Wednesday, June 8, 2011

Speeding up combat with fewer dice

Number three on the list of elements was quicker combats. This is a biggy because combat has steadily slowed across editions and, now, is just crawlin’. There are a lot of ways to make combat quicker and they have consumed a lot of the design focus throughout this project so far. I’m not ready to get into them just yet because a lot is still up in the air, but I do want to discuss some ancillary ways that combat can be sped up. This article is intended to highlight the extent to which the minutiae of game design can impact the play experience.

The big reveal: for the most part, damage expressions should be limited to two dice.

Most damage expressions throughout this homebrew are limited to two dice. Sometimes you’ll roll more because multiple powers are triggered (like sneak attack), but these are the exception rather than the norm. In those cases, the extra time the dice cause is worth it because some exceptional thing is happening. Extra dice are worth the extra time when exceptional events are occurring and I don’t want to get in the way of that. But most things, like routine monster damage, are not exceptional and so are limited to two dice.

The above graph shows two damage expressions with the same average.  One is calculated with 4d8+2 and the other with 2d12+7.  They both have en expected average damage of 20.  Expression A has a range is from 6 to 34 damage and Expression B has a range of 9 to 31.  Expression A, then, is interestingly different when the result is 6-8 or 32-34.  We like when things are interesting.  From here on out, we’ll refer to damage results that Expression A can achieve but B cannot as “interesting.”

Just because they are interesting, however, doesn’t mean they are worthwhile.  Only 0.7% of all damage results ever fall into those interesting regions.  In other words, if you roll one-thousand damage expressions with 4d8+2, seven of those results would not have been achievable with 2d12+7.

The game table is already home to a lot of stuff.  Rolling more dice means you either reroll some dice or you have even more clutter, taking you even longer to find what you need.  You also need to mentally add four numbers instead of two, which takes more time and increases the likelihood of errors.  But let’s presume that you are quick and the act of finding extra dice, rolling extra dice, and summing extra dice only takes a single second.  

The 1000 four-die damage rolls, then, would have taken you 1000 extra seconds or well over two minutes per interesting damage result (1000/7 = 142 seconds).   So the question becomes, when one of those interesting damage results arises, does your group spend the next 142 seconds enjoying it?  Because that is the cost you’ve already paid by making everyone watch the GM search for, roll, and add the extra dice.

You may rebut that higher dice damage expressions also matter with critical hits.  Having more of the expected damage in the variable dice makes a critical hit a much bigger deal.  Returning to the examples above, a critical hit with Expression A would deal 4d8+34 damage while Expression B would deal 2d12+31.  Expression B can’t simulate damage beyond 55 on a critical while Expression A can reach 66.   How often will Expression A result in 56+ damage on a critical hit? About 23% of the time.  So 5% of attacks (critical) will result in interesting damage 23% of the time.  This is the same as 1.2% of all attacks.  Adding critical hits to our analysis above brings our total to 1.9% of attacks or 19 times out of 1000 or ~50 seconds per interesting damage result. 

Of course, critical hits are already interesting.  Even with tighter expression ranges they do notably more damage and may trigger other powers.  The point of this analysis is to determine if the extra time spent to calculate non-interesting damage results is justified by the excitement of interesting results.  So if that incremental excitement is lost in the general excitement of the critical hit, we may again want to rethink our design.  Moreover, at the same time damage expressions begin creeping beyond two dice, magic weapons are already delivering 3+ of their own.  We have plenty of dice to provide a wide range of damage possibilities.

Now consider that for most people, it is probably takes more than a second to find, roll, and add the additional dice. Two or three seconds may even be a modest number, which means we pay multiple minutes for each interesting result. 

As 3e evolved, the number of dice and modifiers added to any attack steadily crept up. My last 3e character was an amazingly fun Duskblade who once crit while channeling through his sword and had to roll 25d6 + 3d4 + a host of modifiers from strength, magic, and power attack. It seriously took like 10 minutes (which I enjoyed and no one else at the table really cared). The point is that dice take time to accrue, time to add, and even though they are simple numbers they get all jumbly in your head and make you lose track of other important things. Fourth edition, then, decided to make multiple [w] the heart of the game. There are plenty of opportunities to roll dice and plenty of opportunities to do addition in D&D that don’t add unnecessary time to the game. Moreover, the middle of the turn is the worst time to force someone to lose their train of thought to do a bunch of math.

