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Rounding the CPA Horn

Like the great navies of historic Europe, every manager of a PPC account has the same basic goals: Glory, Profit, Praise and Power.  More conversions.  Lower CPA.  More high-quality clicks at lower cost.  But to reach these goals you need a map.  And one of the best I know, relative to the amount of work involved, is also one of the simplest.

If you think a bit about how cost-per-acquisition (CPA), the amount of money spent on advertising for each new customer obtained, changes with spending (or, barring that, if you just grab some data by week of ‘CPA vs. spending’ for any large account), you’ll find that the relationship, seen in stylized form in Figure 1, often has a shape I call The CPA Horn.  For any given set of keywords, there must be some maximum possible amount of average weekly spending (if all the words in the account were pushed to position 1) and some (typically, intolerably high) CPA associated with that spending level.  For spending levels near this maximum, CPA tends to rise as the spending rises for the simple reason that the ‘low-hanging fruit’ of customers have already been obtained at lower spending levels.  At very low spending levels, the CPA observed can be all over the map, being very high some weeks, very low some other weeks and averaging higher, lower or about the same as at higher spending levels.


This relationship is easy to explain once you see it before your eyes: As the spending level in an account grows towards its maximum, the account becomes market-limited; that is, there are only so many additional customers available and to win their attention and their business simply means tolerating a higher marginal CPA than the next competitor.  The effect can feel like sailing into the midst of a Napoleonic naval battle: getting more aggressive with low-volume words while pushing high-volume keywords up by fractions of a position can result in CPCs on core terms skyrocketing and formerly well-performing terms hemorrhaging money until they can be reigned back in to safer positions.

At a very low spending level, the pain an advertiser feels is just as real, but often of a different nature.  In this case, the online marketer must make account management decisions in a data-limited environment, facing a fog of uncertainty.  Thus, it can be very difficult to bid well, to know when to pause or delete keywords, and how to identify with confidence clear winners among variants of ad text or landing pages.  Because the number of conversions is limited, the CPA can vary wildly from day-to-day and even week-to-week and it can be difficult to gain and maintain forward momentum.

The waters where the sailing is the smoothest lies between these two extremes, where the account is limited neither by the availability of new customers at any given price nor by the uncertainty imposed by the available data at any given spending level.

For three large-volume accounts I took the weekly spending level and weekly CPA for the entire time I’ve had access to them, as seen in Figure 2.  (For these examples, I’ve thrown out the first few weeks of start-up data for each account and also jettisoned weeks corresponding to major holidays.)  For account A we can see the full CPA Horn for weekly data spanning 2 years on Google, MSN and Yahoo, for all keywords and all matchtypes, on both the search and content networks, for an account that spends a couple hundred thousand dollars per week.   The effect of limited data at low weekly spending levels is clear, as is the uptick in CPA in the market-limited region at higher spending levels.  (A contrasting dot marks the most-recent week in the data set, showing where the account is currently located.  To make them easier to see, these points are also circled.)


Commonly, we see only a portion of the CPA Horn, since few accounts vary their spending levels sufficiently and for long enough periods to see the entire structure.

Account B is that of a nationally known online retailer that does not hold the largest market share in its highly competitive space.  In this case, the influence of market limitations on CPA during the 14 months’ worth of data available is clear.  The three highest-CPA points all occurred in May and June 2009, as this account ramped up spending in an attempt to take market share from competitors, while other high-spending weeks in the upper right-hand portion of the graph occurred the previous July and August.  The lowest-spending and lowest-CPA points all happened during the heart of the economic crisis in late 2008 and early 2009.  As the account has retreated from its higher spending levels in May and June, we see a sort of hysteresis, in that the CPA has not returned to its formerly low levels.

Account C is a business-to-business service provider that struggled to hit CPA targets at one spending level, but saw its CPA’s drop with about a 50% increase in spend as they exited the data-limited region.

(All three of these accounts are sizable, the smallest having a peak spend of about $50,000 per week.)

Obviously, the CPA Horn pattern applies at the campaign level as well as the account level.  In Figure 3 below we see three campaigns from Account A, the largest of which had a peak spending level of about $35,000 per week and the smallest about 1/10th of that.  The top graph is the campaign dedicated to the account’s brand-related terms.  In this case, the x-axis is about 1/32 the scale of the account-level graph in Figure 1 and the y-axis roughly 1/16 the scale.  Yet, the CPA Horn relationship can clearly be seen again.  The second campaign exhibits variability in CPA for low spending levels, stabilizing at higher spending levels as the campaign exits the data-limited region.  The third campaign enters the market-limited region as spending increases.


To perform this analysis, one should ideally have several months of spend and conversion data.  Since few accounts (and even fewer campaigns) see the range of spending levels necessary to see the entire CPA Horn relationship, it is helpful to remember characteristics of each region to be able to identify what you see.

If it is possible to perform a portfolio analysis, using keyword-level ‘clicks vs. position’ and ‘CPC vs. position’ relationships to estimate the maximum combined spending level possible for all of the keywords in an account, then the spending level and CPA at which the tip of the horn occurs can be estimated.  These values are useful for proper scaling of the maximum points on the x- and y-axes of your graph.  (For example, for Account C, the maximum spending level possible is estimated to be about 10% higher than the highest spending level actually seen, and the end of the x-axis is set about 10% higher than that.)

However, you can also begin by plotting the weekly CPA vs. weekly spending levels.  The defining characteristic of the market-limited region is that the CPA tends to slope upwards as spending increases; that is, the points tend to be scattered along a southwest-to-northeast axis.  In the data-limited region, the points are often wildly scattered in a vertical manner, ranging from (in my personal experience) 1/4 to 4 times the account’s target CPA.  The region between the data-limited and market-limited ones can be very narrow or very wide, but either way is characterized by a generally horizontal relationship between CPA and spend.  The ratio of the highest CPAs to the lowest in this region is about 2.  Unfortunately, there are no generally applicable cut-off points that separate one region from the next in terms of spending volume since the end of the data-limited region is determined by the number of clicks per keyword in the account (not the number of dollars spent) and the beginning of the market-limited region varies by the size of the market.

In any case, it is helpful to mark the most recent week(s) to see where along the CPA Horn your account currently lies and in which direction you need to move.  It can take some practice to learn to read these charts, especially for ones done at the campaign level rather than the account level.  As seaman Adams reminds us in Master and Commander, “Any fool can steer a ship, sir.  It’s just knowing where to take it.”

About Bradd Libby

Bradd easily becomes obsessed with small details. He can barely make it through a conversation without drawing a graph of something. He lives in the woods on the side of a hill in Norway. Bradd doesn't willingly wear shoes. He makes maps of places that don't exist. He picks up small shiny things he finds on the ground. He devolves into violent shouting matches with himself. He takes things apart to find out how they work but then can't figure out how to put them back together again. He also writes at Search Engine Land [6], Search Engine Journal [7] and his personal blog [8].