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Kenero wrote on 2011-01-30 23:10
Red stacking does make sense, seeing how it gets less bonus per blade than a 2h.
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qaccy wrote on 2011-02-08 08:15
Something I wanted to bring to your attention in here:
[Image: http://img141.imageshack.us/img141/1449/specialsd.jpg]
Came from the talk page for Special Upgrades on M-World Wiki (
link). Anyone here happen to know why, or more importantly, how the values in the above table and the ones posted in this thread are so different? The table from the Wiki seems to be much lower on the breakeven points across the board.
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Taliya wrote on 2011-02-08 11:49
Quote from qaccy;325519:
Something I wanted to bring to your attention in here:
[Image: http://img141.imageshack.us/img141/1449/specialsd.jpg]
Came from the talk page for Special Upgrades on M-World Wiki (link). Anyone here happen to know why, or more importantly, how the values in the above table and the ones posted in this thread are so different? The table from the Wiki seems to be much lower on the breakeven points across the board.
Because Justified still isn't convinced that R upgrades stack when dual wielding.
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qaccy wrote on 2011-02-08 14:09
But...I wasn't talking about just dual wield >_> Why's everything else so much lower?
For instance, the breakeven point for 2handers right now is 390 in this topic, but on the Wiki's table it's only 369. That's pretty significant IMO.
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Justified wrote on 2011-02-08 17:02
Quote from qaccy;325687:
But...I wasn't talking about just dual wield >_> Why's everything else so much lower?
For instance, the breakeven point for 2handers right now is 390 in this topic, but on the Wiki's table it's only 369. That's pretty significant IMO.
I only calculated for 3rd and 6th upgrades, so it's actually 390 vs 362.
In any case as I illustrated in an earlier post...
Quote from Justified;301063:
390 + 21 = 411 Max (Criticals 30% x 150% = 184.95) = 595.95 average damage
390 = 390 Max (Criticals 30% x 176% = 205.92) = 595.92 average damage
390 is indeed the break-even point.
I don't know how/what/why they did whatever they did to get their numbers, but this is why I don't like accepting things without proof and explanation.
It is possible they included Minimum Damage and Balance somehow (R-Type benefits since bonus always hits Max), but seeing as how people can have vastly different Min/Bal, I don't see how that can be done practically.
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hylianblade wrote on 2011-03-03 06:38
I'm not sure if this would be considered necro-bumping, but that's my table and the calculations are as follows (with mathematical derivation included):
Assumptions: 80% balance, 30% critical rate, Rank 1 Critical Hit
Pmax = Previous Maximum Damage (Before Special Upgrade)
Pmin = Previous Minimum Damage (Before Special Upgrade)
Smax = Maximum Damage added by S-type Upgrade
Smin = Minimum Damage added by S-type Upgrade
Rdamage = Crit damage added by R-type Upgrade
S-type Average Damage = R-type Average Damage
Replace with basic Average Damage formula
Min * (1 - Balance) + Max * (Balance) + Max * Critical Rate * Critical Damage = Min * (1 - Balance) + Max * (Balance) + Max * Critical Rate * Critical Damage
Substitute Min, Max, Balance, Critical Rate, and Critical Damage with their appropriate values for each version
(Pmin + Smin) * 0.2 + (Pmax + Smax) * 0.8 + (Pmax + Smax) * 0.3 * 1.5 = Pmin * 0.8 + Pmax * 0.8 + Pmax * 0.3 * (1.5 + Rdamage)
Expand terms with Distributive Property and regroup with Associative Property
(Pmin * 0.2 + Pmax * 0.8 + Pmax * 0.3 * 1.5) + (Smin * 0.2 + Smax * 0.8 + Smax * 0.3 * 1.5) = (Pmin * 0.2 + Pmax * 0.8 + Pmax * 0.3 * 1.5) + Pmax * 0.3 * Rdamage
Subtract (Pmin * 0.2 + Pmax * 0.8 + Pmax * 0.3 * 1.5) from both sides; Apply Distributive Property in reverse to factor out Smax
Smin * 0.2 + Smax * (0.8 + 0.3 * 1.5) = Pmax * 0.3 * Rdamage
Divide both sides by 0.3 * Rdamage
(Smin * 0.2 + Smax * 1.25) / (0.3 * Rdamage) = Pmax
Which shows that the equivalency can be expressed solely as a value of maximum damage before the special upgrade, calculable without any input of player stats.
Edit: Now that I've looked at Justified's math, the reason for the discrepancy is that he somehow decided that weapons always hit 100% of their max.
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Sneakiest wrote on 2011-03-03 21:06
It concerns me that the first page seems to re-validate the proposed equation with several testimonials.
We start our equations with the same premise, except I use average damage and you use max damage. You skipped a few steps in the original post, but I feel that was wise for the sake of brevity and the resulting equations looks clean. However, when I put these numbers into my equation, the results are different.
(average with s) + (crit bonus w/ s) = (crit bonus w/ r) + (Average damage)
avg + S avg. + 0.45(average+S avg.) = 0.3(avg.)(1.5+r) + Avg.
