Hit point vs. Mana point gearing on a Manna Robe Magician

[Salaryman]

all these nerdy graphs and charts just steal a manastone and play on RED99

[Duik]

Better dead than red.

[Vivitron]

I have only bot maged, but mana over hp seems right to me. Being able to cast an extra coth from fm is a nice win for stabilizing coth engages.

I have a manna robe on my enchanter. If the raid needs me to have mana ASAP I can often get twitches or at least spot heals to cover robe clicks, so max hp isn't typically a major concern for that purpose. (That said he's hp geared for charming already, and enchanters aren't magicians.)

Counterpoint: I have survived a hit while quadding. It's rare to get hit and rarer still for gear to make a difference, but saving a quad would be big.

[Ripqozko]

Originally Posted by Vivitron [You must be logged in to view images. Log in or Register.]

I have only bot maged, but mana over hp seems right to me. Being able to cast an extra coth from fm is a nice win for stabilizing coth engages.

I have a manna robe on my enchanter. If the raid needs me to have mana ASAP I can often get twitches or at least spot heals to cover robe clicks, so max hp isn't typically a major concern for that purpose. (That said he's hp geared for charming already, and enchanters aren't magicians.)

Counterpoint: I have survived a hit while quadding. It's rare to get hit and rarer still for gear to make a difference, but saving a quad would be big.

gear makes a difference for that last statement, i made sure i had a 4k mana pool then i stacked resists and such for survivability. rest doesnt really matter.

[shovelquest]

Originally Posted by Duik [You must be logged in to view images. Log in or Register.]

Better dead than red.

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[Balimon]

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

Although converting variables into numbers can make the calculations easier to follow, it will ultimately be more helpful to have a final equation where everything is a variable, so you can plug in different health regen rates, for example, to see how that will change the conclusions. Let's start with the first equation from the section above:
0 = 3500 - 30 * (health_to_burn / 31) - (t - health_to_burn / 31) * 40
30 is the mana burn rate in the first section: 50 - 20, or mana_burn - mana_regen
31 is the health burn rate: 60 - 29, or health_burn - health_regen
40 is the mana burn rate in the second section: 50 - 10, because we're only clicking the robe once every other tick, since each two ticks we will regain 58 health.

Putting these variables back in we get:
0 = starting_mana - (mana_burn - mana_regen_one) * health_to_burn / (health_burn - health_regen) - (t - health_to_burn / (health_burn - health_regen) * (mana_burn - mana_regen_two)

We can unify the mana regen rates by observing that the mana regen in phase two is equivalent to the mana gain from clicking the robe scaled by how many ticks it takes to regain the 60 health cost:
mana_regen_two = 20 * health_regen / 60 = robe_mana * health_regen / robe_health
mana_regen_one = robe_mana

this gives us:
0 = starting_mana - (mana_burn - robe_mana) * health_to_burn / (health_burn - health_regen) - (t - health_to_burn / (health_burn - health_regen) * (mana_burn - robe_mana * health_regen / robe_health))

I'm not going to try to simplify that, but I will plot the graph of mana over time with Python:

def mana(
    t,
    starting_mana=3500,
    mana_burn=50,
    robe_mana=20,
    health_to_burn=2000,
    health_burn=60,
    health_regen=29,
    robe_health=60
):
    if t < health_to_burn / (health_burn - health_regen):
        return starting_mana - (mana_burn - robe_mana) * t
    mana_spent_phase_one = (mana_burn - robe_mana) * health_to_burn / (health_burn - health_regen)
    mana_spent_phase_two = (t - health_to_burn / (health_burn - health_regen)) * (mana_burn - robe_mana * health_regen / robe_health)
    return starting_mana - mana_spent_phase_one - mana_spent_phase_two

import matplotlib.pyplot as plt
import numpy as np

# Generate x values (time)
t_values = np.linspace(0, 110, 100)  # Adjust range as needed

# Calculate corresponding mana values
mana_values = [mana(t) for t in t_values]

# Plot the graph
plt.plot(t_values, mana_values)
plt.xlabel('Time')
plt.ylabel('Mana')
plt.title('Mana Over Time')
plt.grid(True)
plt.show()

Adding more mana shifts the whole graph upwards, extending the time until mana=0. Adding more health lengthens the first part of the graph.

If you have a Google account you can play around with the assumptions here: https://colab.research.google.com/dr...Yw?usp=sharing

One final note: although I'm assuming canni-dancing the manna robe, I'm not taking into account of medding for mana regen. If you'd like to so do, you can just adjust the mana burn rate per tick to account for that.

