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## Google Mathematics

Ever wonder how Google makes its money? Every time you do a search, an auction occurs....with the winning bidders getting their ads placed first, second etc. above or adjacent to your search results. And, underlying all of this is a constant use of mathematics via a single equation!

The equation is quite simple:

P1 = [B2Q2]/Q1
where P1 is the price paid by the advertizer, B2 is the next-highest-placing ad's bid, Q2 is the "quality score" of next-highest-placing ad, and Q1 is the "quality score" for the winning advertizer. All of it is straight forward, except for the "quality score" which includes relevance to the search word, the ad's "click-through rate," and other criteria not revealed by Google.

The key idea is that this type of auction occurs almost instantaneously, and often, given that Google averages 293.8 million searches per day. And one nice feature is that a company does not have to fear getting stuck with a high "over-bid," since they will pay 1 cent more than the second place bid (i.e. suppose winning company A bids \$100 and second place company bids \$6, the ad will cost company A only \$6.01).

The mathematics is vital to Google. Consider these statements from the source below...

• "The across-the-board emphasis on engineering, mathematical formulas, and data-mining has made Google a new kind of company"
• The people who work for Google "are generally econometricians--sort of a cross between statisticians and economists"
• "Google needs mathematical types that have a rich tool set for looking for signals in noise...the rough rule is one statistician for every 100 computer scientists"
• "What's ubiquitous and cheap...data. And what is scarce? The analytic ability to utilize that data...the kind of technical person who ...will now work at a firm whose business hinges on making smart, daring choices--decisions based on surprising results gleaned from algorithmic spelunking and executed with the confidence that comes from really doing the math."
For more about the equation and Google's use of mathematics, please read Levy's great article...you might even find it on-line by an appropriate Google!

Source: S. Levy, "The Secrets of Googlenomics," Wired, June 2009, pp. 108-115