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Thai_tong

Delve into daemonheim xp

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Hey, I've interested in finding formulae relating your skill level and the amount of xp you receive for completing a daily challenge. Some challenges are different so there is lots to investigate. I am most interested in the delve into daemonheim challenge because that is certainly the most rewarding at high levels so I think this is a good place to start. Of course I cannot test every level myself so I'm looking for your help in collecting a list of the xp at different levels. I wont need to know it at every level, just enough so that I can find a formula for it.

 

At the moment I've collected these figures

 

70 dungeoneering- 50699 xp

80 dungeoneering 67681 xp

88 dungeoneering- 83915 xp

91 dungeoneering- 93012 xp

93 dungeoneering- 97822 xp

96 dungeoneering- 102000 xp

97 dungeoneering- 107993 xp

98 dungeoneering- 107993 xp

99 dungeoneering- 113364 xo

100 dungeoneering- 113364 xp

104 dungeoneering- 124k xp

112 dungeoneering- 149944 xp

113 dungeoneering- 156823 xp

115 dungeoneering- 163k xp

116 dungeoneering- 163943 xp

120 dungeoneering- 178932 xp

 

I would prefer if you could give exact figures instead of rounding it to the neared 1000xp but it wont matter too much if the formula is a little off :)

Edited by Thai_tong

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At 97 Dungeoneering I gain around 102K exp per day, I'll update you in 20 minutes or so as to the exact number.


#KERR2016/17/18/19/20/21.

 

#rpgformod

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Level 70: 50,699

Level 88: 83,915

Level 93: 97,822

Level 100: 113,364

Level 112: 149,944

Level 113: 156,823



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97: 107,993.

 

96 is 102,something thousand.


#KERR2016/17/18/19/20/21.

 

#rpgformod

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I'll post the exact xp at 115 later, and 116 in a couple of days if nobody beats me to it.


Supporter of Zaros | Quest Cape owner since 22 may 2010 | No skills below 99 | Total level 2595 | Completionist Cape owner since 17th June 2013 | Suggestions

99 summoning (18th June 2011, previously untrimmed) | 99 farming (14th July 2011) | 99 prayer (8th September 2011) | 99 constitution (10th September 2011) | 99 dungeoneering (15th November 2011)

99 ranged (28th November 2011) | 99 attack, 99 defence, 99 strength (11th December 2011) | 99 slayer (18th December 2011) | 99 magic (22nd December 2011) | 99 construction (16th March 2012)

99 herblore (22nd March 2012) | 99 firemaking (26th March 2012) | 99 cooking (2nd July 2012) | 99 runecrafting (12th March 2012) | 99 crafting (26th August 2012) | 99 agility (19th November 2012)

99 woodcutting (22nd November 2012) | 99 fletching (31st December 2012) | 99 thieving (3rd January 2013) | 99 hunter (11th January 2013) | 99 mining (21st January 2013) | 99 fishing (21st January 2013)

99 smithing (21st January 2013) | 120 dungeoneering (17th June 2013) | 99 divination (24th November 2013)

Tormented demon drops: twenty effigies, nine pairs of claws, two dragon armour slices and one elite clue | Dagannoth king drops: two dragon hatchets, two elite clues, one archer ring and one warrior ring

Glacor drops: four pairs of ragefire boots, one pair of steadfast boots, six effigies, two hundred lots of Armadyl shards, three elite clues | Nex split: Torva boots | Kalphite King split: off-hand drygore mace

30/30 Shattered Heart statues completed | 16/16 Court Cases completed | 25/25 Choc Chimp Ices delivered | 500/500 Vyrewatch burned | 584/584 tasks completed | 4000/4000 chompies hunted

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Ok I've got it :D

I am still looking for xp rewards data to improve this estimate, particularly at low levels.

The reward xp is related to the base xp you would get for doing your highest floor. This makes sense because Jagex's plan was to make challenge rewards similar xp to what you would normally do. Grimy has the base xp for each floor in his dungeoneering xp spreadsheet https://docs.google....NDdXpKaGc#gid=3

He has manually entered values up to floor 40 and then used a formula to relate floor number and base xp for higher floors but it is a differential equation which clearly Jagex would not use. His formula predicted values must be close though because there is a very strong relationship between his figures and the reward xp (R2=0.9995 which should be 1 for a perfect relationship)

The relationship is Reward= 891.11+ 7.599B

Where B is the base xp for your highest floor. From the data you guys have provided this is off by a max of 2435 xp. A quadratic fit does not produce much better results so I'm sticking to a linear fit.

In the case where your dungoneering level is an even number, for example 80 then your highest floor is 40.5. Taking the average of floor 40 and 41 gives almost the same result as just floor 40.5

 

Grimy's formula is difficult to work with so I tried to use a polynomial to relate floor number and base xp. Neither a linear or quadratic relationship work well. I don't expect Jagex to use a higher order relationship than quadratic but it turns out that a cubic or quartic (degree 4) relationship work much better. To me this indicates that they don't use a polynomial but instead might have a formula like the one for the xp needed for a certain level. The best-fit cubic relationship is base xp= 6.536+ 54.35F+ 0.8515F2+ 0.07736F3. Where F is the floor number. This is off by a maximum of 66xp.

