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Message: <blockquote data-quote="Elric" data-source="post: 4977566" data-attributes="member: 1139">This anecdote does not support your conclusion.  +1 to hit adds 5 percentage points to your chance of hitting going forward (I'm assuming you don't already have to roll a 20 to hit, and don't already hit on a 2+).  Your experience in play with "how much people miss by" makes no difference.  This is an example of why facts cannot be interpreted without the benefit of theory.Edit: To elaborate, a (fair) d20 is equally likely to yield each result.  So if you currently need to roll, say, an 11+ to hit, it's equally likely that you miss by each of 1-10 or hit by each of 0-9.  That means that a +1 to hit causes you to hit 5 percentage points more often in the future.  A +2 to hit causes you to hit 10 percentage points more often in the future, and so on.  Let's suppose that your players always need to roll an 11+ to hit in your current campaign, and have tended to roll more 5-7s than 8-10s.  This doesn't imply that going forward, a +3 to hit is any less valuable than if they've mainly rolled 8-10 as opposed to 5-7 (unless you think the dice aren't fair, in violation of my above premise- if so, get new dice!).  Your experiences don't imply anything about what dice rolls will come up in the future; it's random.In general, people do not have a good innate understanding of probability and statistics (for example, I got the <a href="http://en.wikipedia.org/wiki/Monty_Hall_problem" target="_blank">Monte Hall problem</a> wrong the first time I saw it, as I assume is common).  This is a reason to take courses in these subjects and also to avoid designing your game in a way that gives sophisticated players a major edge.  A sophisticated player will realize that even if he's rolled a lot of 5-7s and few 8-10s so far, +3 to hit is still incredibly valuable.  A less sophisticated player might not realize this.</blockquote>

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