Astro in savage

[Ghishlain]

-Snip-

You seemed to have comprehended most of it, given your response Indeed, there is no simple solution to the "AST buff problem" because AST buffs are highly dependent on so many different factors that are outside of their control. If you end up using Extended Balance at the same time your DRG is popping their burst phase, that's gonna skew the potency of that buff to a higher degree. Likewise despite Expanded Balance being the best DPS increase, if you get that combination in the middle of the add phase of Oppressor, you're probably only going to get 2/3 of your party with that Expand. Also, as you've rightfully mentioned bring an AST will generally lower the contribution from your healer DPS.

It's funny, because if you consider Yoshi-P's comment about how they take zero Healer DPS into account while tuning raids, one can make an educated assumption that they would try to balance AST card buffs around the best steady buff the healers have - Fey Wind.

But we all know that the players won't consider this and instead balance what the total DPS an AST can bring versus WHM and SCH. This in itself is difficult to determine because raw healer DPS is a function of player skill and how good your raid is at dodging "the dodge-able" and mitigating the damage properly. This compounded by the fact that the DPS an AST brings to the table via buffs is directly dependent on the player skill, gear, and job of the DPS and Tanks you have as well as the RNG type situations a raid encounter might put these players through. You can argue this affects all healers, but I would like to think this affects AST a bit more than it would WHM and SCH.

Well, let's go back to the simpler stuff for now and put the obvious out on the table.

1) Yep, you are correct, I did forget to divide the Expanded buff by two, will adjust that calculation a bit later down this post.
2) In your math, you did forget to take into account being able to Shuffle every time you want your "real" draw, and when you include shuffle into your math, you have a 55.5% chance to draw Balance or Arrow after your Royal Road.
3) I also do not also like the assumption that Arrow % increase = DPS % increase because there's a lot of factors that make haste less desirable (has no effect on DoTs) and more desirable (stacking with Huton / Greased Lightning makes it better!). However, since many players are making the assumption that the 1.5% Fey Wind gives = 1.5% raid damage, let's just do it for the sake of easy math.

The math below will be an attempt to balance at what potency Arrow / Balance should be to meet a 1.5% raid DPS check. Like before, I will be assuming you're RRing the first card in any your two draw set and you will be shuffling to get a DPS increasing card for the second draw.

So, let's consider the RR part first:

33.3% chance of getting Extend
33.3% chance of getting Enhance
33.3% chance of getting Expand

However, you wouldn't RR Balance because using Balance and then drawing another Balance in your second draw is equal to getting Extended Balance and Extended Balanced > Enhanced Balance. Therefore your probability changes to:

50.0% chance of getting Extend
16.7% chance of getting Enhance
33.3% chance of getting Expand

So, let's continue to use that A1S parse that was posted and go with the fact that the SMN contributed 19.72% of the party damage as our single target source. Let's consider X to be the value we need to meet our goal.

Extend = X * (30 uptime / 60 downtime) * 19.72% of raid damage * 55.5% chance to get Arrow / Balance * 50% chance for Extend = X * 0.0274
Enhance = X * 1.5 Enhance Bonus * (15 uptime / 60 downtime) * 19.72% of raid damage * 55.5% chance to get Arrow / Balance * 16.7% chance for Enhance = X * 0.0069
Expand = X * 0.5 Expand Penalty * (15 uptime / 60 downtime) * 100.00% of raid damage * 55.5% chance to get Arrow / Balance * 33.3% chance for Expand = X * 0.0231

So, now we solve for X.

0.015 = 0.0274X + 0.0069X + 0.0231X = 0.0574X
X = 0.015/0.0574 = 26.13%

So, in order for AST buffs to match Fey Wind's power, Arrow and Balance need to be buffed to 26.13%.

HOWEVER, consider the following:
1) In that parse, they managed to do 8,020 DPS to Faust and still took 2:34 to complete the fight. Based on what I've seen Faust you need approximately minimum 6200 single target DPS to break him. This means that chances are the OT stacked adds near Faust and was still pummeling Faust and giving the SMN additional DPS via Deathflare and Shadowflare.
2) Healer DPS for this fight will be lower as you will need to change one of the healers for AST.
2a) If you change the WHM to AST, you will most likely lose the 2% the WHM provided and your SCH will probably DPS slightly less to make up for the lost HPS. However, Synastry at an opportune time will probably give the SCH slightly more uptime on their DPS.
2b) If you change the SCH to AST, WHM contribution will probably drop to near 0% to make up for the lower HPS Aspect Benefic will bring compared to Fairy for "regen healing". Likewise, if your AST is DPSing on the same time frame that SCH is, they're damage will be a bit lower as they have 2 "no miss" DoTs (Combust + Combust II) compared to 3 from the SCH (Bio + Bio II + Shadowflare). While Malefic II is higher potency than Broil, Malefic II is subject to accuracy constraints. Like SMN, if you take into account Shadowflare is also pinging the adds, that'll be a further decrease. Gut feeling tells me AST raw DPS contribution would be 2% of raid damage in this case.
3) My math did not take into considering using Time Dilation or Celestial Opposition to extend buffs further
4) Arrow will most likely mean less to this group than Balance because of SMN / SCH DoTs and BRDs can't auto-attack while in WM.

So, despite my massive wall of text, we still don't actually have a real statistical model to calculate what the "appropiate" buff % to Balance and Arrow should because there is still a large amount of variables to the fight that is difficult to "math" for. If you want to expand on this model, you also have to consider the "well, should I shuffle Extend / Enhance and go for Expand and hope I draw a DPS card?" as well as the fact that being able to Spread a card beforehand make shuffling for Expand much more desirable.

TLDR: Lots of variables to consider, what's above is only a simple model of "balancing" AST DPS to other healer DPS that is no where near complete.

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The above is also assuming - the content is on farm and you don't need any other buff that the AST provides to clear it. This will definitely not be the case in progression content - which makes AST even less desirable as 10% on Arrow / Balance only gives an average party buff of 0.92% at this juncture.

Balancing ASTs buffs feels absolutely horrible and I don't think there's any easy way for S-E to do it.
Balancing ASTs healing is a lot easier and should probably be answered first, though I imagine there's a function where S-E wants AST to be slightly weaker and provide buffs to the party that makes them more desirable. That's a very very fine line at this point.

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Thank you for the explanation!

Also, where did my post go?

You're welcome~

For some reason, Richard's post to my wall of text was pruned and I'm not sure why. I personally felt we were making attempts to at least rectify the situation.

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This is a little overcomplicated. All you need to do is calculate the probability of not getting a card you want and inverting that to get the probability of the card you want showing up. Basically, 1 - (2/3)*(2/3) = 0.55555555555555 = 55.5%. It's also quite easy to calculate the chances of drawing the card you want if shuffle can't redraw a card: 1 - (4/6)*(3/6) = 2/3 = 66.6666666666% for getting either arrow or balance and 1 - (5/6) * (4/6) = 44.4444444444444% to draw a specific card using shuffle.

Thanks for this I haven't done statistical analysis for a while so I'm a bit rusty / trying to Google things to make sure I'm correct. I might need to pull out my old statistics text book soon if we keep this up >>;