Statistical Analysis of RotMG Character Stat Distributions

#26

Obviously scripted, how much did OB pay you?

Also does anyone wanna calculate the odds of rolling a max life character?

#27

I’m not great at it, but my take would be…
100, 130, 150, or 200 max HP doesn’t matter, since they all need 570 HP to max.
Considering you get 20 increases in HP, you’ll need to have at least one 30 roll unless you have only 29 HP rolls.
If you were to only go from the flat 29 increases, you’ll have 20 level ups with a 2/21th chance of getting enough; so, (2/21)^20 ≈ 3,768894828730E−21; or about a one-in-265-quintillion chance, if I’m not mistaken.

Of course, there’s a variety of other combinations that also work, and considering I’m lazy not as qualified as father OB, I’m leaving that up to him ^u^

#28

Couple of curiosities that my friends came up with and I was too lazy to calculate:

Chance of insta 8/8 character?

Chance of insta 1/8 wis pally?

#29

Your first question? 0.
Your second question? lim(x);x–>0

#30

-sigh-

I did:

 

Both are zero:

  • Nobody can ever insta 8/8 because no class gains def upon level up.
  • Pally cannot insta 1/8 wis since its cap is 75 wis and the best a fresh-20 pally could have is only 48 wis.
    • #31

    Hey, well, I got pretty close. That’s an achievement I’ll take .w.

    #32

    Right, erm…

    I wasn’t thinking very much, was I

    #33

    Your analysis fell apart early: you only get 19 increases in HP, not 20. As a result, you need that +30hp roll Every. Single. Time. That’s a “1 in 1119” occurrence.

    Still, you tried, and that alone is worth applauding. :clap:

     

    S’okay! Topics that make people think keep everyone on their toes.

    The closest you can get to an insta-8/8 is that it is theoretically possible to insta-4/8 a Paladin (their low stat caps certainly play a major role here), but the odds of that are tiny (and easily left as an exercise for the reader, given the stats posted at the end of post #2 in this thread).

    #34

    ptsd intensifies

    Forgive me if I’m blind again, but I’ve always wondered if you had a goal (let’s say, non-negative hp roll) and could stop before reaching level 20 by looking at thet odds of achieving that goal as levels went on.

    Ok that was non english let me try again with example xD

    • you want a non-negative hp roll
    • at lvl 14, suppose you could calculate that your chances of getting a non-negative hp is 10%
    • you could then decide if you wanna reroll and not have to go to lvl 20, or continue to lvl 20
    #35

    I think I know what you’re going for:

    The analysis I present in the OP handles the special case of lvl = 1 and y = ±0 (which is the only value of y we need to consider when lvl = 1).

    It simplifies things to think about your question in terms of (z - y); that is "at my current level, what are the odds I can improve my current roll by a particular amount before I hit level 20? For that particular question, the above forms of analysis can be used, just for fewer levelups than 19 — if you’re only level 10, you only level up 10 more times, if you’re level 5, you level up 15 more times, etc. So in a generalized case, we can restate the question as:

    Let’s define ΔHP = z - y and x = 20 - lvl:

    For you kiddies thrown by the triangle thing, don’t be. That’s the Greek character “delta” (an upper-case one, to be exact). In calculus, delta- is used to signify “change”, so ΔHP is basically saying “change in HP”. For the other variable, I just use x because math teachers always label the x axis with an x because…well, it’s the x axis. (Duh.)

    Some simple cases to get out of the way:

    x = 19
    Yay, you're only level 1. Please go consult the tables in the OP.
    ΔHP = 0:
    Double yay, you're happy with your current roll and just hope it doesn't get worse. Regardless of your current level, the probability of you maintaining your current roll are generally P = 50%...always slightly higher, in fact, but never by more than a few percentage points, so just think "50-50 chance" and run with it.
    ΔHP = 5x
    Ahh, you want to win out, so to speak — the perfect finish, get a +30hp levelup every time until you hit level 20. The probability here is P(x) = (1/11)x. You're level 16? x = 20-16 = 4, and P(4) = (1/11)4 = 0.0000683.... Trust me, the odds here go down quickly.
    x = 0
    Why are you asking this? You're already done levelling up! P = 1.000 for ΔHP = 0 and P = 0.000 for all other values of ΔHP. (In other words, you got what you got and it can't change any more, so move along.)
    For other values, you can go back to the "cumulative distribution function" equation I posted in the OP, but the "sqrt(95)" term becomes "sqrt(5x)". It's not ugly, but it does get tedious.

    So, I tell you what. If I get some time over the weekend, how about I fire up some spreadsheets and answer that question for you?

    [To be precise, I’d be answering the Other Other Question, not the Other Question or the Original Question.   OB]

    Coming Soon to an Academy Near You: "This Is How We Roll"
    #36

    Not relevant for the thread, bur now I feel happier for my last ninja that got a +46hp roll :smiley:
    Hope I still had the print for proof…

    #38

    Yes please, sir! That would be a very interesting and educational read for sure :slight_smile:

    Would love to be able to have some benchmark and systematically level in a way where I can mentally track how the roll is going.

    #39

    Huh. That was easier than I thought.

    More data later, but here’s some tasty morsels for now:

    ΔHP Level 19 Level 15 Level 10 Level 5 Level 1
    +40 <0.001% 0.045% 0.181%
    +35 0.013% 0.205% 0.575%
    +30 0.112% 0.746% 1.577%
    +25 <0.001% 0.632% 2.231% 3.766%
    +20 0.156% 2.503% 5.592% 7.912%
    +15 1.865% 7.442% 11.946% 14.761%
    +10 9.236% 17.361% 22.080% 24.678%
    +5 9.091% 26.774% 32.863% 35.796% 37.297%
    +0 54.546% 52.732% 51.964% 51.612% 51.436%

    Note ΔHP is the desired improvement in HP from your current point. You need to know your current roll; compute the difference between that and your desired end point, and use that difference. Example: if I have a +5HP roll at level 15, there is a 9.236% chance I’ll finish at +15HP (as 15-5 gives a desired ΔHP of 10).

    #40

    A splendid history of posts bundled overhere.

    Thank you OB for putting your wandering mind to RotMG probabilities again. It is always a joy to read!

    Of course also a thank you to everyone who has asked questions that warranted answers.

    #44

    69 votes and 21 comments so far on Reddit
    Wow redditor is lucky