What are the hidden stats of Valkyrie?
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The description for the Valkyrie tells that it has synergies with other Amazon passive abilities like Avoid, Dodge, Decoy etc.
What are her hidden abilities? I see sometimes she can cast some sort of lightning when being hit or on striking, not sure which. Does she bear any Aura? If yes, are they random or level dependent? Because the lightning started to appear only after a certain level.
And when she is spawned, the color of armor is sometimes different. I've seen red and green, for example. What do these mean?
What are her real stats (Dex, Str, Vit) comprised of, and are they influenced by any of the above mentioned abilities?
Does she have any magic find or any other modifiers?
What are her elemental resistance values? Any immunities, based on level?
She does seem to have a good amount of health regen. How does this scale?
And finally: Is there a way I can force her to 'hurry it up'? She just walks and does not run at all, it seems.
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https://forums.d2jsp.org/topic.php?t=84688347&f=87 and https://diablo.fandom.com/wiki/Valkyrie are the best sources of information I'm aware of for Valkyrie (and they seem to heavily share content; I'm not sure which one came first). I am not entirely sure how the author(s) determined all of this information, but it matches my experience with the ability.
Many of your questions are answered by the various tables/charts on these pages.
What are her hidden abilities?
The valk has exatly the same level of critical strike, dodge, avoid, and evade as you (the player) do.
I see sometimes she can cast some sort of lightning when being hit or on striking, not sure which. Does she bear any Aura? If yes, are they random or level dependent? Because the lightning started to appear only after a certain level.
This is likely a random magical property of the valk's weapon (e.g., % chance to cast chain lightning on hit) or armor (e.g., % chance to cast charged bolt on being struck). Since the item quality and the magical affix ranges increase will valk skill level, it makes sense that you would only see this later.
And when she is spawned, the color of armor is sometimes different. I've seen red and green, for example. What do these mean?
These indicate different magical properties on the armor.
And finally: Is there a way I can force her to 'hurry it up'? She just walks and does not run at all, it seems.
You can use the Teleport skill, either from a weapon/amulet with charges or from Enigma, to reposition the valk. Otherwise, none that I am aware of.