This reminds me of your comparison of vague vs precise theories in A Technical Explanation of Technical Explanation—if both are correct, then the precise theory is more accurate then the vague one. But if the precise theory is incorrect and the vague is correct, the vague theory is more accurate. Preciseness is worthless without correctness.
While the distinction there was about granularity, I think the lesson that preciseness is necessary but not sufficient for accuracy applies here as well. Using numbers makes your argument seem more mathematical, but unless they are the correct numbers—or even a close enough estimate of the correct numbers—can’t make your argument more accurate.
This reminds me of your comparison of vague vs precise theories in A Technical Explanation of Technical Explanation—if both are correct, then the precise theory is more accurate then the vague one. But if the precise theory is incorrect and the vague is correct, the vague theory is more accurate. Preciseness is worthless without correctness.
While the distinction there was about granularity, I think the lesson that preciseness is necessary but not sufficient for accuracy applies here as well. Using numbers makes your argument seem more mathematical, but unless they are the correct numbers—or even a close enough estimate of the correct numbers—can’t make your argument more accurate.