User blog comment:Homuhomu123/Estimation of Radar Modifiers on Artillery Spotting Chance/@comment-25534439-20141213144852/@comment-25534439-20141213224825

Due to the nature of probability, you can't gaurentee a %. A brief explanation of confidence limits: at a confidence limit of 90%, there is a 90% probability that the actual value is within that range. Theoretically if you repeated the overall testing process 1000 times, 900 of them would have the actual CI/DA rate within the calculated range. The remaining 100 would have the actual rate outside of the given interval. For the testing you're doing, my assertion would be that 80% limit (Z=1.28) is probably fine for preliminary examination.

It isn't that the work doesn't pay off; the results just give a rougher estimate (+-5%) than you thought. One last note: the easy calculation given there gets less correct as you get closer to 0 and 100%; you need fewer tests, but at the same time the intervals are less correct. I'd be cautious going over 80% rates and trying to apply the same formula. If you want to test beyond that, you'll probably ought to use WolframAlpha and integrals of the Beta function in the wikipedia article.