# AdWords Enhanced Campaigns: The Math Behind the Multipliers

With the advent of the new Google AdWords Enhanced campaigns, an age-old question has been thrust prominently into the spotlight: exactly how does a percentage multiplier work?

For those who think that this is a pretty basic calculation, the Paid Search teams have noticed an awful lot of confusion on the blogosphere and social media networks with plenty making incorrect calculations.

One widely read blog had a lively discussion on the new percentage multipliers. Simulating a bidding scenario, they hypothesised a bid set at $0.01 then calculated the maximum bid they can reach with the top mobile percentage multiplier of 300% applied. Their resulting bid of $3.00 is incorrect and it's worth quickly recapping how this particular calculation should have been made.

*The Math*

300% does not mean the number 300, but 300/100: in this way a percentage can be viewed like a fraction with a denominator of 100, and so 300% actually means 3. You might think that this means that the top bid available from an initial $0.01 would be $0.03, but this is also wrong. The reason why this is that the percentage multiplier denotes how much you want to increase or decrease your bid on top of your initial bid: your final bid will equal to the initial bid plus the multiplied figure.

Final = Initial + (Initial * Percentage)

Or

Final = Initial + (Initial * (Percentage number/100))

Going back to the example, the final bid from applying a percentage multiplier of 300% onto a $0.01 bid is $0.04. To get their figure of $3.00 you would have to multiply the actual bid of $0.04 by 75. We can work out the percentage multiplier from this using the formula above: (300 = 4 + (4 * ( ?/100 )). You would need a percentage multiplier of 7400%.

The fact that the percentage multiplier applied to the initial bid indicates the increase or decrease on the initial bid is confirmed by the fact that you can have negative multiplier of up to 100%. If this final bid was the result of a straight multiplication, a -100% multiplier on a $1 bid would give a final bid of -$1, which doesn't make sense. In reality, the multiplication gives you the decrease, explaining why the final bid would be zero.

*Examples*

Imagine that you are setting up a new enhanced campaign which rolls Mobile, Desktop and Tablet into one: you have worked out that to achieve a good ROI on Mobile your maximum bids should be 15% less on this device. Let's say your highest traffic keywords in this campaign have a usual maximum bid of $2, whilst the longer tail terms have a bid of $3. If you use a percentage multiplier of -15%, we can work out the maximum bid for the first set of terms:

Final Bid = 2 + (2 * (-15/100))

Working out the part of the formula in brackets first, we get negative 0.3. When adding this negative number to the initial bid of $2, you are in effect subtracting 30 cents, giving you a final bid of $1.70. With the second set of terms you will be subtracting a greater number, since 15% of 3 is larger than 15% of 2:

Final Bid = 3 + (3 * (-15/100))

Again by calculating the second part of the formula first, we can see that this will decrease our initial bid by 45 cents, giving a final bid of $2.55.

*Summary*

To conclude, if you set a multiplier of +57% on a $1 bid, you'll be relieved to know it won't give you a final bid of $57, but $1.57 instead.

If you were already well acquainted with the math behind the new AdWords Enhanced Campaign multipliers, give yourself a firm pat on the back, and if not, we hope we've helped clear up any confusion.