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Experience by level

AhmetAhmet Wherever I wanna beMember Posts: 3,370 @@ - Legendary Achaean
This math has probably been done before, and\ it's relatively useless as xp/dps is never constant, but I was curious so I took some time out to see what the numbers boiled down to and figured I'd share. At the very least bashing dps might be interesting to some.

The following are values for the amount of time required bashing per level (assuming constant essence per dps) compared to a level 80 baseline (without crit pendant), as well as comparative bashing dps values (in parens), so 250% of the baseline breaks down to 2.5x the bashing time (this DOES take dps changes due to crits into account), and a value of (1.25) in parens would mean you were doing 125% of the damage of someone without crit chance. There are also values for crit pendant levels 1/2/3, compared to the same level 80 no-critpendant baseline. In other words, if you hunt at the same xp/dps it will take you 5.3 times as long to bash level 98 to 99 as it will 80 to 81.

Feel free to call me out and make me look like an ass if I made any mistakes.

Snippet: Dragons with lvl 3 crit pendants only do 2.7x the bashing dps as level 80s without (yes I said only)

Snippet: At dragon, going from no crit pendant to crit pendant is a 30% dps increase while bashing (ikr)

Snippet: A level 3 crit pendant cuts your bashing time from 80-99 down by 19.4% compared to no pendant

Baseline:
Level 76: 49.49% (1.18)
Level 77: 57.91% (1.19)
Level 78: 68.80% (1.21)
Level 79: 81.31% (1.23)
Level 80: 100% (1.25)
Level 81: 121.1% (1.27)
Level 82: 144.6% (1.30)
Level 83: 170.0% (1.32)
Level 84: 197.0% (1.35)
Level 85: 225.5% (1.39)
Level 86: 254.9% (1.42)
Level 87: 284.9% (1.46)
Level 88: 315.2% (1.51)
Level 89: 345.3% (1.56)
Level 90: 374.7% (1.61)
Level 91: 403.1% (1.68)
Level 92: 430.0% (1.75)
Level 93: 454.9% (1.82)
Level 94: 477.5% (1.91)
Level 95: 497.5% (2.01)
Level 96: 514.4% (2.13)
Level 97: 528.0% (2.25)
Level 98: 538.1% (2.40)
Level 99: 544.6% (2.56)
Level 100: 608.3%

1 crit Pendant:
Level 76: 47.84% (1.22)
Level 77: 55.92% (1.24)
Level 78: 66.35% (1.26)
Level 79: 78.32% (1.28)
Level 80: 96.17% (1.30)
Level 81: 116.3% (1.33)
Level 82: 138.6% (1.35)
Level 83: 162.7% (1.38)
Level 84: 188.2% (1.42)
Level 85: 214.9% (1.45)
Level 86: 242.5% (1.50)
Level 87: 270.4% (1.54)
Level 88: 298.5% (1.59)
Level 89: 326.1% (1.65)
Level 90: 353.0% (1.71)
Level 91: 378.8% (1.78)
Level 92: 402.9% (1.86)
Level 93: 425.1% (1.95)
Level 94: 445.0% (2.05)
Level 95: 462.3% (2.17)
Level 96: 476.7% (2.29)
Level 97: 488.0% (2.44)
Level 98: 496.0% (2.60)
Level 99: 500.8% (2.79)
Level 100: 558.0%

2 crit Pendant:
Level 76: 46.11% (1.27)
Level 77: 53.83% (1.28)
Level 78: 63.79% (1.31)
Level 79: 75.18% (1.33)
Level 80: 92.18% (1.36)
Level 81: 111.3% (1.39)
Level 82: 132.4% (1.42)
Level 83: 155.1% (1.45)
Level 84: 179.1% (1.49)
Level 85: 204.1% (1.53)
Level 86: 229.7% (1.58)
Level 87: 255.7% (1.63)
Level 88: 281.5% (1.69)
Level 89: 306.8% (1.75)
Level 90: 331.3% (1.83)
Level 91: 354.5% (1.91)
Level 92: 376.1% (2.00)
Level 93: 395.7% (2.10)
Level 94: 413.1% (2.21)
Level 95: 428.0% (2.34)
Level 96: 440.2% (2.48)
Level 97: 449.5% (2.65)
Level 98: 455.8% (2.83)
Level 99: 459.1% (3.04)
Level 100: 510.5%

