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[M.Celestial]

The numbers I've used are based on the current AP regen numbers on the wiki. In particular I will be comparing two situations, Relative DPS while standing still with double tap, and relative DPS assuming the 12.5 regen never kicks in. These situations are not always realistic, but will allow to establish a general pattern of how each perk scales with AP cost and AP regen. I have not taken into account critical hits, or the time a weapon spends in it's animation before it is allowed to refire.

The primary metric I will be using is relative DPS. Since each perk essentially multiplies the DPS of your weapon, it does not matter what the weapons damage is as the damage will always be the same. For example, a relative DPS of 1.15 would mean that with the perk you would be dealing 15% more DPS than without it. I am calculating relative DPS in the following way:
DPS (with perk) / DPS (without any perks)
Where DPS is calculated with:
AP regen / AP cost

The base DPS value shows you how much of your weapons damage you will deal on average, per second. The Relative DPS values show what this number is multiplied by when bRoF or AB is taken.

Similar to my last post my conclusions are based on a spreadsheet I've constructed which may contain errors. This spreadsheet has multiple pages. The first deals with AP regen including the 12.5s for doing nothing or having double tap. The second uses only the AP+ value. The third shows what happens when Fast shot is introduced Because recurring numbers make the spreadsheet less readable I have changed the formatting to use rounding, but have created a second spreadsheet with non-rounded values. This will slightly influence some of the values seen, but in most cases shouldn't fundamentally change what anything means. The spreadsheet itself is very large because I wanted to show differences between a wide range of values for AP cost to shoot, but as it turns out it does not change the statistics in an important way. These areas remain as proof of that.

Rounded:
https://docs.google.com/spreadsheets/d/1NlmXBVVwk-Aw4xSvMbZkFCdioxY9xexTsFpfx3CkYUo/edit?usp=sharing
Non-rounded:
https://docs.google.com/spreadsheets/d/1mXwRZtzHim3yzreZ0q_cf90FKI9s05RRpevZYohp11k/edit?usp=sharing

How does the AP cost of a weapon influence these perks?

Spoiler for Hiden:

The short answer is not at all. Regardless of how much the AP cost of a weapon is changed, for a given AP/S value the relative DPS of both Action Boy and Bonus Rate of Fire will remain the same.

. however, this assumes perfect numbers. Realistically if you lower the AP cost of the weapon with bRoF and receive a decimal value, the game will round the number either up or down. I do not know for sure which this is, but I'm leaning towards rounding down.

If the number was rounded down, then the DPS increase of bRoF would be slightly greater. If the number was rounded up, then the DPS increase of bRoF would be slightly lower.

How important is your existing AP regen and Agility before the perk is added?

Spoiler for Hiden:

Bonus Rate of fire will always multiply your DPS the same amount regardless of how these values change. As can be seen on the spreadsheet bRoF will always increase your DPS by 11.11% of what it was before the perk was taken.

Action Boy on the other hand works the other way around. The more AP regen you already have, the lower the relative DPS increase. While AB will always give you the same damage, it does not scale with your existing AP/S like bRoF does. This means that the relative DPS increase becomes lower as your agility increases.

What if I have Fast shot?

Spoiler for Hiden:

Fast Shot will not influence the relative DPS of Action Boy, though having both will still grant you more DPS.

Fast Shot and bRoF will stack additively meaning that having both will lower AP costs to 80% of their normal value. In this case the relative DPS increase taking both Fast Shot and bRoF compared to taking only one of them is 113%. Since 1.11 * 1.13 = 1.25 taking both will be a 25% increase of DPS compared to taking neither. This means that taking any one buff that lowers the AP cost of firing will make any other buff that does the same thing stronger. This can apply to Fast Shot, Bonus Rate of Fire (as a perk), and the armor perk.

So when will one give me more DPS than the other?

Spoiler for Hiden:

With the full regen (12.5 + AP+) Action Boy will grant between 4-5% more DPS than you would have had otherwise.

With the partial regen (AP+) Action Boy will grant 11-22% more DPS than you would have had otherwise. The 22% is at 1 agility, and the 11% is at 10 agility. An average character of 5 agility will gain 15% DPS in this case, which is 4% above bRoF.

Bonus Rate of Fire will grant 11% more DPS without fast shot, and 13% with it. Any additional cost reductions from armor will further improve the efficiency of taking Bonus Rate of Fire

In a realistic fight you will be spending a mixture of time with your full and partial regen rates. Moving, shooting (without double tap), reloading and swapping weapons will all lower you to the partial rate. Conversely, the 12.5 AP/s is so large that most players will make sure to use it whenever possible, meaning that both rates will see usage.

