# B is x% better than A. How to calculate x? How to report percentages.

 2 What's the correct way to report that B is x% better than A? I see 2 ways: Way 1) x = (B/A - 1) Way 2) x = (1 - A/B) In case the goal is to maximize the value (for example: calculations per second): A = 100 B = 130 (better) Way 1) x = (B/A - 1) => B is 30% better than A Way 2) x = (1 - A/B) => B is 23% better than A C = 500 (best) Note: C is 5 times better than A Way 1) C is 400% better than A Way 2) C is 80% better than A In case the goal is to minimize the value (for example: number of seconds run): A = 100 B = 70 (better) Way 1) x = (B/A - 1) => B is 30% better than A Way 2) x = (1 - A/B) => B is 42% better than A C = 20 (best) Note: C is 5 times better than A Way 1) C is 80% better than A Way 2) C is 400% better than A Due to writing this down, it seems clear that way 1) is the way to report this. This is also they way I 've always used thus far. But is that accepted as the canonical way in the scientific research community? Or is there discussion/variance on how to calculate that something is x% better? asked 13 Feb '14, 06:26 Geoffrey De ... ♦ 3.6k●4●27●65 accept rate: 6%

 1 We (at CPLEX) say B is 1.3x better than A, and C is 5x better than A. Usually we use 'better' for 'faster' ;) A related question is about the computation of the gap. Here each MP solver seems to have a slightly different way of computing it. It may be worth looking at this given it provides a percentage that says how far is the current best solution from the best dual bound. answered 14 Feb '14, 04:39 jfpuget 2.5k●3●10 accept rate: 8% Agreed that avoiding the use of "%" avoids the ambiguity :) (14 Feb '14, 04:53) Geoffrey De ... ♦ IMHO, it's more accurate to say: B is 0.3x better than A [or: B is 1.3x as good as A], and C is 4x better than A [or: C is 5x as good as A]. [ I. e., n times better than ⇒ A+n*A; n times as good as ⇒ n*A ] (14 Feb '14, 05:23) fbahr ♦ @fbahr On this one, I disagree (and therefore agree with @jfpuget): "1.3x as good" doesn't parse well in my brain. (14 Feb '14, 07:49) Geoffrey De ... ♦ @Geoffrey: That's why people _use_ "%" (change). [You probably won't have problems parsing a similar statement incl. 'many' and its comparative 'more': Fry has twice as many eyes as Leela, but he does _not_ have two times more (than Leela has).] (14 Feb '14, 10:12) fbahr ♦
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Last updated: 14 Feb '14, 12:33