3 crit pendant:
Level 76: 44.30% (1.32)
Level 77: 51.65% (1.34)
Level 78: 61.11% (1.36)
Level 79: 71.92% (1.39)
Level 80: 88.03% (1.42)
Level 81: 106.1% (1.45)
Level 82: 126.0% (1.49)
Level 83: 147.3% (1.53)
Level 84: 169.7% (1.57)
Level 85: 193.0% (1.62)
Level 86: 216.8% (1.67)
Level 87: 240.7% (1.73)
Level 88: 264.3% (1.80)
Level 89: 287.4% (1.87)
Level 90: 309.6% (1.95)
Level 91: 330.4% (2.05)
Level 92: 349.6% (2.15)
Level 93: 367.0% (2.26)
Level 94: 382.1% (2.39)
Level 95: 394.9% (2.54)
Level 96: 405.2% (2.70)
Level 97: 412.8% (2.88)
Level 98: 417.7% (3.09)
Level 99: 419.9% (3.32)
Level 100: 466.0%
Huh. Neat.
Jeslyn

Comments

  • AhmetAhmet Wherever I wanna beMember Posts: 3,370 @@ - Legendary Achaean
    This _is_ assuming that experience required per level hasn't been changed by obscene amounts in the recent past, of course.
    Huh. Neat.
  • SenaSena Member Posts: 3,957 @@ - Legendary Achaean
    I'm getting pretty different numbers, from a quick check (haven't redone your entire tables). Dragon with L3 pendant has ~1.9x the DPS of level 80 with no pendant, a L3 pendant only increases a dragon's DPS by ~18% (which means the total reduction in bashing time from <any level> to 99 can't be more than ~16%).

    It could be me that's making a mistake somewhere, though. How are you calculating average crit modifier?
  • MatiasMatias Member Posts: 73 ✭✭✭ - Distinguished
    Looking back at my dragon information, my xp per hour stayed consistent from 90 - 99 at 8-10%. I was bashing the same areas, therefore my hours bashing for each level was consistent too. I am either not understanding your information, or I believe it is wrong.
  • CitrusCitrus Member Posts: 84 ✭✭✭ - Distinguished
    edited February 2016
    Matias said:
    Looking back at my dragon information, my xp per hour stayed consistent from 90 - 99 at 8-10%. I was bashing the same areas, therefore my hours bashing for each level was consistent too. I am either not understanding your information, or I believe it is wrong.
    I haven't hit dragon yet, but the 3.5 levels I've gotten since I have been back 93-96ish, my xp per hour was pretty consistent too.

    Sena said:
    I'm getting pretty different numbers, from a quick check (haven't redone your entire tables). Dragon with L3 pendant has ~1.9x the DPS of level 80 with no pendant, a L3 pendant only increases a dragon's DPS by ~18% (which means the total reduction in bashing time from <any level> to 99 can't be more than ~16%).

    It could be me that's making a mistake somewhere, though. How are you calculating average crit modifier?

    And wow a L3 pendant at dragon is only an 18% DPS increase?  Isn't a L1 mace as Priest like a 25% DPS boost at any level?

  • AhmetAhmet Wherever I wanna beMember Posts: 3,370 @@ - Legendary Achaean
    edited February 2016
    Sena said:
    I'm getting pretty different numbers, from a quick check (haven't redone your entire tables). Dragon with L3 pendant has ~1.9x the DPS of level 80 with no pendant, a L3 pendant only increases a dragon's DPS by ~18% (which means the total reduction in bashing time from <any level> to 99 can't be more than ~16%).

    It could be me that's making a mistake somewhere, though. How are you calculating average crit modifier?
    function critToDps ( crit ) 
    	local dpsTab = {}
    	local dps
    	dpsTab[1] = crit ^ 5
    	dpsTab[2] = crit^4 - crit^5
    	dpsTab[3] = crit^3 - dpsTab[2] - dpsTab[1]
    	dpsTab[4] = crit^2 - dpsTab[3] - dpsTab[2] - dpsTab[1]
    	dpsTab[5] = crit - dpsTab[4] - dpsTab[3] - dpsTab[2] - dpsTab[1]
    	dpsTab[6] = 1 - dpsTab[1] - dpsTab[2] - dpsTab[3] - dpsTab[4] - dpsTab[5]
    	dps = (dpsTab[6]) + (dpsTab[5] * 2) + (dpsTab[4] * 4) + (dpsTab[3] * 8) + (dpsTab[2] * 16) + (dpsTab[1] * 32)
    	echo(tostring(dpsTab[1]+dpsTab[2]+dpsTab[3]+dpsTab[4]+dpsTab[5]+dpsTab[6]).."\n")  -- Always echoes 1
    	return dps
    end
    Where crit chance = ( level - 25 ) ^ 3 / 1000000
     
