Despite being one-shot items, high-level scrolls are not cheap. When purchasing one, you may think your UMD makes you able to use it because the color indicator does not turn red, but apparently that means you have only some chance of successfully using it.
Someone with no UMD knows automatically and with 100 percent probability he or she cannot use a given item without first buying it. Thus, having UMD makes the person having it more ignorant of the very skill they are supposed to have acquired, if he or she cannot at least estimate the probability of using the item.
Is there any formula, then, for knowing the probability of successfully using a given scroll based on a given UMD?