Thursday, 26 September 2013

Musing on Maths

I have been running quite a lot of maths recently to try and work out whether different combat models would work in Monitors, let alone what numbers to use. And this has given me a huge amount of sympathy for people faced with doing this sort of thing professionally.

The thing is, it's relatively simple (by which I mean to say, very complicated) to do calculations for what would happen (on average, of course) if hero X and enemy Y stand still in an enemy room with no features whatsoever and shoot or stab at each other. You can, if you want, tweak the numbers to produce different results, or different distributions - maybe you want pretty reliable combat, perhaps you prefer it dramatically swingy. You might introduce a complicating layer of different attacks, or perhaps multiple combatants, but while these make things even more difficult it's still possible to see how you model it with maths, even if the execution is a pain.

The problem really comes about when you try to introduce other stuff. That is, anything that allows combat to be remotely interesting.

In combat, we want heroes to use cunning and stealth and tactics. They take cover, launch surprise attacks, use suppressing fire. People don't fire endlessly at static targets, but duck and crouch and move around for perceived advantage. Large groups try to encircle smaller groups, while the smaller groups try to use terrain and technology to create bottlenecks, allowing them to face only a few enemies at a time.

How much of an advantage can the hero gain by doing this? Exactly how much do we want the hero to do it - or any particular heroic archetype? Should they be taking cover frequently for a small bonus, occasionally for a large one? How successfully should they be able to bottleneck enemies, and how does that relate to different enemy types? How effective is that suppressing fire?

Very quickly, you end up in the situation where you'd have to picture the whole fight in your head in detail in order to work out exactly what kinds of factors you want to come in and how effective you want them to be. You end up with an unmanageable number of things to take into account, and potentially with a massively-spiralling set of rules to handle it all. Or else you resort to alpha-testing each possible set of rules in detail, each time having to decide not only what effects you care about, but the numbers that should be attached to them. Real game designers have my sincere sympathy. I have no idea how they handle this stuff.

Which is to say nothing of Grapple rules.


  1. I think this might be where mechanical unification is your friend. If cover, for example, just adds Armour/Defence/Whatever then you've already factored it into your calculations.

    It isn't possible to predict every possible combination of actions or special circumstances that could apply in a fight, and remember that it isn't actually the designer's job to make a game work right in play, it's the GM's (assuming a standard GM-having game). No matter how effective or ineffective you make - say - cover, whether players use it will depend on what cover the GM puts in their missions, and on whether the PCs are the sorts of people who deal with that sort of thing.

    I'd also point out that "stand in a featureless room and blast" is more interesting than you might think. I mean most RPG combats do actually just come down to variations on the basic attack, mixed in with things which the designers can't anticipate and GMs have to adjudicate on the fly anyway.

    1. I think maybe I haven't managed to pin my (vague, wishy-washy) point down. Let's see...

      So I'm not actually planning to produce an exhaustive set of rules combat for my silly little game, for starters.

      I suppose the issue is something like integrating the narrative and mechanical outcomes when you're basing things loosely on existing genres, and working out what narrative you're actually using. It doesn't matter, in a fairly loose ruleset, what tactics a character uses or whatever; but I think it does matter to some extent what the norm is you're working off. There's a substantial difference between "can defeat ten 3rd-class warbots with lasguns at once when standing still in a featureless room", "can defeat ten etc. when using tactics or blast weapons to reduce their advantage of numbers", and "can defeat ten etc. when ambushed by dug-in opponents". It's not just about that situation, but what happens when you switch to another. If you can take ten bots standing in the open dishing out hundreds of shots, you're not going to worry about any but the most terrifying individual enemy. So it's about trying to work out what the power curve actually is, where different types of PCs should fit on it, and how you want to represent various opponents to fit that, in order to make combat with a range of different PCs and opponents reasonably interesting and fun without being utterly broken.

      Right now it looks to me like numbers of enemies are the main issue, simply because of the sheer number of attacks a group can put out compared to your rate of killing (well, 'killing') them. But I'm about to try experimenting with the armour save model we mentioned, which will make a difference here, I think.

  2. It's true that there's a *genre* difference between "can defeat ten 3rd class warbots with lasguns at once when standing still in a featureless room" and "can defeat ten etc when using tactics or blast weapons to reduce their advantage of numbers" but, crucially, that difference does not absolutely *have* to be baked into the mechanics. It can be left up to individual groups to decide how they describe their characters' battles against the warbots (is it "I leap for cover and snap off a few shots with my rifle" or "I stand up and blaze away as their shots scatter around me").

    If it's more a question of whether you want to make it *possible* for players to fight ten or twenty warbots, and you're concerned about numbers being too overwhelming, you could use something like the Deathwatch Horde rules.

    1. ...not really, I think?

      Maybe we're still talking at cross-purposes here. When I talk about tactics, I mean (for example) taking cover in a building so they have to split up to search for you and you can fight them in pairs rather than all at once. Unless you're going to take a very abstract view of combat, at which point round-by-round isn't really sensible, that's a major difference from stand and shoot against all ten at once.

      I think another point is, even assuming one big warehouse, flattening those factors could affect play. If you *can't* mechanically gain any advantage by creative thinking or taking cover, then there's no reason for your wimpy professor to do anything but fire ineffectually. At the same time, Iron McArmouredPants doesn't get the satisfaction of striding out and hearing shots ping off her plating while the clothies cower behind a crate.

