Sunday, July 10, 2011

Math changes

As I shift over into designing class material I had to put stakes in the ground with regards to math. This, it seems, is always harder than one intends. This is actually my second or third pass over “the math” because different design goals call for different math. Each time, I’ve been more satisfied with the results. This time, though, it called for some sacrifices.

The sacrifices:
  • Twenty levels. I wanted the game to work across twenty levels and it did. The problem was that it was hard to make the math work at the top of the game with the simple mechanisms that I wanted at the bottom of the game. By hard, I mean I had to use the solver function in Excel to resolve each cell and then work backwards to develop mechanics that satisfied the requirements of said cell. So… hard.
  • Defensive magic items provide numerical bonuses.

The why on the sacrifices:

Twenty levels. The main reason I fought for this is because of the legacy of D&D. I’ve raised this argument before, and each time you folks convince me away from that as a rationale, and each time I’ve found exciting new design spaces as a result. It turns out the math is pretty amazing over 15 levels but really broke down over those last five. It is a much tighter design and there are some exciting little mathematical artifacts that follow 15 levels but do not follow 20.

Defensive magic items. Here’s the thing. Offensive magic items can be given exciting powers that the player chooses to activate when the player chooses to do neat things. But defensive items are passive, which means they are basically always on. If you decide to balance an offensive item by letting it be turned on only occasionally, that is neat and empowers the character. If you do the same for defensive magic items, you have a harder time. They just aren’t the same beast since a player attacks (roughly) once per round and is attacked (roughly) more than once per round.

Now take that same logic and think about how it overlays to class powers. The +5 from magic items that go to attack create interesting tradeoffs when you’re deciding to activate it for your attack. But if you are choosing to activate it for your defense, it becomes a no-brainer because you might be attacked five times. On the other hand, maybe you’re a ranged attacked and won’t be attacked at all. Now it is a no-brainer to *not* activate the defensive power and funnel all your resources into offensive class powers. Making a significant portion of defensive capability come from allocating resources during your turn just doesn't really work.

Offense and defense just don’t work the same way, so I had two options:
  • hard-code defensive bonuses into the math via some unavoidable, non-decision based route; or,
  • return numerical defensive based items to the game.
The positive system assumptions says we should choose the route that is the easiest to alter. Giving inherent bonuses for free is super easy, so (limited) magical pluses are back in. This actually has some benefits. You can give “overpowered” items (i.e. strong non-numerical powers) which basically have an expiration date when the plus is no longer powerful enough and you can differentiate characters by giving some items early and other items late. Moreover, because defensive magic items are passive, they are probably best represented by better defending you. Pluses are a simple way to represent that.

The good news is that I’m close to being able to publish classes, and then we are just a stone’s throw away from being able to actually play a game.


  1. This defensive bonus thing is true. However, may I give you my solution to it. Assume that characters can perform a "standard" action, a "move" action and a number of "swift" actions. The number of swift actions a character has in a round is dependent upon their skill, raw dexterity and thus the options that are chosen for them.

    One of the important roles of swift actions is to power "reactions". One of the more common swift reactions is to either parry or block (thus raising the defense against that specific attack). If this happens once in a round, most characters will be fine but if they have to defend themselves against multiple attackers, their capacity to react will quickly run out.

    I think this a nice, simple dynamic myself that gives a natural benefit to the more skillful as well as good tactics to the weak to overcome the strong but as always food for thought.

    {The computer ate my big encumbrance response by the way, so I'll have to retype that one in tomorrow.}

    Best Regards
    Herremann the Wise

  2. This is probably my third cycle through classes and the first two included a recommendation like yours. I rather enjoyed the ability for different classes to produce different defenses (I didn't use swift actions but rather "stances" which incurred other tradeoffs).

    The problem was that it just made too many moving parts. On any given round, a player had to balance the tradeoff between his limited resources (action points and actions) to produce the highest offense possible but also keep in mind the tradeoff for resources outside his round (hit points and defenses) using those same finite actions. It just proved too much to reasonably expect a player to balance, much less a new player.

    Hence, I moved away from it. Although, I must say, the more you talk about your game the more I'm intrigued if for nothing else than to mine the hell out of it. Someday soon you'll have to post a link!

