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Message: <blockquote data-quote="Cadfan" data-source="post: 5031203" data-attributes="member: 40961">He assumed that 85% of the possible outcomes will be things that would have either been a success even without the +3, or things that are a failure in spite of the +3.  In other words, if you need a 15 to succeed, and you have a base +5, you will fail on a 1 to 9 and succeed on a 10 to 20.  If you take a skill focus feat that gives you a +3 to the relevant skill, you now fail on a 1 to 6, and succeed on a 7 to 20.For values of 1 to 6, you failed on both checks.  For values of 10 to 20, you succeeded on both checks.  Only the 7, 8, and 9 were altered in their outcome.Note that this reasoning only works on checks that involve a single check versus a static DC where degree of failure is irrelevant.  If you care about degree of success (knowledge, certain athletics, etc), then +3 always matters.  If you are making an opposed check (do these still exist?), the math is different.  If you care about consistency or trustworthiness of outcomes, the way you care about your skill will cause you to want to use different math as well in interpreting the advantages of a +3.Personally, I'm not a huge fan of the +3 feats, because I'd rather take one of the +2 or +1 feats that gives some non numerical bonus.  But this is how they work.</blockquote>