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Click Volume Versus Click Profitability In Pay-Per-Click Bidding

watermelontruck Two brothers drove out to the farm and filled their truck with 200 watermelons for $200.

They drove to the city market, where they sold their melons at $1 apiece.

At day’s end, after selling out, they counted up their cash, and realized they ended up with no more money than they’d started with.

“See!” said the first brother. “I told you we should of rented the bigger truck!”

Question: Can you bid more than your target efficiency and make it up in volume?

Answer: Typically, no.

This question comes up periodically from our clients. Here’s the situation.

Suppose a client has an important keyword (“widget”) with considerable traffic. Our bidding system is highly flexible and can optimize different metrics, but most of our clients wisely instruct us to bid to a target economic efficiency, often expressed as an A/S ratio. Let’s say this advertiser wants a 25% A/S target, and “widget” has a sales-per-click of $2.00 on Google.

(Rambling digression: determining sales-per-click — or margin per click, or conversion, or whatever the relevant success metric — is the true secret sauce of paid search bidding. SPC varies by phrase, by engine, by season, by matchtype, by day of week, by time of day. The big trick is getting SPC right in the long tail, where the data are thin. More on best practices for PPC bidding here.)

With a $2.00 SPC, we can bid at most 50c on “widget” to hit a 25% A/S target, and this places our client in (let’s say) the fourth position, on average.

“But”, you might protest, “you don’t deposit percentages in bank. Might it be the case that bidding higher, perhaps 75c, would increase click quantity so much that the lower profit-per-click is made up in volume?”

Theoretically, yes. Practically, usually not.

Forgive me some basic algebra.

Here’s the formula for the current marketing contribution on “widget”:

eqn1

where P1 is daily profit dollars, N1 is daily clicks, S is sales per click, c is the COGS fraction, v is variable marketing cost fraction (pick-pack-ship, credit card discount, warehouse labor, etc), and B1 is the average cost-per-click; all for “widget”.

Assuming “widget” isn’t at the top of the page, when would increasing the bid generate more profit dollars?

Here’s the formula for profit dollars at our higher bid, B2:

eqn2

Nobody would suggest that the COGS and variable cost fractions vary with bid. Some might argue sales-per-click does vary with position and thus does vary with bid. To a reasonable first-order approximation, however, it doesn’t. SPC is largely position-invariant. Here, we’ll treat it as completely so.

Let’s represent B2 as the original bid B1 plus an increase, representing the bump by delta, like so

eqn3

and let’s use rho to represent current marketing contribution per click (MCPC)

eqn6

OK. When does bumping the bid by delta cents increase click volume enough to generate more total profit dollars? In algebra,

eqn4

requires

eqn5

Equivalently

eqn7

or

eqn8

That last equation nails it on the head, so no more algebra. (Whew.) In English, it says, “to generate more total profit dollars by moving higher on the page, clicks have to rise faster than per-click profit falls.”

I began this blog post arguing that for an advertiser bidding by economics, increasing bids further and “making it up in volume” frequently isn’t possible. Here’s why.

Many advertisers are already pushing the gas so hard with bids that their marketing contribution per click is quite small. Raising the bid by a few pennies translates into a huge percentage decrease in MCPC. And those few pennies aren’t enough to outbid the advertiser in the position above. Or, the position above doesn’t provide a sufficiently high percentage increase in clicks. Or both.

Going back to the “widget” example, let’s continue with S=$2.00, B1=$0.50, COGS c=50%, variable costs of v=10%, and average position=4.

With these values, rho = 2(1-0.5-0.1)-0.5 = 0.30.

That is, MCPC is 30 cents before we bump the bid.

Let’s suppose that bumping the bid by 25c, from 50c up to 75c, would move our ad up a full position, from an average 4 to an average position 3.

The 25c bid increase drops MCPC by 25c, from 30c to 5c. In percentage terms, bidding up a quarter drops MCPC by 83%.

To make this up in volume, position 3 would need to have six times the click volume as position 4. Six times! No way.

The impact of position on click volume varies greatly by term. Let’s take the average Google click potential curve as reported by Atlas (Microsoft):

atlas-click-volume

Their curve isn’t accurate, but it is good enough to illustrate the point. Divide the click potential in each position by click potential of the position above it.

atlas-click-volume-change

From this average curve, we see the greatest increase in click volume comes from moving from position 2 up to position 1. For first page ranks, in no case does moving up one average position double the click volume — it is always far less.

Our own data supports this conclusion. Moving up on page one by one position does increase traffic, but never by many 100s of percent.

