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Message: <blockquote data-quote="komi" data-source="post: 4353286" data-attributes="member: 60878">(Because graphs are fun <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile    :)"  data-smilie="1"data-shortname=":)" />  and this was similar to what I did for the Improved Init vs. Danger Sense discussion...)(EDIT: I don't know why message board is distorting my image.  If you view the image directly it will be much clearer.)Mathematically there is a difference when rolling against active perception and passive perception.  Here's a chart of the chance of success on stealth vs. perception for both active and passive checks.  The x-axis shows the difference in skill modifiers between stealth and perception.  Positive means the person attempting stealth is better than the person trying to perceive.<img src="http://img71.imageshack.us/img71/7398/passvact1cf8.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />So, if the stealther is better than the perceiver (delta modifier is positive), it's better for the stealther to roll against passive.We can take the change from active to passive as a modifier on an active check.  Say you're stealth skill modifier is five higher than the person you're hiding from.  From the chart above, you have an 80% chance of success on a passive check (e.g. 1d20+5 vs. DC 10).  What modifier would you need on the active chart to achieve an 80% chance of success?  Looking at the blue line on the chart above, you get about 7 (6.84 from interpolation).  So if we look at chance of success, rolling with a +5 versus a passive check is about the same as rolling with a +7 versus an active check.(1d20+5 vs. DC 10) ~= (1d20+7 vs. 1d20)So you get an effective +2 bonus to your stealth when your DM decides you can roll against passive to save dice rolling.   Here's a chart that shows this.  The blue line is the actual interpolated results.  The red dots show the same data rounded to the nearest integer.<img src="http://img115.imageshack.us/img115/1929/passvact3wo6.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />The break even point where active and passive are the same is -4.  At 9, you're getting a +10 to your check.  You can mentally see this if you think that (1d20+9 vs. DC 10) is always a success.  To get a guaranteed success for an active check you need to be +19 better than your opponent.  (1d20+19 vs. 1d20) will always succeed.  You have an effective +10 to your check when rolling against passive.I'm not writing this to show anything is broken nor to state an opinion, but rather to better convey the math behind it.  You can go with passive checks, but be aware that people using stealth a lot will be specialized and will very likely be in the positive x-axis domain above.  In fact, once you're +9 better than you're opponent it's impossible to be seen until they attempt a minor action perception.  Conversely, requiring mostly active checks means a lot of dice to be rolled and might painfully slow the game down.  So when we understand both sides, we as DMs can make better decisions.</blockquote>

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