# Google’s Chief Economist Hal Varian Talks Stats 101

In an interview with CNET’s Tom Krazit, Google Chief Economist Hal Varian made a nice argument regarding the relative advantages of scale to a search engine:

On this data issue, people keep talking about how more data gives you a bigger advantage. But when you look at data, there’s a small statistical point that the accuracy with which you can measure things as they go up is the square root of the sample size. So there’s a kind of natural diminishing returns to scale just because of statistics: you have to have four times as big a sample to get twice as good an estimate.

Another point that I think is very important to remember…query traffic is growing at over 40 percent a year. If you have something that is growing at 40 percent a year, that means it doubles in two years.

So the amount of traffic that Yahoo, say, has now is about what Google had two years ago. So where’s this scale business? I mean, this is kind of crazy.

The other thing is, when we do improvements at Google, everything we do essentially is tested on a 1 percent or 0.5 percent experiment to see whether it’s really offering an improvement. So, if you’re half the size, well, you run a 2 percent experiment.

For those

In an interview with CNET’s Tom Krazit, Google Chief Economist Hal Varian made a nice argument regarding the relative advantages of scale to a search engine:

On this data issue, people keep talking about how more data gives you a bigger advantage. But when you look at data, there’s a small statistical point that the accuracy with which you can measure things as they go up is the square root of the sample size. So there’s a kind of natural diminishing returns to scale just because of statistics: you have to have four times as big a sample to get twice as good an estimate.

Another point that I think is very important to remember…query traffic is growing at over 40 percent a year. If you have something that is growing at 40 percent a year, that means it doubles in two years.

So the amount of traffic that Yahoo, say, has now is about what Google had two years ago. So where’s this scale business? I mean, this is kind of crazy.

The other thing is, when we do improvements at Google, everything we do essentially is tested on a 1 percent or 0.5 percent experiment to see whether it’s really offering an improvement. So, if you’re half the size, well, you run a 2 percent experiment.

For those unfamiliar with statistics, I encourage you to look at the Wikipedia entry on standard deviation. Varian is obviously reducing the argument to a sound bite, but the sound bite rings true. More is better, but there’s a dramatically diminishing return at the scale of either Microsoft or Google.

However, I do think there’s a big difference when you start talking about running lots of experiments on small subsets of your users. The ability to run twice as many simultaneous tests without noticeably disrupting overall user experience is a major competitive advantage. But even there quality trumps quality–how you choose what to test matters a lot more than how many tests you run.

What does strike me as ironic is that the moral here is a great counterpoint to the Varian’s colleagues’ arguments about the “unreasonable effectiveness of data“. Granted, it’s apples and oranges–Alon Halevy, Peter Norvig, and Fernando Pereira are talking about data scale, not user scale. Still, the same arguments apply. Sampling is sampling.

ps. Also check out Nick Carr’s commentary here.