5 is smaller than 1.9!

10 Feb

“In the late 1990s, the leading methods caught about 80 percent of fraudulent transactions. These rates improved to 90–95 percent in 2000 and to 98–99.9 percent today. That last jump is a result of machine learning; the change from 98 percent to 99.9 percent has been transformational.

An improvement from 85 percent to 90 percent accuracy means that mistakes fall by one-third. An improvement from 98 percent to 99.9 percent means mistakes fall by a factor of twenty. An improvement of twenty no longer seems incremental.”

From Prediction Machines by Agarwal, Gans, and Goldfarb.

One way to compare the improvements is to compare differences in percentages —5 and 1.9. That is what I would have done. That is so because conditional on the same difference in percentages, lower the base, the greater the multiplicative factor, which makes it a cheap way of making small improvements look better. Even then, for consistency, the comparison would have been between percentage increases in accuracy, between (90 – 85)/85 and (99.9 – 98)/98. But, AGG had to flip the estimand to percentage errors to make the latter relative change look better.

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