Handling many modifiers on a probability curve

Question

So I've been working on a 2d20 based system for a side project, and it's playing out as a hybrid of a roleplaying system and a simulation-heavy combat game. This means that the engine has quickly become hard to use; it's a game in which the player characters are all using battlesuits to fight fantastical science-fiction nemeses, but the problem is that modifiers begin to stack on characters very quickly-for instance, by the time one's in combat they're looking at up to 15 points just from their weapon, battlesuit, and training.

One thing I've tried to do to balance this back out is to make the combat heavily focused on per-bullet ammunition expenditure. Each shot fired causes recoil, and each attack is handled separately, with a quick and lethal system that focuses on putting down a ton of lead as quickly as possible. The idea is that one shot almost kills someone, and five is almost a guaranteed kill against all but (mini)bosses or PC's. However, I've found fairly quickly that what this means is that it turns into a sliding scale on the target numbers; the goal is to roll below a threshold, but that starter threshold may be up at 50 before sliding all the way down to ~15 or so with a really long burst of a heavy weapon spraying an area.

For the most part this is acceptable; player characters are effectively space ninjas, so there's no issue with them not missing with the first shot in any combat. However, I'd like to know if there's any example of people trying to resolve this sort of thing-having a guaranteed hit for your first several bullets and then a near-guaranteed hit for another two (worst case) or five (best case) is a mite much.

Here's roughly how the system works.

The game itself is meant to mechanically model a video game; in such a way that it is possible to convert items from one to the other if their numerical values are known (the tabletop is "low-resolution" if you will, typically focusing on dividing these numbers).

The core system of the game is a 2d20 "roll under" system, with target numbers assigned somewhat arbitrarily. In combat, this is the enemy's Defense Rating, which varies from between 5 (really tiny, fast, annoying foes) and 35 (slow bosses).

To make an attack, players calculate:

• Their character's accuracy value. (Variable)
• Their weapon's accuracy value. (Variable)
• Their battlesuit's accuracy value. (Variable)
• Any other appropriate modifiers, such as movement, lighting, and distance. (Variable)
• Whether or not they're attacking multiple opponents, whether they are doing so in a single attack, or as multiple. (-5)
• A penalty for all prior separate attacks. (-5 per, but only for successive attacks).
• A penalty for all prior rounds fired, except for earlier rounds of the same short burst (-3 per, may turn into variable based on ranged weapon damage).

The weapons themselves have stats that will seem eerily familiar to anyone who's played any of the 40k RPG's, with an accuracy value, a damage value, and a range increment as well as their available attack rates (if multiple are available) and special effects (shotguns, for instance, have a special effect).

This means that someone firing a second attack with a semiautomatic weapon is facing a -8 penalty, but if they're attacking two foes they're facing a -5 on their first and a -13 on the second, making it progressively more difficult to hit as more lead flies through the air. For the most part I don't see it being too clunky, since most modifiers are pretty static, but that's a really large potential range (high-end weapons and characters may be looking at +15 accuracy, meaning they'd have a 50% chance of hitting even the most nimble foes in the game with a single attack).

Answer 1

The usual solution to an explosion of modifiers is to pre-calculate as much as possible.

Instead of having a bunch of bonuses that you apply to the roll every time, build those bonuses into target numbers (TNs) that you can write down. Reading a number off a die and comparing it to a TN is much faster than reading a number, adding to it, and then comparing it to a TN.

Per-character lookup tables

If you have a complex set of variable TNs, then a per-character table may be the way to go. It seems like a lot of fuss and bother at first, but that's the whole point – pre-calculate these things, and then you can do a quick lookup during play. Have a two-row table with every possible die result running along one side, with corresponding blanks to be filled in with the pre-calculated TN that the roll would hit after bonuses are considered. This makes the mostly-static variables for a character "invisible", encoded in that table, and you can forget about them entirely during combat. Situational bonuses during attack resolution are applied to the TN (bringing it down) instead of applied as a bonus to the roll result, so that the die results table doesn't have to go above 40.

Instinctually we assume that something that is visually complicated is procedurally complicated too, but in reality a lookup table looks complicated and is procedurally simple, so I can only say, "try it," and judge how well it works with actual playtesting. It takes up a strip of character sheet space, and it means that you have to fill out 39 blanks in order to be ready for combat, but in practice filling it out is quick after you've calculated one TN: since adjacent TNs in the table will always be ±1 of each other, once you have one you can fill them in quickly just going down the line.

Per-attack lookup tables

Where this starts to get unwieldy is if your bonuses vary with each attack form as well – then you have to either have a single "base" table and then treat the differences between the base and the actual attack form being used as a situational modifier (changing the TN as above), or you have to have a lookup table for each attack form.

Having a per-weapon TN table is not a bad way to go either, though. It means that you can calculate a whole bunch of stuff during character setup, but you get a lot of detail and granularity while having a system that scales to larger combats trivially during play because your resolution procedure is light weight. As a bonus, having a thin table along the bottom or top of a weapon entry on the character sheet suits a science-fiction æsthetic.