Thank you for all this! What an incredible amount of work you've done, so I finally had a chance to dig into your posts and play around with the graphs. It seems to me, after plugging in different numbers that 1 mana is at least twice as effective as hit points in delaying zero mana. Do you think that spam clicking the robe would change the results at all? Are those the results you're seeing as well?

[bcbrown]

Originally Posted by Balimon [You must be logged in to view images. Log in or Register.]

Thank you for all this! What an incredible amount of work you've done, so I finally had a chance to dig into your posts and play around with the graphs. It seems to me, after plugging in different numbers that 1 mana is at least twice as effective as hit points in delaying zero mana. Do you think that spam clicking the robe would change the results at all? Are those the results you're seeing as well?

I'm glad you appreciate the posts. Hopefully it's helpful in giving you a better understanding of the mana/health gearing tradeoffs.

Two things initially come to mind: first, without someone else checking carefully checking my calculations there's a good chance I made a mistake somewhere. If you read to the end of the thread that prompted you to reach out to me, you'll see an example of my fallibility. Second is the difference between the map and the territory. I made a bunch of assumptions, some more and less realistic. For example, canni-dancing for ten minutes while also doing everything else you need to do is clearly unrealistic. So it's always better to trust your real-life experiences over the predictions of a model. A model can only inform your estimates, not replace reality as it confronts you.

In terms of thinking about whether spam clicking would change the results, I would approach that through looking at that graph I posted. There's two sections, first where you have excess health and you're clicking the robe frequently, and then afterwards where you're just clicking to burn off regenerated health. You can think about the two sections as each having two attributes. First, there's the vertical distance traveled by the segment. Second, there's the slope of the line for that segment.

Increasing the vertical distance increases the length of the segment. Flattening the slope (lowering the number) increases the length of the segment. Each depends on the other: if you increase the vertical distance a constant value, it will extend the segment further if the slope is less. You can think about it like base jumping off a cliff: if you sink like a stone, it doesn't really matter how high the cliff you jump off, while if you can glide like a glider, your distance before you land is strongly influence by how high the cliff is.

In the first segment, the horizontal length kind of represents how much excess health you have. The slope is how much mana you're burning/regenerating. So if you're hitting the robe as fast as you can the first section will have a shallower slope, since you'll be regenerating more mana and therefore having a lower burn rate. However, the horizontal (time) length will be shorter, because you'll burn through your health faster.

So in each section, horizontal or vertical stretching depends on either gearing/buffing choices or behavior choices. In the first section, the health buffer depends on the gearing/hp-buffing, the slope depends on the behavior/regen-buffing. Once you know the slope, the health buffer will tell you the length of the segment.

In the second segment you're constrained by hp regeneration for how often you can click the robe, so there's not as many options where behavior can change the graph.

I know that didn't directly answer the question but did it help? Keep asking questions!

Originally Posted by Ripqozko [You must be logged in to view images. Log in or Register.]

good luck to yall with all that, if you want to move a whole raid fast you stack more necros. all i care about is the few fights where its competitive to coth quickly, rest doesnt matter if its .2 sec slower waiting on a necro to pump me. the competitive ones only your pool matters, after the first 5-8 coths you either won or didnt.

This is a much more thoughtful post than your initial response. Why you gotta be so mean at first? For what it's worth, I agree with you. Initial burst used well with good communication being more important than sustained mana generation is a reasonable position. But good communication can't be improved with better gear, and once your pool is sufficient it seems reasonable to optimize for longer scenarios. Finally, and somewhat defensively, I'll point out that I didn't type that all out just for the hell of it. Balimon specifically asked me for my thoughts.

Originally Posted by shovelquest [You must be logged in to view images. Log in or Register.]

Mage trying to mage-ana-dance while answering tells from 40 different players in the raid

Good objection and clear weakness in the assumptions. However, I also did not include any mana regeneration from medding. How about standing the entire time and clicking the robe 6 times a minute? You can also change the assumption to be only 3 times a minute, in which case both segments will have the same slope and the math is much simplified. More detail can improve the model.

Originally Posted by Salaryman [You must be logged in to view images. Log in or Register.]

all these nerdy graphs and charts just steal a manastone and play on RED99

Maybe if you had more intelligence than a gnoll or more charisma than a troll your server would have more players than I have fingers and toes.

[Balimon]

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

I'm glad you appreciate the posts. Hopefully it's helpful in giving you a better understanding of the mana/health gearing tradeoffs.

