One mistake digital marketers repeatedly make is to use the budgeting function in Google AdWords to limit their spending. You should *never* limit your spending by your budget – there are other ways to control the spending.

To reach this conclusion, it’s essential to understand the fundamental dynamics of how search engines allocate impressions across the individual bidders in the auctions.

Each search term has a certain search volume per day. For simplicity, I will assume that this number is stable and known by the search engine ahead of time (data fluctuates, but search engines generally have a good idea due to their vast amounts of data). I’ll use the terminology of Google, but this is conceptually the same across search engines – Google just happens to be the most widespread.

## How Google determines how often to display your ad

The illustration below displays the relationship between Ad Rank and the allocated share of impressions. The blue graph denotes the total searches for a given search query over a given time span. Depending on your Ad Rank relative to the other players in the auction, the search engine will display your ad for a certain share of the impressions (known as *Impression share*) as indicated by the red graph below.

In the example below, the green line indicates a certain Ad Rank. Again, the red line indicates the relationship between Ad Rank and impression share. At this Ad Rank, impressions are allocated to the ad up until the dotted line. In this case, the number is lower than the blue line. The impressions between the blue and red line are Google’s way of penalizing the bidder for not having a good enough, quality-adjusted offer, relative to other bidders.

Google AdWords denotes the percentage of impressions between the blue and the dotted line as Lost Impression Share (Rank), which you can add as a column in the online interface. For simplicity, I will refer to Lost Impression Share as LIS throughout this post.

“What does this have to do with budgets,” you may ask. Let’s introduce an illustration of why having a budget cap will be counterproductive. Again, for simplicity, let’s assume that we can’t change the ads, the landing pages, the keywords, etc. over the time span that we evaluate, but only bids and budgets. When this is the case, our CTR is stable across impressions and our quality score doesn’t change.

This allows us to re-write our axes by a factor, given that:

- Impressions * CTR = Clicks
- Ad Rank = Max CPC bid * Quality Score (incl. device adjustment)

In layman terms, first, by dividing Ad Rank by the quality score (which is fixed), we get to Max CPC bid on the horizontal x-axis. Secondly, when multiplying impressions by CTR (also fixed), we get clicks on the vertical y-axis. In both cases, the absolute values of the axes may of course change, but the correlations between them (i.e. the graph) doesn’t change. If the blue line used to denominate for example 100 impressions, it may now denominate 20 clicks, if your CTR is 20%. Similarly, doubling your CPC would double your Ad Rank when QS is fixed.

The new denomination shows you why Google suggests that you increase your bid to receive more impressions. It is obviously not such that Google will run out and ask more people to search for your queries; they simply just allocate you a larger percentage of the search volume when you increase your CPC (or quality score).

## The AdWords Budget Constraints

With these new denominations on the axes, we can now add the graph for the budget constraint. For simplicity, we assume that we intend to spend the entire budget. That means we aim for a situation where our cost equals our budget.

- Budget = Cost = CPC * Clicks

Given the set budget, Google will continuously bid for all relevant searches on your behalf until you have reached your budget limit. For any given CPC bid, what we are interested in is how many clicks we will get. Given that CTRs and budget are fixed, CPC is now the only variable we can use to influence the number of clicks. This means we can re-write the above cost function to:

- Cost = CPC * Clicks => Clicks = Cost / CPC

The relationship is clear, if we spend, say $20, then the number of clicks we get only depends on how much we pay per click. The grey graph below denominates the above relationship between clicks and CPC on the budget graph. Note the convex relationship as the maximum cost is fixed given the budget cap – the more you spend per click, the fewer clicks it takes to reach your budget cap.

Individually, the graphs dictate that it is impossible to get a number of clicks above the graphs for any particular CPC level. Just like the red Ad Rank graph, the grey budget graph serves as a ceiling over how many clicks you can get, given your Ad Rank (and indirectly, your CPC bid). In other words, for CPC levels to the left of the intersection of the two graphs, the red graph denominates the maximum number of clicks available. Similarly, to the right of the intersection, the grey graph denominates the maximum number of clicks you can get before you run out of budget.

We know that as CPC goes up, the Ad Rank will always either increase or stay flat (once it assimilates the blue line). Contrary to the Ad Rank graph, the Budget graph falls as CPC increases. This means that global maximum volume of clicks available (i.e. across all possible CPC bids) always will be at the intersection of the two graphs.

This insight has one important implication: If you are to the right of the intersection and want to maximize volume of traffic for your money, you are always better off by bidding less!

If you are to the right of the intersection and want to maximize volume of traffic for your money, you are always better off by bidding less!

The reason is that for any point on the grey graph to the right of the intersection will have a corresponding point on the red graph with the same amount of clicks, but at a lower cost *and *with a lower total cost (CPC * clicks)! More conceptually, remember that the red graph is Google’s attempt to penalize you for bidding to low (or having too low QS), so you know that when you hit it, you are pushing the envelope for how little you can bit for that amount of traffic!

This raises one fundamental question: *How do I know if I am on the right of the intersection?* The great thing is that Google gives you the answer indirectly.

I earlier explained how LIS (Rank) works: you will always miss the impressions above the red graph. Tough luck, but you aren’t bidding enough. However, if you are on the right side of the intersection, you will run out of money before Google will limit you on the impressions. Once you hit the grey graph, you won’t get any more impressions.

The diagram above displays how the impression share is derived as total impressions deducted LIS budget and rank. Note that on the left of the intersection, *all* impressions above the red graph stay as part of LIS (Rank). In other words, on the left side of the intersection, LIS (Budget) will always be 0%. On the other hand, this means that the moment LIS (Budget) is higher than 0%, you know that you are on the wrong side of the intersection and hence overpaying!

…the moment LIS (Budget) is higher than 0%, you know that you are on the wrong side of the intersection and hence overpaying! (Tweet This)

## Control Spending By Bids, Not By Budget!

The conclusion is simple: If you can only afford to spend a certain dollar amount, then you are better off controlling your spending by adjusting the bids rather than by setting budget caps. Remember to look for that ‘sweet spot’ where you maximize the number of impressions allocated to you before you hit the amount you want to spend. Budget caps are only good as a last resort to make sure you don’t overspend if impressions suddenly spike (however, even then you should only do this for cash flow reasons).

Remember, this graph alone must not dictate your CPC level. The order of your considerations must be:

- How much can I afford to pay per click (i.e.
*Max CPA you can afford * Exp. Conversion Rate * (1 – Exp. Drop-out rate*) - Can I finance this volume of traffic? (I.e. will I run out of cash before I get the revenue if I invest at this level?)
- Am I better off bidding less for the same or higher amount of traffic, as per the diagram above?

**I hope this post has been helpful. If you liked it, you can share it on twitter here (you can edit first). Let me and others know in the comments below if you have other tips. Happy optimizing!**

**– Stefan**

Awesome article. I love how you use numbers, graphs, math to explain this concept, rather than anecdotes.

Thanks – happy that you like it!

very compelling argument. love the quant focus

Thanks