# Statistical Accuracy

I was reading about statistical filters, and I came across a sentence that I didn't understand:

You might be thinking that there's not much difference between 95 percent and 99.5 percent. But you would be wrong. A filter with a 99.5 percent accuracy rate is not merely 4.5 percent more effective than one that is 95 percent accurate, but 900 percent more effective!

Can someone explain how a filter that is 99.5 percent accurate is 900 percent more effective than 95 percent?

• This is from a book called Ending Spam: Bayesian Content Filtering and The Art of Statistical Language Classification – S. Sharma Mar 27 at 14:43

Let's consider a system with a $$95~\%$$ certainty. It means that for every $$10~000$$ inputs (or cases, whichever you want), there would be about $$(1-0.95)\times 10~000\approx 500$$ errors.
Then compare it to a system with $$99.5~\%$$ certainty. Now the number is $$(1-0.995)\times 10~000\approx 50$$.
The first system has $$\frac{500-50}{50}\approx 900~\%$$ more errors. That's what the text is trying to communicate.