If you want the turn to go quick, the math in the middle of them has to be simpler. Limiting damage expressions to two dice actually goes a long way towards achieving that and doesn’t have a big impact on play; it just makes it quicker.


  1. This is a little sad that I'm leaving the first comment on my own site, but it didn't really fit above and isn't worth its own post, so...

    I think part of the reason summing more dice takes so long is the manner in which we sum. Since the process is done in your head, it doesn't feel as rote as I'm about to describe, but I think this is accurate.

    If I want to sum four dice (say, 1, 4, 4, 6) I don't just instantly sum them. I would take 1 and 4 is 5, plus 4 is 9, plus 6 is 15. More likely, I'd look for patterns and decide that 4 and 6 is 10 plus 4 is 14 plus 1 is 15. The takeaway here is that when I sum four dice, I'm not dealing with four numbers but with seven because I need to keep the running total throughout the process.

    The formula for this is [2x dice]-1. So the 25d6+3d4 above is 28 dice requiring 55 numbers to be maintained throughout the process. While most things never reach that absurd a level, a critical hit with a 3[w] power when wielding a +2 magical 2d4 weapon isn't that crazy and now we're up to 8 dice (15 numbers) before we consider other abilities or the fact that you have to add modifiers or maximize pre-crit damage and so on. It makes sense why that takes a while and it isn't really *fun* time for the table as a whole.

  2. I was going to comment earlier today! .. But I found out that my phone doesn't display the captcha, so it had to wait. Here's the comment:

    I only skimmed this post, but I agree that finding and adding dice do take up considerable time. Are you going to adress the other culprit, modifiers, in a separate post? I am in favor of flattening the curves in general, be it attack bonuses or whatever.

    Also, I just want you to know that I have read your other posts and am planning to comment, but you post more than I have time for! I usually read from my phone, but it is not ideal for formulating a reply on (note: and not even possible apparently).
    But what you've shown so far looks very interesting, so keep up the good work.

  3. Haha--no worries. This is a pet project and while I enthusiastically appreciate support and participation I don't actually expect it. You're right that I've been posting more than most people can probably keep up with.

    I checked some box yesterday that "activated mobile templates." Hopefully that made things more pleasant for mobile browsers. On the same token, I'm not really committed to anything on this site. If readers want something changed I'm happy to try and oblige. Just let me know--there's only like two of you so I can accommodate.

  4. I definitely agree with your thought process regarding speeding up combat and play. The game I'm currently working on uses Static damage numbers for weapons and spells, modified by abilities and the margin of success on the roll to attack. It makes things a bit more predictable and easy to calculate, while still allowing for lucky hits.

    I'm also planning on linking various effects to the different levels of attack success based off of advantages and what not.

  5. With regards to "the other culprit" I definitely think modifiers need to be addressed but I'd even go a step further. Adding +2, +3, +8, +4 from different sources certainly takes time, but having to remember if this attack is +12 or +14 or +16 (i.e. no adding, just figuring out which modifier to add) also takes time.

    The key is to make things more consistent so that people can become more familiar more quickly. Familiarity --> speed.

    As a result, everything in the game is an ability check + modifier + bonus if applicable. Since there are only four abilities, these will get real familiar real quick. Modifiers will also be consistent and recorded on the character sheet. So Affinities are a modifier applicable to most skills, weapons will have a proficiency modifier applicable to most attacks, etc. These don't change too often and so will also become familiar.

    Bonuses, then, are the during play thing that keeps things spicy and helps people stay interested. Bonuses can come from powers (i.e. rage), allies (i.e. bard song), magic items (i.e. potions), or even circumstance (i.e. flank).

    The result is that someone will usually have a really good idea of their ability and modifier and then just have to focus on the bonus. Bonuses provide a range of numbers but also riders (like adding conditions). This means tactically minded players can balance numerical bonuses and riders but more casual players can just "do whatevs" and still be in the same ballpark as power gamers.

  6. Sorry, just for clarity on my above comment, you'll pick a single modifier and a single bonus. So if two bonuses apply, you pick one and the other does nothing.

    From a game design perspective, this lets you introduce more and more varied options without them stacking so far that they break the game.

    From a logic perspective, the idea is that you can't be simultaneously studying your opponent to find their moment of lapse (flank) while also enjoying your bard-buddies rousing song about how great you are.

