier (NM) of +100% to your current $0.25 bid. You would use the below formula to calculate your new bid (NB) of $0.50:

NB = CB * (NM + 1)
NB = $0.25 * (100% +1)
NB = $0.25 * 2
NB = $0.50

Ultimately in the above scenario we are going from a beginning bid of $1.00 to a new bid of $0.50, which required a stacked multiplier (SM) of -50%. You can use the below formula to calculate your stacked multiplier:

NB = BB * (SM + 1)

Isolate the variable SM:

SM + 1 = NB/BB
SM = NB/BB – 1

Input your NB and BB to solve for SM:

SM = $0.50/$1.00 – 1
SM = 50% – 1
SM = -50%

Now we have three formulas which use the variables Beginning Bid, Current Multiplier, Current Bid, New Multiplier, New Bid, and Stacked Multiplier.

CB = BB * (CM + 1)
NB = CB * (NM + 1)
SM = NB/BB – 1

But the variables BB, CB, and NB are going to differ for every keyword/device/time/day/geo in your account. We need to combine these three formulas and cancel out the variables BB, CB, and NB in order to find a universal formula for calculating stacked multipliers based on the current multiplier and new multiplier. First, insert the NB formula into the SM formula:

SM = [CB * (NM + 1)]/BB – 1

Then insert the CB formula:

SM = {[BB * (CM + 1)] * (NM + 1)}/BB – 1

Simplify:

SM = {[(BB * CM) + BB] * (NM + 1)]}/BB – 1

Use the FOIL method to multiply the two binomials in the numerator:

SM = [(BB * CM * NM) + (BB * CM) + (BB * NM) + BB]/BB – 1

Isolate the common factor in the numerator:

SM = {BB * [(CM * NM) + CM + NM + 1]}/BB – 1

Simplify:

SM = {BB * [(CM * NM) + CM + NM + 1]}/BB – 1
SM = (CM * NM) + CM + NM + 1 – 1
SM = (CM * NM) + CM + NM

There you have it!
Stacked multiplier = (current multiplier * new multiplier) + current multiplier + new multiplier