My personal opinion is that in general Bonus Rate of Fire is the preferred perk because:
-At average agility values the difference in the max DPS gained from Action Boy compared to bRoF is fairly small
-bRoF scales with Fast Shot and the armor perk
-It is preferable to regen 12.5 AP/s as much as possible and bRoF has a significant advantage while this is the case

Closing notes

Spoiler for Hiden:

-Bonus rate of fire, in general, seems to grant a higher bonus DPS than Action Boy
-Bonus rate of fire scales with Fast Shot
-Bonus rate of fire remains as effective regardless of agility
-Bonus rate of fire is only influenced by weapon AP cost if there is rounding. I am unsure how the game rounds this, but I think it rounds in favor of the perk.
--Rounding up makes bRoF slightly worse
--Rounding down makes bRoF slightly better
-Action Boy is not influenced by weapon AP cost
-Action Boy does not scale with Fast Shot
-Action Boy gets worse the higher your agility is
-The more you can maintain the 12.5 AP/s for standing still/using double tap the better bRoF gets compared to Action Boy

Factors resulting in potential inaccuracies:
-I have primarily used the rounded spreadsheet for my conclusions
-Using unrealistic situations then relying on logic to determine what I would expect in a more realistic situation
-During the time while a weapon is firing the lower regen value is used, but this is not calculated
-No calculation of what happens when you unload starting from 100AP, again because I don't know the animation time
-Not factoring in critical hits, though I imagine these would influence both perks equally anyway
-Any mistakes I may have made, or anything I have forgotten

Answers to questions

Taking Action Boy if you already have Bonus Rate of Fire, and possibly Fast Shot

Spoiler for Hiden:

Perhaps I should have been more Clear on this, since most of my post was comparing the two against each other.

If you have Fast Shot, it makes Bonus Rate of Fire a bit more effective to take. In terms of how much AB multiplies your DPS having fast shot doesn't change anything, but that doesn't directly make AB worse when you have Fast Shot, just less preferable to Bonus Rate of Fire.

At 5 Agility and full AP Regeneration AB will grant 5% more DPS regardless of whether or not you have Fast Shot, bRoF, or both. But, since having Fast Shot increases your DPS in the first place that 5% will be a greater number. For example, if you have 100 base DPS and no fast shot, AB will grant 5 more DPS in that scenario. If you take Fast Shot first, then your DPS would be 111, and therefore AB would add 111 *1.05 = 116.55DPS. An increase of 5.55 which is actually greater than before but still only 5%. In the same case bRoF would increase 111 by about 13% (Compared to it's 11% without fast shot) which means that not only will it scale with having a higher DPS, but the multiplier will become greater with Fast Shot already taken.

If your build doesn't have too high an Agility already, or you just want to maximize DPS, then AB is still worth considering if there aren't any better perk options left for that slot.

[Deathproof]

Thanks ! Keep it up, since I have no idea how to do math behind perks your comparison is helpful.

[SnowCrash]

Very interesting! I was wondering which one of those will be better to pick

[paragon]

I didn't get yet what do I put to the character planner from this xD

[Hang-Lip]

So if you have fast shot and Brof, AB isnt worth it? I was panning this route.

[M.Celestial]

Perhaps I should have been more clear on this, since most of my post was comparing the two against each other.

If you have Fast Shot, it makes Bonus Rate of Fire a bit more effective to take. In terms of how much AB multiplies your DPS having fast shot doesn't change anything, but that doesn't directly make AB worse when you have Fast Shot, just less preferable to Bonus Rate of Fire.

At 5 agility and full AP regeneration AB will grant 5% more DPS regardless of whether or not you have Fast Shot, bRoF, or both. But, since having Fast Shot increases your DPS in the first place that 5% will be a greater number. For example, if you have 100 base DPS and no fast shot, AB will grant 5 more DPS in that scenario. If you take Fast Shot first, then your DPS would be 111, and therefore AB would add 111 *1.05 = 116.55DPS. An increase of 5.55 which is actually greater than before but still only 5%. In the same case bRoF would increase 111 by about 13% (Compared to it's 11% without fast shot) which means that not only will it scale with having a higher DPS, but the multiplier will become greater with Fast Shot already taken.

If your build doesn't have too high an agility already, or you just want to maximize DPS, then AB is still worth considering if there aren't any better perk options left for that slot.

[hell]

Love it. GJ

[paragon]

Also we (I mean, you) don't take in count twice as much of misses from Fast Shot trait in those calculations.

[lvhoang]

Also we (I mean, you) don't take in count twice as much of misses from Fast Shot trait in those calculations.

Hum sorry what do you mean?
Your hit % is lowered from 95% to 90%.
So the penalty is very low, or am I missing something? I man 5% less really shouldnt change anything?

[Myakot]

Create a character with a "fast shot" you will notice the difference. And you will miss... a lot.

[paragon]

Hum sorry what do you mean?
Your hit % is lowered from 95% to 90%.
So the penalty is very low, or am I missing something? I man 5% less really shouldnt change anything?

95% CtH is 1 / 20 misses.
90% CtH is 2 / 20 = 1 / 10 misses.
Which is twice more.

[PusiteGA]

you confused me a litle i am building mele doctor and have 4 agi shoud i pick brof or gain agi or action boy?