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I have some two models and I need to compare the efficiency of one to another one.

But if one model produces negative result e.g. -10 and another one positive eg 30, mathematically the ratio is 30/-10 = -3 meaning the first one is -300% effective to another one, which is mathematically correct, but incorrect otherwise.

What is the ratio in this case you think? I would say 400% because it is one piece of 10 to the zero, and then another 3 pieces up to 30.

Another question is what if one is 30 and another 0 that is 30/0. It is illegal in math to divide by zero, but how to express the efficiency in this case? Is it 30x or what is it? Hard to express again.

Mathematically it is infinity or illegal, but in reality it's not that big.

luky
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    Perhaps what you want is this: Percentage effectiveness of Model A w.r.t Model B= ${R_A-R_B \over R_B}×100$ ,where $R_A$ and $R_B$ are results produced by Model A and Model B respectively and $R_B\neq 0$. In case $R_B=0$, you don't calculate the effectiveness of any other model with respect to a model with zero result, i.e., Model B. – Aman Kushwaha Aug 25 '21 at 08:56
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    @AmanKushwaha If you intend that that the denominator is $R_B$, which is allowed to be $< 0$, while $R_A$ is forced to be $> 0$, then I forsee problems. That is, as the OP questioned, what does the ratio $(30,10) \to \frac{30}{-10}$ actually mean? How does its efficiency ratio compare to those of $(30,10), (40,10),~$ or $~(50,10)$? – user2661923 Aug 25 '21 at 10:43
  • @user2661923 First of all I would like to emphasize the first word of my comment, i.e, 'perhaps'. The question is lacking context which is why concluding anything at this moment will not make any sense unless the OP edit the question to express his query more clearly. Coming back to your question, I think a negative percentage is completely fine. For example, when $R_A=30, R_B=-10$, I would say Model A is $400%$ ineffective as compared to Model B. Similarly when $R_A=30, R_B=10$, I would say Model A is $200%$ effective as compared to Model B. – Aman Kushwaha Aug 25 '21 at 11:17
  • @AmanKushwaha I completely agree with your comment. The difficulty is that often, when the OP is vague presenting the context in his question, it means that the OP is himself unsure what the context should be. Anyway, based on your proposed formula, which seems to be $\frac{R_A - R_B}{|R_B|}$, you would have the ratios generated by $(50,10)$ and $(30,-10)$ as being equivalently efficient. Then the OP is going to have the real world challenge of asking himself if this is what he wants. – user2661923 Aug 25 '21 at 11:24
  • @user2661923 "based on your proposed formula, which seems to be..." read my previous comment again. I said it is $400%$ "ineffective" not effective because my formula says it is $-400%$ effective – Aman Kushwaha Aug 25 '21 at 11:32
  • @AmanKushwaha My carelessness. Nice rebuttal. – user2661923 Aug 25 '21 at 11:33
  • No problem @user2661923 :) – Aman Kushwaha Aug 25 '21 at 11:35

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