Yet, for ads with low marketing contribution per click, the typical bid increase required to jump up a position crushes MCPC so substantially that the position above would need to provide many 100s of percent more click volume to make it up in volume. Getting the bigger watermelon truck doesn’t help.

Of course, models can only go so far. The only way to be absolutely certain of the elasticity of the profit dollars versus ad rank curve is to test it.

We’ve often conducted these tests for clients. The typical result? Much more ad cost. A bit more sales. And much less profit, both in percentage and in absolute dollar terms.

(Aside: Google loves these “stomp-on-the-gas” tests. Not only does one advertiser pay more, often additional advertisers who rely on position crawler bidders scramble up the deformed bid landscape as well. CPCs soar, sales stay flat. Bad for the advertisers, great for Google shareholders. See George Michie’s post, Why Position Bidding Wastes Money.)

To wrap up, we’ll repeat our bidding advice for generating maximum profit. It sounds deceptively simple, but it works.

  1. Determine what fraction of sales you can invest in advertising. This is your target A/S ratio.
  2. At the most granular level, calculate what each ad produces in sales-per-click.
  3. Multiply these two numbers. That’s your economically-based rational bid.
  4. Adjust for other factors as needed.

And a final tip: you can often produce even more profit by swapping the word “margin” for the word “sales” in that recipe.

  • Alan Rimm-Kaufman
    Alan Rimm-Kaufman founded the Rimm-Kaufman Group...
  • Comments
    19 Responses to “Click Volume Versus Click Profitability In Pay-Per-Click Bidding”
    1. Jim Novo says:

      Well done, Alan.

      Now, how do we get people to actually care about profits?

      Sounds silly I know, but most marketers outside of pure DM folks are managed to sales and not profits.

      Any ideas on how we get alignment on this?

      To me, that’s the largest challenge we have left – cultural.

      Obviously you have as clients companies who have the cultural stamina to forgo sales for profits. Did you have to convince them to do this, or did they already “get it”?

    2. Thanks, Jim. Praise from you means alot. Yes, most of our clients have a bottom-line focus. We’re flexible in our approach and in our systems and we’re a service organization, so we’ll steer the ship where the client wants the ship to go. But we’re not shy about offering advice when we think a client is choosing strategies which reduce profit. It comes down to a fit issue — we’re a good fit for some clients and less so for others. We try very hard to present our approach and strengths and weaknesses during the sales process, to ensure the greatest chance of a good match. “Cultural stamina” is right — the discipline required by DM perspective is sometimes tough.

    3. Hey Jim,

      Just to pick up on Alan’s note: there is definitely a “selection bias.” Our blog, our conference talks, our marketing materials all focus on the quantitative, complicated side of the business. Those messages resonate most with retailers who think like us. Retailers looking for the “shiniest package” and the slickest sales pitch don’t really get our value prop.

      I do think that in 2009, more companies will be forced to focus on the bottom line, and we hope they’ll give us a call :-)

      George

    4. Josh says:

      Alan – great analysis… puts some great math against something that a lot of PPC marketers have acquired an intuitive feel for over the years.

    5. Robert says:

      Alan

      Great article that really shows the objectivity that is needed to effectively manage PPC. At the end of the day it is all about profits.

      This is my first time on your blog so pardon me if I ask a question you have already addressed. How would you factor in life time value of a customer into your above equations. Some customers may have a very high LTV as compared to others. Is that factored into the “sales” part of your equation when you are calculating the % of sales factor?

    6. @Robert: Thanks for the comment, great question!

      Many advertisers simply don’t factor in LTV, or they do so implicitly via their A/S target.

      When you say “some customers may have a very high LTV”, are you speaking from on online longitudinal data — say, at least 12 months of sales data from each cohort by segment — or are you speaking from extrapolation/analogy from direct mail/DRTV/catalog?

      LTV is powerful when used correctly, but can also be misused as an excuse to overspend on marginal advertising.

    7. Hi Robert,

      Some folks take the view that their average online buyer makes an additional 0.3 orders over the next 12 months (or whatever the number is) and is willing to invest that much in acquiring customers. They fold that into the A/S target essentially the same way people factor in offline sales and cookie breakage. If I’m comfortable spending 25% of the total sales generated factoring in cookie breakage, LTV and channel spillover then every $100 in observed sales is really $100 + LTV + breakage + spillover, and I should set my observed target to 25% of that total.

      All that said, many of our long time clients have seen LTV erosion and aren’t comfortable factoring in LTV calculations that may not hold up over the next 12 months.

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