The best-fit quartic relationship is base xp= 82.59+ 31.14F+ 2.531F2+ 0.03477F3+ 0.0003491F4. This is off by a maximum of 13xp.

 

Combining these equations of reward as a function of base xp and base xp as a function of floor, and taking floor=(level+1)/2 the equation for reward xp becomes

Reward= 1641.91+128.04L+4.901L2+0.033692L3+0.00016581L4

Where L is level.

Comparing the predicted rewards to the data here I find that the prediction is off by a maximum of 7724xp at level 108. This is quite large but all the other errors are less than 2500xp.

 

Or for the cubic fit

Reward= 1149+209.97L+1.83817L2+0.734858L3

The predictions made by this are surprisingly far off

 

You may have thought that I could just fit a polynomial to the original data collected on this thread but that polynomial would be skewed because all the data here is for high levels. I tired this and the results for low levels is either ridiculously high or negative. The intermediate step of using Grimy's floor data which includes low levels reduces the bias to high levels.

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From the limited data sample that we have, it seems that there is always a jump in XP after a new floor is unlocked.

 

That leads me to believe that highest possible Dungeoneering prestige bonus is involved in the formula. How exactly prestige works isn't known either, as far as I know, so it might be nearly impossible to find out this formula.

 

Why do people always search for polynomial formulas anyway? A lot of formulas in RS are of exponential nature.

 

By the way, you can get pretty close matches with stuff like a*level*2^(level/40)+b where a and b are constants.

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163943 xp at 116. I'm not sure that is even an increase over the xp at 115 (which I forgot to note -.-).


Supporter of Zaros | Quest Cape owner since 22 may 2010 | No skills below 99 | Total level 2595 | Completionist Cape owner since 17th June 2013 | Suggestions

99 summoning (18th June 2011, previously untrimmed) | 99 farming (14th July 2011) | 99 prayer (8th September 2011) | 99 constitution (10th September 2011) | 99 dungeoneering (15th November 2011)

99 ranged (28th November 2011) | 99 attack, 99 defence, 99 strength (11th December 2011) | 99 slayer (18th December 2011) | 99 magic (22nd December 2011) | 99 construction (16th March 2012)

99 herblore (22nd March 2012) | 99 firemaking (26th March 2012) | 99 cooking (2nd July 2012) | 99 runecrafting (12th March 2012) | 99 crafting (26th August 2012) | 99 agility (19th November 2012)

99 woodcutting (22nd November 2012) | 99 fletching (31st December 2012) | 99 thieving (3rd January 2013) | 99 hunter (11th January 2013) | 99 mining (21st January 2013) | 99 fishing (21st January 2013)

99 smithing (21st January 2013) | 120 dungeoneering (17th June 2013) | 99 divination (24th November 2013)

Tormented demon drops: twenty effigies, nine pairs of claws, two dragon armour slices and one elite clue | Dagannoth king drops: two dragon hatchets, two elite clues, one archer ring and one warrior ring

Glacor drops: four pairs of ragefire boots, one pair of steadfast boots, six effigies, two hundred lots of Armadyl shards, three elite clues | Nex split: Torva boots | Kalphite King split: off-hand drygore mace

30/30 Shattered Heart statues completed | 16/16 Court Cases completed | 25/25 Choc Chimp Ices delivered | 500/500 Vyrewatch burned | 584/584 tasks completed | 4000/4000 chompies hunted

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I don't think the xp gained through dg daily challenges changes from 117-120.

 

Also it increases every odd level (or new floor), but I'm not sure why this does not happen at 119.


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It would make perfect sense if there was a jump when a floor was unlocked.

 

Why do people always search for polynomial formulas anyway? A lot of formulas in RS are of exponential nature.

 

By the way, you can get pretty close matches with stuff like a*level*2^(level/40)+b where a and b are constants.

I tried an exponential relationship of the form a*b^(c*level) but that didnt fit. I will try it again with a constant added. I don't know any exponential formulae in runescape that weren't added in EoC except for the effigy drop rate formula. High order polynomials should be a good approximation to any function because any function can be expressed as a polynomial.

 

Edit. I generally don't search for non polynomial functions because I don't expect Jagex to use anything more than simple functions. When I can't find an exact solution then a high order polynomial will be a good approximation.

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I know it isn't an exact formula but from myself, friends and dungeoneerers from clan the xp for the task seems to be roughly tied to a perfect 5 man large with max prestige of your top floor in dg. Hence why there is a pattern where by odd levels (floor unlocks) to even levels don't move much whilst even levels to odd levels jump a fair bit (new floor)


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It would make perfect sense if there was a jump when a floor was unlocked.