Speaking of æsthetics, if you go with per-attack lookup tables, one thing to consider is that this might, in layout terms, cramp a character sheet. If your weapons have many other things to note down on the character sheet, you might consider having attack forms and weapons be their own separate sheet, much like fantasy games often have separate spell sheets for spellcasters. Alternatively, if a character's loadout is expected to change often but each weapon is expected to remain relatively static for that character, you might make the weapons have individual, notecard-sized sheets. That would make changing loadouts just a matter of selecting the attack form cards you want to mount from your larger arsenal.

Answer 2

That's a serious problem in any game that tries to reflect real-world conditions: life is complicated. I can think of three ways to reduce the complexity.

• Pre-calculate (SevenSidedDie alluded to this). The key here is to ensure that modifiers for weapons, skills, etc. very rarely change, so you can total them up during downtime and just use the total during combat. As a counter-example, I'd probably disallow ability score damage if I was DMing D&D, because it would disrupt this, forcing recalculation of ability modifiers.
• Combine modifiers. Instead of having four separate modifiers for darkness, target movement, flanking, and position, make a single comprehensive judgement on battle conditions. "Your muzzle flares are the only illumination as the aliens swarm through the bulkhead, fighting through your suppressive fire. Everyone is at -5 for poor field conditions!"
• Reduce resolution. Mechanically, there's little difference between a +2 in a d20 game and a +1 in a d10-based game, but for most people it's easier to add up smaller modifiers. Also, having a lower resolution discourages trivial modifiers. You may be tempted to have a +1 modifier for a slightly-larger-than-man-sized target, or -1 for using a laser sight in a foggy environment, just because you can on a 2d20 scale; if your core roll was 2d6, you'd be forced to pare it down.

There are other approaches, though I suspect they wouldn't give you the crunch you want:

• FATE make battlefield conditions a kind of game mechanic which players and the GM use to create modifiers as needed (I guess, I haven't actually used it).
• D&D Next throws out many combat modifiers in favor of simply establishing "combat advantage" or "combat disadvantage." In the former case you roll d20 twice and take highest, in the latter you roll twice and take lowest.
• You could have difficult situations entail rolling extra "risk dice" which add a chance for critical failure. Normally you don't accidentally shoot your pal in the back, but if you have to roll three risk dice with your normal two skill dice, the odds of rolling three skulls becomes significant. I think the new Warhammer game uses something similar.

Something I've been experimenting with on situational modifiers: rather than consider illumination, uneven footing, panic, or other factors for each attack roll, reevaluate them only when circumstances drastically change, at most once per battle. To keep things interesting, let players make a roll to see how well they're coping. A successful Will roll means only -1 penalty for being wounded, compared to -3 on failure, say. This lets characters' skills other than "shooting" be more relevant in combat. Compare Lieutenant Gorman's behavior to Ripley's when fighting first broke out on colony LV-426.

Answer 3

Yes, I know, I'm answering my own question after I selected an answer, but that's because I had some free time and was reading stuff when I had an epiphany.

Use caps.

Force certain actions to have caps on their modifiers, which prevents astronomical modifiers from having any effect, but also means that modifiers can still apply. There are two ways to do this; hard caps, and soft caps.

Hard Caps

Hard caps are exactly what it says on the tin; whenever a number goes too high, chop it down. The upside of this system is that it discourages min-maxing and provides an incentive to branch out rather than hyper-specialize in the end game. Caps on player skill and input start immediately when the maximum modifier is reached, so that the sum of modifiers they put in are not greater than the cap. For instance, a player cannot have more than a +15 modifier, even if their stats and gear say they should get +23.

Soft Caps

These are like hard caps, but hurt less when you fall. Essentially, when you want to have something that you want to give infinite potential prowess in, but not allow it to overly affect the game, you use soft caps. Rather than working on the amount of modifiers that players can put in, soft caps only have an impact on the outcome. Rather than only bringing +15 to the table, for instance, they could bring +23, but only apply the points in excess to other modifiers, such as firing a weapon in the dark. What this means is that essentially they could never succeed with a roll that is more than fifteen points above the original target number, but they can bring this pool of fifteen along even if they have other negative modifiers.

Caps are the future!

Okay, maybe not really, but it's an idea I got from the Shadowrun 5th development blog, so it's not exactly something that I unearthed from a tomb. The nice thing about caps is that you can apply them in certain ways and modify them (assuming, of course, that you keep an eye out for not going too far with the modifiers and making them clunky; they should be relatively static). If you want, you can make the cap for a ranged attack be based around a firearm; an assault rifle may have a cap of 10, a sniper rifle could have a cap of 15, and a handgun might have a cap of 5-each is meant to portray a different amount of maximum accuracy. Alternatively, heavy armor might assign a cap on stealth, while being unarmored or wearing armor designed with stealth in mind would not.

Answer 4

I’m imagining one of those rotary gatling guns

You know, the ones with the belts of bullets that fire very rapidly? They seem to be the best design for rapidly filling the air with lead (the assault rifle recoil-based auto seems far better for burst-fire than full-auto). I don’t really know anything about guns; I’m only basing this on movies and video games. But then even if it’s not true, there may be some tropes in this direction.

Anyway, what I’m getting at is that these rotary gatling guns need to spin up first. That could offer a delay and possibly an initial penalty to using these guns – which you could stat as the fastest guns. Smaller initial delay/penalty guns might be accordingly somewhat slower.