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In many video games, movies, and cartoons there are characters who can move so fast that they leave afterimages of themselves that others can attack (thus missing the person who they intended to hit).

I am wanting to make an NPC who does this, basically a good guy who says "look, if you can't touch me, you have no business even trying to go up against the BBEG, because I'm way less powerful than he." Think of the pokemon who give multiple afterimages by running in circles.

Are there any rules governing this without using the Mirror image spell statistics for such movement? Even homebrew would work if there are no official rules.

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    \$\begingroup\$ Relevant TVTropes articles describing this effect (warning: time-sink): Flash Step with (as the end of the article notes) a Doppelgänger Spin. \$\endgroup\$ Commented Jan 29, 2017 at 21:09

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Yep!

Me and my friends briefly played a pathfinder-based homebrew pokemon RPG (disclaimer: we trashed it in favor of a homebrew Runequest based pokemon RPG after like 0 sessions. There was some battle testing and some chargen for a handful of different homebrews and then we decided that the Runequest one was best. I still think this will work for you, though)

Double Team (Ex):

Requirements:

Speed 90ft or greater in any movement form. Ability to move at least 5 ft via that movement form.

Benefit:

The user moves so fast they appear to be in multiple places at the same time. Activating this ability requires a standard action and it lasts 1 minute per level. This ability grants a 50% miss chance that can be negated with a successful perception check DC users speed/5 or via any method that bypasses total concealment. While this ability is active you do not provoke attacks of opportunity by exiting threatened spaces. You take a -10 penalty to Reflex Saves to avoid traps or when forced to make a save by a terrain effect, however. You may end these effects as a swift action.

In the combat test the ability allowed one of the players to wipe the floor with the other team with his Dodrio, but it didn't work so good in the second round when the reflex save penalty meant he got hit by a stealth rock for a OHKO. I think the rules fit the effect you are looking for. Be warned, however, that properly made level 1 pathfinder characters can deal with a character relying on this (or similar) abilities quite simply, via effects like True Strike, caltrops, tanglefoot bags, etc.

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The swiftblade class has Blurred Alacrity and Evasive Celerity as class features... In sum, those class features gives miss chances to attacks and targeted spells...

Blurred Alacrity (Ex): At 2nd level, your understanding of the haste spell makes you difficult to target with melee and ranged attacks. While under the effect of a haste spell that you cast yourself, you gain concealment (20% miss chance). This miss chance increases by +10% at 3rd, 4th, and 5th level. The effect of this ability does not stack with blur, displacement, or similar spell effects.

Evasive Celerity (Ex): At 5th level, your knowledge of the haste spell makes you difficult to target with spells. While under the effect of a haste spell that you cast yourself, individually targeted spells have a 20% chance of failing against you. This spell failure chance increases by +10% at 6th, 7th, and 8th level. The effect of this ability does not stack with blink or similar spell effects.

One can rule that this failure chance are due to the attacker targeting your afterimages instead of you.

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