The Algebra of Click Fraud

Last time, I explained why Google and Yahoo were going to end up as expensive wholesalers for the Internet advertisers’ statistical needs. That by itself is problematic to the nascent advertiser, but not fatal. What is much more dangerous is click fraud.

Banner ads and the like give the illusion of providing more information than traditional media. Note that I said illusion — the additional information is not statistically relevant to the effectiveness of the ad and can easily be corrupted against the advertiser’s favor.

In traditional mass media advertising, the success of the campaign was determined by the change in revenue: the marketer runs a campaign, then sees how much product was moved after the campaign. The idea was that you could view the relationship as a simple formula:

revenue = α × c

where c is the number of clicks and α is the conversion rate — the fraction of clicks that result in a sale. Advertisers would like to pay for purchases (known as CPA) and site owners wanted to be paid for views (known as CPA); with the Internet, the compromise is to pay for clicks:

charge = CPC × c

Estimating the right value for the CPC is an art, but the basic logic is this: Suppose that the client is willing to spend a given fraction of his revenue on advertising; call this fraction β. Then the CPC charge above must equal that fraction times their revenue, and the maximum acceptable CPC for the advertiser can be derived simply:

charge = β × revenue = β × (α × c)
    ⇒ CPC_max = α × β

This worked — for a time. Then unscrupulous people realized that they were paid whether or not the advertiser’s revenue remained high, so they started engaging in click fraud: either using bots or farms of low-paid unskilled workers to click on ads. Now our equation looks like:

charge′ = CPC × (c + b)

At first, charge′ > charge, and the fraudulent advertiser is rewarded for his deviousness. But advertisers still assume the old model, with no bad (b) clicks. Now α is dropping, β remains steady, so CPC must be lowered so that the pre-fraud charge is the same as the post-fraud charge. In essence, CPC ∝ 1/b.

Thus begins the rapid decay of internet advertising: since click fraud lowers the conversion rate, content publishers rely more on click fraud to turn a profit. “Honest publishers” are squeezed out of the equation. Eventually, the conversion factor becomes so low it is subsumed by the base cost for the advertiser, and the advertiser will pull out of the market.

There is no solution for this problem as long as the number of clicks is used as a measure of effectiveness; but because it is such a convenient metric to track everyone will continue to use it until the market implodes.