Mathemagic! Put your favorite ROTMG math stuff here!

#44

0 because the others died remaxing the first.

#45

cba to update but in like 2016 i calc’d the fastest way to walk in rotmg

basically: ur gonna need a 100 mp pet, 8/8 trickster with t0 prism, and just keep running and teleporting

#46

#47

Yeah that sounds about right; but the trix only needs to be 3/8 in mp, speed and wisdom.

#48

Well I hurt my brain trying to figure this one out, so maybe someone can help me. There is an ongoing dispute among some in the community about “consistent damage.” I am on the side of “the damage range of a weapon doesn’t matter because dps rapidly approaches weapon avg due to RoF (and the Law of Large Numbers).” I would really like to see a mathematical analysis of how quickly dps approaches weapon avg (for maxed characters). That is, how many seconds does it take to get a 90-95% probability that your dps is within 1 of the weapons’ avg?

Key cases are:
Fallen vs. Condu: condu has 2x the damage range of fallen but about 1.5x the RoF.
Spirit vs. T12 dagger: spirit has 2.5x the damage range of T12, same RoF.

#49

Yeah even anecdotally tricksters are usually faster than ninjas given high enough mp heal.

If we use these basic assumptions:

  • t0 needs 60 mp
  • 100mheal pet heals 45 mp/s
  • trickster has 60 wis => 4.1 mp/s
  • each tp is ~11 tiles
  • trickster has 75 speed => 9.1 tiles/s

Then we get the number,
(running speed) + (tp'ing speed)
= [9.1 tiles/s] + [(4.1 + 45 mp/s) * (1/60 mp) * (11 tiles)]
= 18.1 tiles/s

which roughly speaking means you’re flying through the realm at around 1.5 screen lengths (with off-centered) per second.

Comparatively a speedy ninja with 60 speed will be travelling at 12.72 tiles per second.

Of course I oversimplify everything and ignore set builds (i.e. putting a candy ring + leaf hide on ninja), initial mp pool (i.e. if you have full mana on trickster, you can “burst” tp until you’re out) etc. but that’s beside the point, trickster number one in terms of speed.

An interesting question, however, would be to find the mp heal level that is the turning point where one becomes faster than the other. I.e. at what level will a trickster surpass the speed of a ninja, since only a 71 mheal pet is required to permaspeedy on a ninja while the higher the pet, the better for trickster.

Again using the assumptions in the bullet points above we could construct two equations: one measuring the speed in tiles/second for trickster and the other for ninja and find the intersection.

Since we’re assuming ninja to have constant speed, let’s just denote s(m)ninja= 12.72 where s(m) is speed as a function of mheal level.

For trickster, s(m)trickster = 9.1 + [(4.1+x)*(1/60)*(11)] where x is the mp/s corresponding to mheal level m.

There’s no actual formula for mp/s as a function of pet level and the trendline Excel gave wasn’t accurate so we’ll just guess values for x. A level 81 mheal gives 15.91 mp/s and so s(m)trickster = 12.76 tiles per second which is tad bit faster than a speedy 60 spd ninja.

But how about if the ninja was wearing better equipment, say a candy ring + leaf hide as before? Then the ninja will have 76 speed and be travelling at 14.512 tiles per second. Again we find that a level 92 mheal pet gives 26.20 mp/s so s(m)trickster = 14.66 tiles per second, a bit faster than the 76 speed ninja.

TL;DR:

  • If a permaspeedy 60 spd ninja races a trickster…
    • the trickster needs at least level 81 mheal to be faster than the ninja where trickster uses t0 prism, 60 wis, 75 speed.
  • If a permaspeedy 76 spd ninja (best spd equips) races a trickster…
    • the trickster needs at least level 92 mheal to be faster than the ninja.
#50

…but the trickster can get best speed equips in that second race too.
Actually, the cring would give speed but take away wis and mp, so it would give less advantage than ninja’s would. UB Spd might be better on trix. But equiping leaf hide would increase it a bit as well

#51

Yeah I wasn’t sure how to optimize trickster gear (i.e at what point is a mp/wis/speed build better?) and of course I didn’t include initial tp bursts.