  3. Another thing to consider regarding defensive magic items is that you can have powers that are always on but are more circumstantial and interesting than "a +1 to defense". Things like being able to redirect attacks of a certain type, being able to shield another from attack, protecting their wielder against certain types of energy, summoning a guardian spirit bound to the shield...stuff like that.

    One thing that I've come to understand is that if you eliminate magic item bonuses on both sides (offensive and defensive) and make sure that their are equal options for people to increase their offensive and defensive capabilities (through feats, trades, weapon and armor selection etc) then you don't need bonuses.

  4. The problem with introducing that defensive math through feats, class powers, or armor is that all of those things are a pool of resources that also fuel other things. The more resources you put in a general pool, the more easily someone can break the system by rerouting resources intended for defense into, say, offense. So I would have had to have created an additional mechanism to ensure resources didn't bleed into other areas. Note--some bleeding over is good because that is customization, but this, I determined, would have been too much.

    The other option was to just reduce the math so that they aren't needed. I would have loved to have done this but it made progressions wonky instead of fluid. By far, the simplest route was to just use magic items to increase defense (or allow people who prefer to just assign the inherent bonuses).

  5. But wouldn't such a problem be self-correcting? A character who puts all of their resources into attack is certainly going to be formidable in combat, but will draw attention to themselves in battle and be relatively easy to strike down. While a character who completely neglects their offense in combat in favor of survivability will likely find themselves ignored in battle to their allies's detriment but will definitely have an edge in survivability. So long as the differences between "Otis Mc Offense" and "Danny Mc Defense" don't stretch the math of the game to it's breaking point, it's just a matter of what trade offs a character is willing to make.

    A good example of this is, at least in my opinion Mutants and Masterminds. In that game, a character's maximum offensive and defensive characteristics are based on their PL or power level-making all characters of the same power level on the same page effectiveness-wise.

    What makes the system interesting is that you can perform trades between defense and durability, and attack and damage to create your vision of a perfect character. You might choose to create a "glass cannon" with high defense, low survivability, moderate attack, and high damage, or a "tank" with huge amounts of durability and damage but very little attack and defense. What's cool about the system, is that all of these archetypes are balanced with one another, and each will find ways that it excells and situations that it's challenged in. What I propose is putting this sort of thing in the player's hands, so that they're able to guide the development of their character as they see fit.

    On a related note, I'm very much against the axiom that all characters must be equally effective in a given situation. So long as everyone has something to do in a situation, and everyone is as useful overall (ie. has roughly the same number of tools to solve problems in the game world)then balance is achieved. A lot of people would disagree with me, pointing to the difference in combat ability between a Rogue maxing out Diplomacy and taking Skill Focus repeatedly in 3.5 and a min-maxed wizard, but that's just a matter of tweaking each classes abilities and making sure that every class has something to do in every forum (even if that situation isn't their specialty).

  6. To a point it is self-correcting and I think we are actually in agreement. Let me put up hypothetical up as a framework to help the discussion.

    Hypo-super simple RPG with three stats: Atk, Def, HP.
    Attacks are d20 + Atk.
    Defense is 10 + Def.
    Hit points begin at 3.
    A success deals 1 damage. The game gives you four resources to increase anything you want by +1.

    There really isn't any combination that breaks the game. You could attack really well, defend really well, be able to take a bunch of hits, whatever. Some builds might edge out others, but the game will still be pretty playable.

    Now imagine if the game gives you 30 resources. The game presumes (and hopes) that you distribute those resources around 10-10-10 into each category. But you're smart, and so you put 9 into Atk and 21 into Def. Most of your opponents are +10 atk, which means they cannot hit your 31 defense even on a natural 20. You are +9 atk (one worse than them), but you hit on an 11 instead of the "balanced" hit on a 10. You only have 3 hit points while they have 13, but since you are never hit that isn't an issue.

    In order for me to have that last 5 units of defense "purchased" with resources, I had to flood the common pool. I felt it was approaching the second scenario and it would diminish the overall game. (As an aside, I recognize that in your post you agree that the second scenario is bad. I don't think it reflects your stance.)

    I've built in enough flexibility in progression that someone could tailor their character quite a bit (about +5/-5 on atk/def over the course of all levels). It is enough that even two rogues who take the same abilities will have a different play experience if the order in which they took said abilities differs. But, hopefully, it isn't so much that it allows for exploiting the system.