 

Why do people always search for polynomial formulas anyway? A lot of formulas in RS are of exponential nature.

 

By the way, you can get pretty close matches with stuff like a*level*2^(level/40)+b where a and b are constants.

I tried an exponential relationship of the form a*b^(c*level) but that didnt fit. I will try it again with a constant added. I don't know any exponential formulae in runescape that weren't added in EoC except for the effigy drop rate formula. High order polynomials should be a good approximation to any function because any function can be expressed as a polynomial.

 

Edit. I generally don't search for non polynomial functions because I don't expect Jagex to use anything more than simple functions. When I can't find an exact solution then a high order polynomial will be a good approximation.

 

XP required for a level formula, for example, is an exponential one. That could be very closely related to the formula you're looking for.

 

Polynomials can be fit for a finite number of points in a plane. Not all functions can be represented as polynomials. A lot of functions can be represented as power series, though (especially locally).

 

My problem with polynomial approximations is that it yields very silly-looking formulas, in lines of 0.89738497984736434x^2+6757.3579454x-46.46234786935237. There is no way that it was coded in like that; it's probably just exponential or something else.

 

I think Sy_Accursed's answer might be the right one; that's how Jagex supposedly balanced it.

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The xp formula is not exponential it is this http://www.mirekw.com/rs/RSDOnline/Guides/guide.aspx?file=Experience%20formula.html

 

Using Taylor series any differentiable function can be represented as an infinite polynomial (or well approximated with a high order polynomial).

We all realise that Jagex don't use high order polynomials, if I could find a simple function I would use it but I can't so I'll use a polynomial instead. Being a little off the true answer doesn't matter for my uses and polynomials are also easier to use than a summation. Finding the xp gotten from this task is quite a niche use so it isn't much to ask someone to type 8 digit numbers when they need it.

The xp from a perfect floor is a multiple of the base xp so we wont need to test every level for a perfect floor, we can continue using grimy's figures :)

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67,681 at 80 dungeoneering, to be exact.

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Though I know you've already determined it goes up with a new floor, it's still 107,993 at 98.


#KERR2016/17/18/19/20/21.

 

#rpgformod

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Since we now know xp only increases every 2nd floor I took another look at the

 

I took a closer look at grimy's data and where he uses a formula to predict floor xp for higher floors based on data for lower floors is a bit off. I took another look at the data comparing max floor xp and challenge xp. The challenge xp was nearly constantly 8 times the floor xp. I am removing the level 108 info someone provided because it sticks out like a sore thumb.

 

This is a graph of the difference between the previous floor xp http://puu.sh/2yRDb

 

So grimy's predictions seem to be off by almost a fixed amount.

 

It turns out that him underestimating by 247xp gives figures that best match the trend of [challenge xp]= 8*[base floor xp] so from now on I will use that figure to adjust floors 42+

We could even work backwards and get better figures for base xp by dividing the challenge xp by 8.

 

The tricky part still remains, to find the function relating floor and base xp. The graph for it is here http://puu.sh/2yTtW

I'm open to suggestions.

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171310 xp at 117.


Supporter of Zaros | Quest Cape owner since 22 may 2010 | No skills below 99 | Total level 2595 | Completionist Cape owner since 17th June 2013 | Suggestions

99 summoning (18th June 2011, previously untrimmed) | 99 farming (14th July 2011) | 99 prayer (8th September 2011) | 99 constitution (10th September 2011) | 99 dungeoneering (15th November 2011)

99 ranged (28th November 2011) | 99 attack, 99 defence, 99 strength (11th December 2011) | 99 slayer (18th December 2011) | 99 magic (22nd December 2011) | 99 construction (16th March 2012)

99 herblore (22nd March 2012) | 99 firemaking (26th March 2012) | 99 cooking (2nd July 2012) | 99 runecrafting (12th March 2012) | 99 crafting (26th August 2012) | 99 agility (19th November 2012)

99 woodcutting (22nd November 2012) | 99 fletching (31st December 2012) | 99 thieving (3rd January 2013) | 99 hunter (11th January 2013) | 99 mining (21st January 2013) | 99 fishing (21st January 2013)

99 smithing (21st January 2013) | 120 dungeoneering (17th June 2013) | 99 divination (24th November 2013)

Tormented demon drops: twenty effigies, nine pairs of claws, two dragon armour slices and one elite clue | Dagannoth king drops: two dragon hatchets, two elite clues, one archer ring and one warrior ring

Glacor drops: four pairs of ragefire boots, one pair of steadfast boots, six effigies, two hundred lots of Armadyl shards, three elite clues | Nex split: Torva boots | Kalphite King split: off-hand drygore mace

30/30 Shattered Heart statues completed | 16/16 Court Cases completed | 25/25 Choc Chimp Ices delivered | 500/500 Vyrewatch burned | 584/584 tasks completed | 4000/4000 chompies hunted

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