      But yeah, one of the things on my to-do list is thinking about enemy types.

    2. I'd have thought that sort of thing was very much outside the scope of rules, though. "We split them up so they can only fight us a few at a time" isn't something you need a specific mechanic for, it's something the GM judges on the fly. My players very often used those sorts of tactics in D&D, but we never looked to the rulebook to work out how it worked, we just made judgement calls.

      I think the important thing to recognise here is that if you want to reward creative thinking, you don't have to do it through game mechanics (and arguably game mechanics aren't the best way to do it at all, because then the system does the thinking for you). As you observe, fighting two guys at once is very different to fighting ten guys at once - the existing system should cover that difference perfectly.

    3. It's more a question of working out what the assumptions are you're using, I think, and trying to ensure the genre expectations fit the results. So I suppose this isn't exactly a "maths" issue at all and perhaps I explained badly (to be fair, I wrote the entire post in about five minutes). It helps that I know what's in the next couple of draft posts because I've spent several hours on them, whereas you don't...

      Basically I ended up spending a while trying to work out whether, when you picture someone fighting their way through (say) ten robots, you do in fact expect them to fight ten robots, or whether you're actually thinking of several groups of three robots in quick succession. This makes a big difference to the maths. Media quite often have people fighting while severely outnumbered, but on reflection I think in almost all cases the technically quite large groups very quickly get treated as smaller ones that can be believably defeated, either by physical obstacles, or because things like suppressing fire make most of them hang back. I'm not necessarily thinking I want to model anything very complex, but working out what my assumptions actually are seems important.

    4. Ah, I see what you mean.

      For what it's worth another thing worth considering here might be duration of combat rounds. Rolling for ten attacks is a lot slower than rolling for three.

      If you're thinking in terms of cinematic "fighting while extremely outnumbered" then again, I suggest thinking in terms of the Deathwatch Horde rules. Although fighting three lots of three enemies is a lot easier than fighting one lot of nine enemies, three lots of three can have the Keep on the Shadowfell problem - "hang on, didn't we just fight a bunch of guys like this".

    5. 'tis true.

      I was vaguely intending on a sort of 10-12 secondish round, during which you can do two things. Might be move and attack, move twice, attack twice... Any thoughts?

      For large numbers of worthless enemies I'm deffo thinking some kind of horde is in order, where the horde would have fewer mechanical attacks than its outward number suggests just to keep things manageable. That way you can just imagine the rest going wild or pinging off uselessly. Again, something I need to do a post on.

    6. Sorry, when I said "length of a combat round" I meant "actual length of OOC time". The problem with allowing the players to heroically fight very many enemies is that each enemy takes a whole extra turn. The reason I like Horde-style rules for mooks is simply that rolling for dozens of attacks can get really tiresome. Particularly since PC parties tend to be quite large, and so if you want the players to be decently outnumbered you normally need at least six NPCs, potentially more like a dozen.

    7. Ah, gotcha. I have an idea for that! To follow shortly.

    8. I definitely see where Shimmin Beg is coming from here, though Dan H's point is worth consideration. A game with high lethality that rewards cover as one of the few things between you and death in a fire fight *should* see PCs head for cover. However, that's not to say it will. Genre conventions often make it more or less likely.

      I once ran a D&D 3.5 game using modified gun rules and because it was a cowboy wild west fantasy game, people took a lot of cover. Ironically enough, it was TOO effective and both sides shot ineffectually at each other which was quite genre-appropriate but the PCs needed to figure out that you pin them down and then do something clever to take out the enemies rather than relying on random gunplay. D&D 3.5 is quite open to the idea of people standing there and shooting at each other without tactics against most enemies at your CR, but the players weren't thinking in tune with that.

      On the other hand, World of Darkness gives you very few health levels and cover is quite effective, yet it is exceedingly rare that my PCs will ever use it. Players who will memorise reams of fighting styles will nevertheless forget about the simpler rules of cover and concealment. I blame their LARP background.

      Call of Cthulhu has a high likelihood for death yet still few folks look to cover.

      So while you need suitable mechanics and difficulty in place, the genre conventions that are tilted in the favor of one style or the other need to be clearly in place in the game. Groups that buy into that genre tilt will go with it. Those that don't want to, will either die first or tone down the lethality.

    9. That's some very good points. I think in general genre conventions and expectations are really important to games, and we've run into issues before (Hellcats?) where muddying them hamper the game.

      I wonder if the cover issue is also partly that the environment can fade into the background in combat - you keep track of things like braziers to push over or pits, but because you're not seeing objects and relative positions it you aren't as aware of cover as you might be in reality? 4E and other battlemaps games should improve that, but then it's mostly about the melée combat.

      In terms of things like tactics, I think there's also an issue that mechanics rarely support things like psychology and surprise outside very specific situations, so whereas popping up being the enemy patrol or surrounding them is generally an effective real-life tactic, there's usually very little mechanical reason to do it, and less lifelike options may be more mechanically rewarding. Thinking again about D&D, a generous DM might give you a surprise-like bonus even mid-combat for something like that, but that's not likely to let you wreak havoc on the monsters; a slightly better hit chance, a bit of extra damage. Whereas sticking together in a mob often offers flanking bonuses, protection from flanking, auras, backup, and in 4E also lots of power-based options. I do actually have in my mental design notes for Monitors that there needs to be a significant bonus for just generally doing the unexpected.