A Brief Angry Message

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I am not dead. Here’s what happened. My life has been kind of eventful lately. Mostly in good ways, mainly unexpected ways, but also some very stressful ways. Because June is one of those five week months (by the way I count), I decided to take the first week off. I usually post a little update when I do that, I know. Sorry about that. I had to semi-unexpectedly go out of town and several personal matters distracted me. In addition, some problems with my ISP actually knocked out my internet access for several days. Again, sorry about that.

I’m still on track to deliver the feature content you know and love this month. Wednesday will see a nice, shiny new article. Next Monday, Megadungeon will return with a discussion of doors and setting DCs. Sorry Megadungeon went on a forced vacation.

The Sailor Moon charity drive will start a little later in the month. There’s been a slight problem that, hopefully, will get resolved quickly so as not to prevent the event from happening. I will keep you posted on that.

Meanwhile, as part of a project, I’ve been playing with some probability math and it occured to me that probability and statistics is somewhat arcane to some GMs. That’s okay because game systems (theoretically) do most of the math anyway. But if you guys would like an article thinking through a specific probability question from the standpoint of an interested layperson as a way to discuss how to understand probability math in RPGs, post a comment below and let me know. Otherwise, I’ll see you back here on Wednesday.

47 thoughts on “A Brief Angry Message

  1. I think it would be AMAZING for you to do a post on statistics and probability in relation to game mechanics. I’m not sure what you had thought you might discuss in such an article, but I definitely think it would be a great topic. I know that there have been TOO MANY times that I had to explain to my players that rolling 2d6 is different than rolling 1d12 and ignoring/re-rolling a 1.

  2. I’d be interested in an article on dice rolling and probabilities and how the mechanic you choose would change your game.

  3. Glad you are Not Dead.

    Somewhat ambivalent on the statistics article. I’m sure you could make it interesting, but I feel that people tend to get hung up on statistics sometimes.

    • Second. I like statistics, but not sure what positive, usefull conclusions it could result in.

  4. Only if you point out the high variability of a flat d20 roll. People get too caught up on expected value, and neglect the variance.

  5. If you’re going to talk about how to use probability to achieve whatever effects you actually want to see in games from a design perspective, that sounds pretty cool. I’ve thought a lot about it before when designing different mechanics for encounters and for general game mechanics.

    If the article would just generally talk about probability and statistics, and how games implement them loosely, then I feel like there’s a;ready a lot out there that talks about that, but I haven’t actually looked into it, so I that may just be my impression.

    • I agree. I’m sure it would be mroe than just “Here’s the chance of rolling a three on 3d6,” but dice math isn’t that hard to get a handle on, for the most part, and it’s not something that I see needing a unique perspective on. I’d want to see an article about how different curves affect the way a game feels, or something along those lines.

      But who am I kidding, I’ll read it no matter what.

  6. Yep, I would definitely like to hear what you have to say about probability and statistics because your articles make me think. Since I’m designing my own RPG, I’m playing with probability and numbers quite a bit.

  7. Running a system based on a 3d6 bell curve I’m always finding trouble giving bonuses/penalties because they get so far out of whack so easily. Happy to hear anything you want to put out there about statistics, sure!

  8. Ooooo! A perfect opportunity to ask exactly how the math works out so that the “average” hit die rolls in 5th edition are always half+1! Why is that?

    • Because the devs rounded them up, instead of down.
      Take a d6, for example. The possible results are 1, 2, 3, 4, 5, and 6. Sum them up, and you get 21. Divide by 6, and you get 3.5. This means that the average on a d6 is 3.5. If you round it to the nearest whole number, you get 4.

      This also means that choosing whether to roll or not is a real choice. You have the choice between guaranteeing a certain amount of HP each level, or rolling for it. Rolling will, on average, give you less HP (0.5 HP per level, so 9.5 HP by level 20), but you have the chance of rolling higher.
      Statistically, it doesn’t make sense to roll, ever. The chance of breaking even over all 20 levels is between 11 and 27 %, depending on your class (lowest being d6 hit dice, highest the barbarian).
      But it’s more choice than rounding down, where you’ve got a 74 % chance of getting at least the average (rounded down) as a barbarian, and about 90 % as a wizard. At least this way, there’s a chance of gambling your way to a better score as the d10 and d12 classes.

  9. Yes, lay it down for us Angry, yet another reason to extol the educational virtues of RPGs.

  10. Thanks for the update, Angry! A stats article for the layman sounds great. Statistics is one of the most counterintuitive fields of mathematics.

  11. Sorry things’ve been stressful. Stress is bad.

    I’d like to see your explanation of D&D stats. I have a pretty solid understanding of dice probabilities and such (not amazing, but good enough), but I’m sure I’d learn more. I’m even surer that something you write on the topic will be something I can reference when discussing dice statistics – “No, see, it works this way – go read this explanation by this guy who’s better at explaining things than I am.”

    On a related note, http://anydice.com/ is amazing.

