There is nothing like bidding to fix performance, or ruin it, in an instant. Today we’re going to look at bidding basics and build up to some of the more nuanced aspects.

To demonstrate bidding practically we will consider two keywords: Keyword 1 and Keyword 2.  The stats presented about these keywords comes from bid simulator data from a real account.  Bid simulators are provided by Google and other search engines to show how clicks and conversions would vary across different CPCs.

You can see the key data for yourself at the end of this article.  Below is a chart showing one aspect of the data: how clicks vary by average CPC:

As you would expect, clicks increase as bids increase.   In this analysis we’re only considering average CPC even though advertisers usually set a maximum CPC. There can be a considerable difference between the two but exploring that topic is for another article.

## The goal of bidding

You can’t get very far with bidding optimization until you have a clearly defined goal.  It is surprising to me how many companies can’t define their search marketing goals. Or they are defined in a way that is contradictory or very difficult for marketing teams to link to their bidding.  I have two preferred goals that are well defined and many businesses use them.  Choosing between them tends to come down to whether businesses see themselves primarily as acquiring customers or acquiring sales of goods / services:

• Customer Centric Goal:
• Maximize customers for a given cost per customer acquisition (CPA) or cost per lead (CPL)
• Sales Centric Goal:
• Maximize sales for a given return on investment (ROI) or return on ad spend (ROAS)

One reason the goals as expressed above are good is that they readily resolve to a simple formula that determines the right cost per click (CPC).

## Bidding formulas

These formulas are some of the most important in search marketing:

CPC = Conversion Rate * CPA_{target} \thickspace (CPA\enspace Goal)

E.g. If I have a conversion rate of 2% and a CPA goal of $50 then I will need to pay 0.02 * 50 =$1.00 for each click.

CPC = \frac{ConversionRate * Margin_{per sale}}{ROI_{target}} \thickspace (ROI\enspace Goal)

E.g. If I have a conversion rate of 2%, make $50 per sale and wish to earn$2 for every $1 spent (an ROI of 2) then my CPC is: 0.02 * 50 / 2 =$0.50

In these formulas CPL can be exchanged for CPA if you have a CPL goal, and ROAS can be exchanged for ROI if you have a ROAS goal.

## Achieving the bidding goal

For the following examples we’re going to define our goal as:

Maximize conversions for an overall CPA less than $50 Now I have all I need. I have my formulas, my keywords and a goal – let’s dive in! ### Single keyword account Let’s assume we only have one keyword in our account – Keyword 1. This keyword has a conversion rate of 1.33%. If I have a CPA target of$50 then I can calculate my average CPC:

CPC = ConversionRate * CPA_{target} = 1.33\% * \$50 = \$0.665 = \$0.66 \enspace (rounded \enspace down) For this bid I will achieve 77,179 clicks and make 1,029 conversions. If I raise my bid higher I will make more bookings, but exceed my CPA goal, and if I lower my bid I will not be maximizing the conversions available to me. If instead, this account had only Keyword 2, which has a conversion rate of 1.03% then I can calculate my average CPC: CPC = ConversionRate * CPA_{target} = 1.03\% * \$50 = \$0.515 = \$0.51 \enspace (rounded\enspace down)

This then equates to 55,372 clicks and 571 conversions for Keyword 2

So far so good, If I had only Keyword 1 in my account the correct bid to achieve my goal is $0.66 and if I had only Keyword 2 in my account the correct bid to achieve my goal is$0.51.