    By having different numerical bonuses and different riders, these remain interesting tradeoffs at all levels of play.

  7. Welcome, Veritomancer.

    From the few times I've looked at that game model it seems like it can play really fast and really dynamic. The one limitation is that there aren't enough variables to allow for the amount of variation a lot of games demand. For instance, making more than 10 or so weapons starts to prove problematic.

    I like the design in general and I'd love to read more.

  8. "You'll pick a single modifier and a single bonus. So if two bonuses apply, you pick one and the other does nothing."
    Very interesting! I had a thought about a week ago of doing something similar to flatten the math in regards to skills. Basically you add your ability modifier, unless you are trained (my system has no ability modifier increases). I haven't given it much more thought than that, as it would reward characters that are trained in skills they are innately bad at - which I am not sure if I am okay with.

    And yes, I noticed you enabled the mobile template, but were still unable to comment. I wouldn't want to write lengthy comments on the phone anyway.

  9. I'm sorry, I realised that my previous comment completely failed to get the point across in regards to flattening the skill modifiers.
    Normally in 4e, you add both your ability modifier and a +5 if you are trained. I was contemplating letting it be either or. If you aren't trained, your ability modifier is used, but if you are trained the +5 from trained is used instead (as I don't have ability scores that increase with level, a +5 is the best you can ever get in this regard). So you are penalized for super-specializing (with an 18 Str, being trained in Athletics only rewards a +1), but it also does not seem realistic to be trained in something you are really bad at. Most physically weak, but charismatic people do not become boxers. :)

  10. Yeah, I can see the disincentive there. Training provides the greatest compensation in areas in which you have no natural talent. It isn't *indefensible*, just doesn't have the type of reward structure most people expect.

    One potential solution is that you could say training increases the bonus by +2 to a minimum of +5. So someone with a +1 stat jumps to +5, someone with +4 goes to +6, and anyone above +5 to begin with just gains a steady benefit. This way everyone improves (albeit to different degrees) and you still have a quick, simple mechanic. I'm not sure I love it, but it might be headed in the direction of a good rule.

  11. I understand where you guys are going with the flattening of the skill curve and I think it's an admirable goal I think perhaps that a different route might be in order. With the first solution you run into the problem of it being the best decision, numerically to always train in skills you're bad in which is counter-intuitive to say the least.

    I like runeward's solution a bit better, but the problem is still there, albeit to a lesser degree. With that system setup (assuming no modifiers like "affinity focus") the most talented athlete in the world (Str +4) is only going to have a +6 modifier compared to the weakest person in the world (Str -5) having a +5 mod. Even accounting for +3 in bonuses for the great athlete because of a feat, you've only got a difference in the roll results you'll get of 20%. Using D&D 4e rules as they currently stand, there would instead be a 40% difference in roll results between the two of them.

    Does flattening the skill curve that much make designing encounters easier? Yes. Do I support it? More or less. But I feel flattening it that drastically results in characters feeling very much the same skillwise, assuming that they're trained. I feel like this will also present a problem in play, as you're likely to see a lot of -1 Cunning barbarians picking intellectually-based tasks for their affinities. I feel like except in rare cases (an unusual backstory), that sort of thing doesn't encourage the sort of play that most people expect from an epic fantasy game or even a swords and sorcery game.

  12. I think Veritomancer's (valid) criticisms are a good example of the idea I was talking about earlier with the output of the rules supporting our expectations. It isn't that the rule doesn't work or that it fails to introduce relevant incentives across different levels of play, it is that under certain situations the incentives and rewards feel disproportionate to what would be *believable.*

    We can address this in a handful of ways. One is to spend time trying to make "better" rules which is what we're doing now. Another is to spend time redefining what is "believable." Pulp or Superhero games spend a lot of time up front investing in the feel of play so that letting a 90 pound weakling spend a superhero point (or whatever) and throw a car.

    A third solution is to reset expectations via math. With a d20, results are linear and a +1 gets you 5% higher. If you rolled 2d10 instead, a +1 would represent a statistically larger jump and is therefore more valuable. At 3d6 a +1 is even more important.

    This interpretation looks at results as though they are logarithmic. If 10 is average, a result of 11 is a marked improvement, and a result of 14 is pretty masterful. Under this approach, you can tighten bonuses and modifiers because smaller boons matter more. This has the added benefit of making oddities in the rules *feel* less unbelievable.