  12. Would prefer an article about something else than probability math more, honestly. Unless you find something rather specific you want to highlight, maybe a detail people often overlook?

    • Well, one thing I found out by doing some probability math is that rolling for HP in 5e isn’t worth it. The class with the best chance of rolling better than the average (barbarian) has only a 27 % chance of breaking even (or higher) by rolling, and the average from rolling is 8 % higher. For wizards and sorcerers, the chance of breaking even is only 11.4 %, and you lose an average of 15 % of your HP by rolling.
      It’s certainly possible to get slightly more HP as a barbarian when rolling, but it’s very unlikely.

  13. I think an article about dice and probabilities might help highlight why it is a bit silly to rely on dice rolls (especially D20 rolls) to resolve certain situations. For example, it simply does not make sense to resolve an arm wrestling contest between a farmer with a strength of 12 and a body builder with a strength of 18 by making opposed strength checks… the variability on the D20 compared to the bonuses added is one many reasons.

    As you alluded to on twitter, I also think it would be helpful for DMs and players to understand the approximate equivalence between “advantage/disadvantage on a D20 roll” and a D20+/-? for estimating the likelihood of success on a given check.

    Finally I think it would be interesting to know how the “exploding dice” used in some systems can impact dice roll probabilities.

  14. I am going to be the lone voice that says “Boo statistics, boooooring, do something else.” Just in case you need an excuse to take a longer break.

  15. I would be really interested in an article about probability related to RPGs. I taught myself the equivalent of a college course on probability about 8 years ago in order to design the perfect loot distribution system for my WoW guild (short version: I created a mechanically perfect distribution system and then subsequently learned a ton about human psychology while trying to figure out why it failed), so I would love to get a thorough breakdown of its use in RPGs. I’ve always been fan of Alternity’s use of dice, where you roll a d20 and then modify the result with the roll of another dice (usually a d4 through d12), created a nice bell curve of the results instead of a linear line the way a straight d20 does.

  16. As a current actuarial science student, I’d love to read an article about the probability math behind rpgs, especially to see if my own homemade calculations (I sometimes calculate a few rough expected values to see how winnable an encounter I’m planning actualy is) are correct or if I’m missing something.

    Also, glad to know you’re alive!!

    • Oh hey, same thing here! Except my school calls it biostatistics which is pretty rad. I would love to see more numbers on the internet.

  17. I would also like an article on statistics, but not just the raw math. I would like to see the advantages and disadvantages of the different resolution mechanics: d20, 2d6 – Traveller, dice pools – ShadowRun, Fixed target but different dice – Savage Worlds. Also how the different mechanics interact with psychology and game theory. What kind of game style do the different mechanics support and why would a player get more enjoyment from one mechanic over another?

  18. I’m currently studying for a stats and probability exam, so distracting me with an article about probability sounds like the perfect way to convince myself I’m doing work!

  19. I would absolutely love a stats article, especially if you go into how the designer’s choice of distribution affects the players choices. As an aspiring indie game dev, that would be super useful for designing stuff like combat systems.

  20. I would love an article about probability math in RPG’s.

    Maybe something along the lines of your Monster Building series? One part Dissecting Probability (the raw math) and one part Probability Practicum (how to use and apply the raw math in-game)?

  21. Welcome back! I would love to see an article on stats from you, or whatever you’d like to write about.

  22. I feel like I’ve already read about the statistics of advantage and disadvantage.

  23. I’d certainly like to see an article on probability and statistics. Particularly, in your experience, how probability and resolution systems in general have an effect on “tone” or “feel.”

    For anyone interested in D&D statistics, I highly recommend Daniel Collins’ Blog: http://deltasdnd.blogspot.com/. His primary area of interest is in Original D&D (think 1974 with a sprinkling of Greyhawk), but even if your interest is in more modern games, it is always thought provoking. I thoroughly enjoy reading his articles.

    Seeing the above reference to anydice prompts me to plug Troll Dice Roller and Probability Calculator:

  24. +1 vote for a stats article. I mean, it’s you, so I’ll read pretty much anything you write.

  25. I would love to see some staticstics being done. DM’s are always comign up with small mini-sytems to solve issues with the system at large, or to streamline mechanics. I do this quite often but a lot of what I do is by hand (or brute force code) because I’ve forgotten all those wonderful equations that we learned in high school maths. Questions like, what is the chance or rolling higher than a 17 on 4d6. Or what’re the chances that a roll of 5d4 will beat 2d10?

    • 5d4 vs 2d10 is a pretty solvable question actually. the easy answer though is often, since 5d4 average is 12.5, 2d10 average is 11, 2d10 also has quite a few outcomes that roll below 5d4’s minimum. to actually solve the problem quickly you’d need a computer (it’s annoying to compute all the possible outcomes of 5d4, though 2d10 is pretty easy) but the short answer is that 4d4 versus 2d10 is a more interesting question than 5d4 versus 2d10

      also +1 upvotes on any stats-type article, I love stats

  26. I would love a statistics and probability article, mostly so that I can steal it and pass it on to my students 😛

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