Counterbalance is the only perk that actually affects balance. Rodeo only affects it by making the firestream not veer off to the right or left as much -does buggar all really- and Persistence only affects hip fire accuracy. Now if Zen Moment were to pop up on the Arminius-D that'd be worth it, but it hasn't and won't because that'd be too powerful in Bungie's warped little brains.
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Rodeo actually reduces the kick upwards but still has the side to side kick. Counterbalance makes the kick go straight up and down but has more vertical kick than rodeo
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Persistence does effect ads accuracy, it's just that the spread is much tighter when aimed so it is very hard to notice.
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Persistence barely affects ADS accuracy unless your going for ranges that aren't normal for ARs. But for the most part it is good on Arminius-D and Doctrine cause they hold 54-62 bullets that'd be good for firing from the hip at close range.