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Originally Posted by bcbrown
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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.
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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.
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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!
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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.