    My numbers were a slight bit off in the first post, but I'm still getting that dps increase from drag to drag with lvl 3 pendant is 27% increase and from 80 to lvl3drag is 2.6x

    It's also very possible that this math is completely wrong and I've made a mistake, but I double-checked cause a few numbers had me questioning, and didn't see anything weird.
    Huh. Neat.
  • EldEld Member Posts: 3,946 @@ - Legendary Achaean
    That calculation looks right to me, though it would be much simpler to just write it as
    dps = 1+crit+2*crit^2+4*crit^3+8*crit^4+16*crit^5

    Your 27% looks about right to me. Crit rate is .405 at 99, .465 with L3 pendant. DPS is base_dps*2.39 without pendant, base_dps*3.02 with L3. Comes out to about a 26.5% increase.

  • AhmetAhmet Wherever I wanna beMember Posts: 3,370 @@ - Legendary Achaean
    Eld said:
    That calculation looks right to me, though it would be much simpler to just write it as
    dps = 1+crit+2*crit^2+4*crit^3+8*crit^4+16*crit^5

    Your 27% looks about right to me. Crit rate is .405 at 99, .465 with L3 pendant. DPS is base_dps*2.39 without pendant, base_dps*3.02 with L3. Comes out to about a 26.5% increase.

    Your equation doesn't take into account the percentage of crits that end up being higher tier crits.
    Huh. Neat.
  • EldEld Member Posts: 3,946 @@ - Legendary Achaean
    Ahmet said:
    Eld said:
    That calculation looks right to me, though it would be much simpler to just write it as
    dps = 1+crit+2*crit^2+4*crit^3+8*crit^4+16*crit^5

    Your 27% looks about right to me. Crit rate is .405 at 99, .465 with L3 pendant. DPS is base_dps*2.39 without pendant, base_dps*3.02 with L3. Comes out to about a 26.5% increase.

    Your equation doesn't take into account the percentage of crits that end up being higher tier crits.
    Yes it does. For each level of critical n (n=0 for no crit, n=1 for critical, n=2 for crushing, etc), with crit rate c, the percentage of crits at that level or is c^(n). For each level except n=5 (world-crushing), the percentage of crits at exactly that level is c^n(1-c); for n=5, it's just c^n. Damage at each level is multiplied by 2^n, so the average DPS multiplier is
        dps = sum(2^n*c^n*(1-c), n=0...4) + 32c^5
               = (1-c)+2(c-c^2)+4(c^2-c^3)+8(c^3-c^4)+16(c^4-c^5)+32c^5
               = 1+c+2c^2+4c^3+8c^4+16c^5

    Could also just do

        function dps(c)
            d = 32*c^5
            for n=0,4 do 
                d = d + (1-c)*(2*c)^n
            end
            return d
        end

    Nothing wrong with your calculation, just suggesting cleaner ways to write the function because I had to write some stuff out to convince myself that yours was correct.

  • AhmetAhmet Wherever I wanna beMember Posts: 3,370 @@ - Legendary Achaean
    Eld said:

    Stuff
    Sicknasty, missed the halvings in your original equation.  Bootiful.
    Huh. Neat.
  • SenaSena Member Posts: 3,957 @@ - Legendary Achaean
    I see what I was doing now. I had the multipliers halved, but also had them multiplied by 1-crit (probably left in when I updated the spreadsheet at some point), applying the reduction twice.
  • KietKiet Member Posts: 3,263 @@ - Legendary Achaean
    edited February 2016
    Sena said:
    I see what I was doing now. I had the multipliers halved, but also had them multiplied by 1-crit (probably left in when I updated the spreadsheet at some point), applying the reduction twice.
    So the c rit numbers you said the other day were wrong? Not to call you out or something obviously, just double checking to know the right numbers
    Sena
  • SenaSena Member Posts: 3,957 @@ - Legendary Achaean
    Yeah, just corrected the numbers.
  • DochithaDochitha Member Posts: 1,413 @ - Epic Achaean
    Let us get L4-5 crit upgrade. @Tecton March promo pls. 
    Sarathai
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