Let’s now assume both Keyword 1 and Keyword 2 are in the same account with the same goal. Here are our two keywords summarized from before. We make 1,600 conversions in total and our CPA is still below $50 as required:: ### The two keyword paradox Can the above be improved upon? On first sight it wouldn’t appear so. But if we bid down on Keyword 1 by$0.01 and bid up on Keyword 2 by $0.02 this happens: We have made 5 more conversions and our CPA is still within target! There is no sleight of hand here, but before we explain this behaviour let’s review all 4 of the common methods people use to solve the two keyword problem. ### Bidding method 1: Subsidize the big keywords with the cheap long tail The thinking here is that my big keywords are so important for driving high conversion volume that I can’t bid down. Instead I’ll subsidize those high CPA keywords with lower CPA keywords elsewhere in the account. This is how it works out: My CPA is still on target, but I have made nearly 200 less bookings than before. Now sometimes there are branding considerations or attribution considerations that may justify this tactic, but there is no mathematical sense in it. It is a poor technique! ### Bidding method 2: Bid based on overall performance Why don’t I keep the same formula as before but just work on the basis of combined performance. I will use my average conversion rate, and bid the same on both keywords. Here is what we get: A 4 booking drop from our initial total may not seem much, but it’s still not optimal! Setting bids based on average performance across multiple keywords is not the right technique. It’s one of the reasons we go to the effort of building all those keywords in the first place. ### Bidding method 3: Bid each keyword to the CPA target The third method is the one we started with. We assume that we will maximize conversions for a given CPA when each keyword individually is performing at that CPA target. This method is not bad and it is how most bidding algorithms work, but as we’ve already seen it is not optimal. ### Bidding Method 4: Bid based on marginal performance Finally we come to the best answer – to bid based on marginal performance! But what is marginal performance? Marginal performance is the performance (clicks, costs, bookings etc.) of the next click. So if I’m already buying 1000 clicks, what is the extra cost or extra bookings that I get by acquiring that 1 extra click (ie. a total of 1001 clicks)? Look at the illustration below (where I use fractional conversions to help make the math work better) On an average basis there is almost no difference in performance. My average CPC has gone up from$1.000 to $1.001 (we have to use 3 decimal places to see the change!). The average CPA has also gone up by a barely perceptible$0.01.  But how much did that one extra click actually cost us.  That one extra click was actually expensive – it cost us $2.00 which is twice the average. It made us 0.1 extra conversions which gives us a marginal CPA of$20 which is also twice our average.

Let’s assume that I earn 12 from each customer. I may see my average performance and think I’m making a healthy 20% profit margin. But what about that last click I bought? I’m losing money on that click! So do I want to buy that 1001st click? Not if I’m trying to maximize my profits. But would I have been able to make that decision if I only had the average performance to hand? In reality bid simulator data doesn’t give you the price of each marginal click but we can work out marginal performance for each increase in CPC. The table at the end of the article shows the full workings. Let’s look again at the original bids we calculated, and the better ones, but this time we will include the marginal performance: In our first method the average CPAs were the same, but marginal CPAs were a bit different. In our improved version we have aligned the marginal CPAs (at132 each).  Now despite Keyword 2 having an average CPA over target, in total we are within our CPA target and we have made more bookings!

Here is another way to think of marginal bidding:

The answer to this is difficult.  In most cases algorithms will iterate to the answer.  They will try, say, a marginal CPA of $120 and realise the average CPA is too low, so raise it a bit and see what they get then. #### Why does marginal CPA look so high and unprofitable? In most cases the last click you buy really is very expensive and very unprofitable! Notice that while Google’s bid simulator product does give you numbers to calculate your marginal CPA, it doesn’t actually show it to customers directly! In many cases search marketers are bidding inefficiently and reviewing marginal performance will have a big improvement in profitability! #### What is better: an average CPA goal or a marginal CPA goal? Marginal CPA is a very important metric, but it is hard to measure and quite hard to understand across a business. So for practical reasons an average CPA is better. However, the setting of the CPA goal should be informed by the marginal CPA. If in our account I make$100 per customer I can conclude that paying a marginal CPA of $132 is too high. Even though on average I’m making good money, I am buying quite a few unprofitable clicks. So maybe an average CPA target of$40 would make more business sense.

In conclusion then our goal, for practical purposes, is best set based on an average CPA, but for bidding optimisation purposes we should work on a marginal CPA basis to achieve our goal of maximizing conversions.  Periodically we should review the marginal CPA targets that our bidding algorithms are using to check that our average CPA goal is a good one.

## Conclusion

You don’t need a PhD in statistics to be a great digital marketer but a basic understanding of bidding is crucial. If you can ensure your company has a well defined marketing goal, and then ask critical questions about how that goal is being achieved you will be well on your way to delivering maximum performance.