1.45(S avg.) + 0.45avg = 0.45avg.+0.3r(avg)
1.45(S avg.)=0.3(avg)(r %)
I will complete this for bows below (if you don't have 80 balance you shouldn't even overupgrade a bow, lol. And it's pretty fair to assume that bow users aim for 30% crit--especially elves.)
g13
xxxx(average damage eq.)
1.45(10+0.8[21-10]) = 0.3(avg)(.26)
1.45(18.8)=0.078(avg)
0.078(avg)=27.26
Avg= 27.26 / (0.078)
Breakeven Point = Average Damage of 349.487179487
Example of breakeven damage with bow before upgrades:
220-370, better adding S type
270-370, better off with R-type (assuming 30% crit rate on opponent)
That said, I feel that your Special Considerations of "Average Damage < Consistent Damage" and "Sometimes you need to crit hard" really sum it up best.
Also, if you believe that Critical hits really add 150% of Max damage rather than multiplying the Weighted damage by 250% then the breakeven point would lower further, eventhough S type would also receive a greater boost from crits.
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hylianblade wrote on 2011-03-03 21:43
Quote from Sneakiest;358111:
Also, if you believe that Critical hits really add 150% of Max damage rather than multiplying the Weighted damage by 250% then the breakeven point would lower further, eventhough S type would also receive a greater boost from crits.
This has been tested and proven to be true. Refer to my previous post for the correct calculation method for S/R equivalency.
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Fracture wrote on 2011-03-03 22:53
Quote from Sneakiest;358111:
Also, if you believe that Critical hits really add 150% of Max damage rather than multiplying the Weighted damage by 250% then the breakeven point would lower further, eventhough S type would also receive a greater boost from crits.
...You do realize, right, that adding 150% of damage is the exact same thing as multiplying damage by 250%?
100 + (100*1.5) = 250
100*2.5 = 250
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hylianblade wrote on 2011-03-03 23:00
Quote from Fracture;358273:
...You do realize, right, that adding 150% of damage is the exact same thing as multiplying damage by 250%?
100 + (100*1.5) = 250
100*2.5 = 250
It's not, because it's 150% of MAX DAMAGE. rand(min~max, balance) + 1.5 * max != 2.5 * rand(min~max, balance)
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Justified wrote on 2011-03-03 23:16
hylianblade's calculations look right.
When I tried to include minimum damage and balance, I didn't distribute it out as nicely so I didn't have a clean formula like his. So his calculations would be correct for average damage, while mine is only valid for potential damage.
On a side note, I am curious why ( 0.2 * Min + 0.8 * Max ) is generally accepted as the formula for average damage. I haven't really done much in the area of probability density, but how does that reflect a bell curve of an unknown standard deviation around the 80th percentile?
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hylianblade wrote on 2011-03-03 23:39
Quote from Justified;358293:
hylianblade's calculations look right.
When I tried to include minimum damage and balance, I didn't distribute it out as nicely so I didn't have a clean formula like his. So his calculations would be correct for average damage, while mine is only valid for potential damage.
On a side note, I am curious why ( 0.2 * Min + 0.8 * Max ) is generally accepted as the formula for average damage. I haven't really done much in the area of probability density, but how does that reflect a bell curve of an unknown standard deviation around the 80th percentile?
Max * Balance + Min * (1 - Balance) is actually the formula for median damage. This is clear when you start considering situations like 0% balance, or 100% balance (for magic). While it's somewhat fallacious mathematically to use this with what is essentially a mean calculation when you incorporate crit, calculating the actual arithmetical mean damage would both require data that I don't personally have in order to get a clearer picture of the nature of the bell curve, and also be mathematically much more involved.
As far as the formula itself, it's just a standard weighted average, re-expressed mathematically to make it easier to work with.
(Max - Min) * Balance + Min = Max * Balance - Min * Balance + Min = Max * Balance + Min - Min * Balance = Max * Balance + Min * (1 - Balance)
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Justified wrote on 2011-03-04 00:06
Yea, I understand how the formula we use was derived, it's just that in practice it doesn't seem to follow that kind of distribution.
That's another reason I like to work with just the maximum damage (the main reason being laziness :P)
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hylianblade wrote on 2011-03-04 00:38
Yeah. It's an average, just maybe not the average you want depending on the situation. Median is great for estimating where most of your hits will lie, but it doesn't give the most accurate picture of damage over time. Which is why it's slightly fallacious to use it when averaging in crit, because when you start calculating normalized damage per hit, you really ought to be using an arithmetic mean, not a median. But median is what we have and so that's what we use. If anything, the mean would lie closer to the 50% mark of your damage range--thus its effect on the equivalency calculation would be to lower the equivalency point.
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Sneakiest wrote on 2011-03-06 23:58
Quote from hylianblade;358182:
This has been tested and proven to be true. Refer to my previous post for the correct calculation method for S/R equivalency.
Alright I will trust the crit bonus modifier. I hope this really is true, kind of justifies communal lust for max damage enchants.
It seems easy enough to start with a large damage range low balance char, say 20% balance 20-120 damage and see if all of the crits land within 200-300, but frankly I have never gotten off my ass with most damage calculation verification experiments. Koo I guess my bows are ready for some White UG Stones :>