If a pay-per-click (PPC) advertising account that normally spends $500/day needed to be reduced to only $100/day, the account manager would typically be best off restricting spending to only the terms that get the most conversions per dollar, like brand terms and low-volume, but highly efficient, long tail keywords.

If the budget were raised to $200/day, the manager could restore the second tier of top performers, and with $300/day, those that got even fewer conversions per dollar. Call it ‘diminishing returns’ or ‘low-hanging fruit’ or the square-root rule of advertising spending ^{[1]}, the underlying concept is the same: each additional increment in spending will tend to bring in fewer conversions than the previous one.

Graphically, this relationship tends to look like:

Notice that the maximum expected daily number of conversions tend to increase as daily average spend increases, but with a decreasing slope. The curve ends at a terminus (marked by a blue circle) where all of the words in the account are in top position. It simply isn’t possible to spend more per day (on average) with this set of keywords. The relationship shown is for one advertising campaign of a client that runs a website of online ‘social’ video games where users can win cash. Actual average daily conversions and actual average daily spend from the first eight weeks of 2010, starting January 1, are marked with red diamonds.

(Some mistakenly refer to this conversion-to-spend relationship as an “efficient frontier” (EF), though an EF is actually a different concept. Markowitz won the Nobel Prize for determining how to optimally allocate money to classes of assets by comparing the *average return* on a basket of those assets to the *covariance* of the value of that basket. Only that relationship is called an ‘efficient frontier’. The curve above is simply what economists call a ‘production function’ – not as sexy a name as “efficient frontier”, but more accurate.)

Account managers often speak about the ‘volume vs. efficiency’ tradeoff – where additional conversions are desired, but gaining them drives up the overall cost-per-conversion to an unacceptable level. So, an account manager told me that, for each account, he either attempts to maximize the number of conversions within a given budget limit, or overall cost-per-acquisition (CPA) limit. Let’s look at each of those cases.

**The Budget-Limited Manager**

The terminus of the curve shown above represents the maximum spending level per day and maximum number of conversions per day (on average) that the account could generate, even if every keyword were pushed into top position.

If the account’s budget limit is *at or above* this maximum spending level, then the easiest way to meet the budget target is to add more keywords. Since these new words will likely be more peripheral to one’s business than existing words in the account, the slope of the curve is likely to be no higher than near the terminus. Thus, the lighter green point marking the best-case number of conversions per day the account could generate with additional keywords added to it can be estimated simply by projecting the production function forward to the desired spending level, as shown in the graph below.

More likely, the budget limit will be *less* than maximum spending level and the account manager’s goal then is simply to maximize the number of conversions attained within that limit. In that case, the darker green point marking where the budget limit intersects the production function shows the maximum number of conversions expected per day. This is also the ‘target point’ for the account.

Some search marketing firms claim that it is in an account manager’s best interest to move the actual performance of the account as close to the production function as possible, because for any position below the line one can either obtain more conversions at the same spending level (by moving upwards on the graph) or obtain the same number of conversions at lower cost (by moving to the left). However, it is clear from the chart that it is actually in the budget-limited manager’s best interest when additional budget is available to move ‘*northeast*‘ from any of the given red diamonds, not ‘west’ or just ‘north’.

**The Efficiency-Seeking Manager**

Some account managers, though, are given an efficiency limit, that is, a maximum spending level tolerated *per conversion* (or equivalently, a minimum number of conversions tolerated per dollar spent). When overlaid onto the production function, we can see that there are only three realistic scenarios for a given efficiency limit. In one extreme, the account requires so many conversions per dollar spent that no (or very few) keywords in the account can deliver that level of efficiency. (In that case, the actual spending and conversions level in the account will necessarily be very low.) In the other extreme, the account can tolerate such a low number of conversions per dollar spent that any spending level up to (and including) the account’s spending capacity will be expected, according to the production function, to generate enough conversions to surpass that limit.

The typical case, though, is that the efficiency limit intersects the production function at one point, defining the target spending level and target conversion volume. For this demonstration, an arbitrary efficiency line is shown on the graph. (The campaign in question actually has a different efficiency goal.) As with the previous case, if the actual performance of the account deviates from the point where the efficiency limit intersects the production function (the ‘target point’, shown here as a pink circle), it is to the account manager’s advantage to drive performance toward this point through bidding, keyword activation/pausing, or other techniques depending on the particular circumstances of the account.

So, we can see from the graphs above that one’s goals as a budget-limited manager or an efficiency-seeking manager are, in reality, the same thing. Since CPA = Cost/Conversions, and Conversions are related to Cost, choose an efficiency limit, a minimum acceptable conversion volume or a maximum permissible budget, and you are effectively choosing the other two as well. (In physics parlance, the system has only one ‘degree of freedom’.) Your goal as an account manager, then, is simply to drive the performance of the account toward that target point, not toward just any random position on the production function as some others in the industry might suggest.