Comment by bscphil

Excellent comment. I think the issue is that "better" is underspecified and needs some precisification to be useful. The metric you are using here is the proper response to the question "how many times more surprising is it when method A fails than method B?". This is in many cases what we care about. Probably, it's what we care about here. The odds ratio seems to do a good job of capturing the scale of the achievement.

On the other hand, it's not necessarily the only thing we might care about under that description. If I have a manufacturing process that is 99.99% successful (the remaining 0.01% has to be thrown out), it probably does not strike me as a 10x improvement if the process is improved to 99.999% success. What I care about is the cost to produce the average product that can be sent to market, and this "10x improvement" changes that only a very small amount.