#52

Here, let’s set up a race. Say… from the first middle vault to the oryx statue. Who’ll win?
/s

#53

noice math

just a few revisions: i cant be arsed to load rotmg but is the tp dist the highest you can get (w/o hacks)? off-center + hypotenuse to top left/right?

also: its not too hard to see that speed on gear >>>> wis on gear

cdirk is BiS, it’s the only weapon that gives stats, and its wis.
t0 prism is BiS
leaf armor is BiS
assuming the -10 wis isn’t detrimental, candy ring is BiS

ofc we’ll need to try out a few other combinations with more wis and less spd to make sure spd is the best

#54

Uh I got 11 tiles using the flash full screen hack (with those jiggly black tiles). So yeah tried rotating diagonally and couldn’t get past 11 tiles.

Guess we could try that combo and recalculate but I’m not gonna do it for a while, at least this weekend (I’m a math major, do enough of that shit already T_T).

#55

Seelpit’s thread on most amount of shots per second got me thinking about damage xD

What’s the highest DPS you can get in the game?

I think it’s:


Consume 4x (the +10 atk christmas consumables)
Consume 5x
Get boosted with + (Berserk and Damaging)
Inflict enemy with + (Curse and Exposed)
…all the while spellbombing as much as possible.

Pfiffel doesn’t have Exposed yet but here’s the picture w/out Exposed:

High Dps

2018-09-23_13-04-15
2018-09-23_13-04-15.png841x629 68.4 KB

Also I don’t think that they calculate ability DPS properly, because it barely changes when you include it on the graph.

All in all its over 30k DPS which is crazy enough alread x).

#56

I spent like 5 minutes trying to figure out how the weapon range fit into all of this until I realized you meant damage range.

But yes, this is interesting. I’ll think about it

edit: what distribution does the random variable follow? uniformly distributed?

#57

1 ogmur + 2 knights = one with no ogmur

#58

Here it is.

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Edit: I programmed a simulation (for the condu) just for fun, but when I ran it, it didn’t match up with the math.
Here’s my source code (Python 2.7.11)
image
Out of 10000 trials, there was NOT A SINGLE trial that failed. From the math above, you would expect around 500 trials to fail. Personally, when I got my final results in the paper above, I was very surprised by the large numbers. I’m suspecting the math is incorrect. What gives?

I'm struggling pls halp
I have conduct/wand of the fallen on a sorc, when is it better to use fallen?
#59

Currently one attempt runs until its close to the average and then checks how many shots its done. What you probably wanted to do is to simulate a fixed number of shots and then check if the average is \eps-close

#60

The math doesn’t suggest anything about the average, just how large N should be to be confident of success.

But I did check anyway and the averages were much lower than expected (like 50 for condu)

#61

Thank you so much for this! And what a shocking result: Condu does more consistent damage than Fallen! I think a lot of people will be surprised.

Although, the results on your paper require careful interpretation. You’ve shown that RoF is more important than base damage range for getting consistent damage over a long period of time. The N values you’ve found equate to almost 11.5 minutes for Condu on maxed Sorc (12.2 on Priest) and over 14 minutes for Fallen (over 15 on Priest). (BTW, your adjusted values do not take into account the 4 dex on Condu.)

Your simulation provides additional information:

I take you mean that most of the time, it takes about 50 Condu shots to reach average weapon dmg. I am guessing the reason this sounds counter to the paper N values is that our subjective threshold for “most of the time” is much lower than p = .95. It also seems somewhat like a median vs mean issue–N is more like a mean, and 50 shots is more like a median.

I wonder how the results would change if we lowered p to .9 or .67, or if we raised e to 2 or more? Is there a set of values where Fallen becomes more consistent, that is, where weapon damage range outweighs rate of fire?

Could we determine the p-values given a certain number of shots? This would be relevant for which weapon to use when you want to do a few thousand damage in a reliable about of time.

#62

I believe it is uniformly distributed. So it’s a single [dmg range]-sided die roll.

#63

No, intuitively, if condu is more consistent than fallen for one set of values, there’s no reason to believe that should change for another set of vaues.

I’m not trying to infer anything about the population. p-values aren’t of much use here unfortunately.

My computer simulation got much smaller answers all around, but it agreed that condu was more consistent than fallen and foul more consistent than spirit

I have conduct/wand of the fallen on a sorc, when is it better to use fallen?