Two things initially come to mind: first, without someone else checking carefully checking my calculations there's a good chance I made a mistake somewhere. If you read to the end of the thread that prompted you to reach out to me, you'll see an example of my fallibility. Second is the difference between the map and the territory. I made a bunch of assumptions, some more and less realistic. For example, canni-dancing for ten minutes while also doing everything else you need to do is clearly unrealistic. So it's always better to trust your real-life experiences over the predictions of a model. A model can only inform your estimates, not replace reality as it confronts you.

I'm not sure how many other people on the forums are qualified to check your math, certainly not me, I can plug your equations in and make them work and beyond that my eyes glaze over. I agree that canni dancing for ten minutes is unrealistic for most people, although I know a few people who play that hardcore. Personally on raids I would canni pretty much constantly while I wasn't doing anything else.

In terms of thinking about whether spam clicking would change the results, I would approach that through looking at that graph I posted. There's two sections, first where you have excess health and you're clicking the robe frequently, and then afterwards where you're just clicking to burn off regenerated health. You can think about the two sections as each having two attributes. First, there's the vertical distance traveled by the segment. Second, there's the slope of the line for that segment.

Increasing the vertical distance increases the length of the segment. Flattening the slope (lowering the number) increases the length of the segment. Each depends on the other: if you increase the vertical distance a constant value, it will extend the segment further if the slope is less. You can think about it like base jumping off a cliff: if you sink like a stone, it doesn't really matter how high the cliff you jump off, while if you can glide like a glider, your distance before you land is strongly influence by how high the cliff is.

In the first segment, the horizontal length kind of represents how much excess health you have. The slope is how much mana you're burning/regenerating. So if you're hitting the robe as fast as you can the first section will have a shallower slope, since you'll be regenerating more mana and therefore having a lower burn rate. However, the horizontal (time) length will be shorter, because you'll burn through your health faster.

So in each section, horizontal or vertical stretching depends on either gearing/buffing choices or behavior choices. In the first section, the health buffer depends on the gearing/hp-buffing, the slope depends on the behavior/regen-buffing. Once you know the slope, the health buffer will tell you the length of the segment.

In the second segment you're constrained by hp regeneration for how often you can click the robe, so there's not as many options where behavior can change the graph.

I know that didn't directly answer the question but did it help? Keep asking questions!

Noted, I'll play around with it some more. It didn't answer all my questions, however it did give me a better idea of what I was working with. I knew that hit points were weighted heavier with a manna robe, and I knew that past 3500 mana (7 CoTH's, as other have mentioned is sort of the magic number) hit points should have a different weight.

While I was right, it wasn't as strong as my gut believed, I'm glad to know that 1 mp = 2hp. What's interesting to me about this result is that it's not obvious considering we only knew that 3hp = 1mp or that 4hp > 1mp before. Calculating in standing regeneration really is the 'X' factor that allows us to see a more clear vision of how the stats are weighted this is admittedly obscure situation since no one plays mages much (especially on blue). I think on green people still do use mages fulltime on raids in ToV for example.

In regards specifically to the essay that I wrote where I was curious if two HGL's were actually an upgrade considering they weren't a straight 3 to 1 hp to mp ratio, I traded 75 mana for 163 hit points. This is indeed a minor upgrade according to your calculations, I always 'felt' this, and now I can know this. Thank you!

Random thought about standing regen, robe, and CoTH: In a CoTH race situation like Vulak, in the time it takes to cast CoTH 7 times with 3500 starting mana, you would click the robe 7 times, for 140 mana and regen 17.5 ticks at 21 standing mana regen is 367.5 mana, or 507.5 mana. Draw your own conclusions.

[bcbrown]

Originally Posted by Balimon [You must be logged in to view images. Log in or Register.]

While I was right, it wasn't as strong as my gut believed, I'm glad to know that 1 mp = 2hp. What's interesting to me about this result is that it's not obvious considering we only knew that 3hp = 1mp or that 4hp > 1mp before. Calculating in standing regeneration really is the 'X' factor that allows us to see a more clear vision of how the stats are weighted this is admittedly obscure situation since no one plays mages much (especially on blue). I think on green people still do use mages fulltime on raids in ToV for example.

How did you reach the conclusion that 1 mp = 2 hp? That's not what I took away from my analysis.

[loramin]

Bcbrown, your posts were ... long. Too long for me to review.

But I will point out that this whole calculus has been done already a ton in this forum (and on Reddit too I think) ... only with Shaman cannibalizing (both with and without "cann dancing", ie. trying to catch med ticks).

Obviously Mana Robe isn't exactly the same as casting Cannibalize (I through IV) ... but the all the math should be basically the same, with just a couple of the initial numbers changing.

One simple way to verify your numbers is to find one of those calculation threads, take someone else's calculations, plug the Mana Robe numbers in, and see if you get similar numbers to your's.