Friday, December 2, 2011

Some Math for Icons and Savage Worlds

ICONS has some pretty simple math. Abilities are rated from 1-10 and players roll 1d6 - 1d6 then add the result to the relevant ability to beat the target number which is typically an opponent's ability score. Since the roll tends to give a result of zero you can pretty reliably predict whether or not the characters will be able to succeed at a given task. There are things that can modify the target (darkness, etc.)  There are also ways to gain bonuses to rolls. There is some motivation to do these things as exceeding the target by 3 is a special success and by 5 is a major success and can yield some additional benefits beyond "you did it".

Character creation uses a table that limits character stats to a 1-8 range weighted towards 4, 5, or 6. A straight 3d4-2 roll would accomplish a similar effect while leaving the slight possibility of a 9 or 10 stat out there if someone wanted to go that route. As it is the "global" average lines up very well with the "global" target number. If you want to make things harder, give your villains higher stats and lower stats will make things easier. The good thing here is that assuming the human average is a 3 means that heroes averaging a 5 will clean up against them easily, as they should. Bumping "quality" thugs up to a 4 and "Elites" up to a 5 for their main stats should provide a noticeable bump in difficulty without being overwhelming - that comes in with the 8's, 9's, and 10's.

As with most things ICONS, the simplicity of the mechanics conceals the elegance of the design - the math works really well. ICONS tends to not be a very crunch heavy game anyway so this approach fits perfectly.

Savage Worlds has a little more crunch to it. The base target number is always 4, with 8 being a "raise" and each subsequent jump of 4 equals another raise. There are modifers to different tasks that can change this but let's use 4 as a baseline.

1d4 = 25% chance of success (which will then explode and give a chance of a raise at 6% - that's a 4 plus another 4)

1d6 = 50% chance of success (exploding for a raise happens 14.9% of the time - that's a 6 plus a 2+ on the next roll)

1d8 = 62.5% chance of success and the possibility of a raise on the initial die roll (12.5%)

1d10 = 70% chance of success (Raise is now at 30%)

1d12 = 75% chance of success (Raise is now at 41.7%)

Ratings can go above a d12. The next step is d12 +1, then d12 +2, etc.

1d12+1 = 83% chance of success (Raise = 50%)

1d12+2 = 91.6% chance of success (Raise = 58%)

1d12+3= 100% chance of success (Raise = 66.7%)

Further increases are really just upping your chance of a raise, which hits 100% at +7

There is also the Wild Die, which is an extra d6 that all PC's and important NPC's get to roll alongside their normal die type. The higher of the two applies. This is a "PC's are Special" type rule that ups the chance of success somewhat (especially noticeable if you're rolling d4's and d6's otherwise) but since it applies to all player characters equally then I think we can ignore it for now.

So...are there sweet spots in the Savage Worlds system?  Well there is that weird kink in the curve for raises on a d6 where it's slightly better than the chance of a raise on a d8. For normal successes though, a d6 is twice as good as a d4 and the rate of change drops at each incremental increase after that.Clearly the jump from a d4 to a d6 is the most bang for the buck, especially considering that base attributes start as d4's and have to be raised beyond that. Based on this I suspect that it's better to raise all five attributes to d6's than it is to have 2 d8's, a d6, and 2 d4's but only if you have an intentionally broad character! If you intend to specialize in certain skills tied to one attribute then I think the d10 level is pretty effective as it pushes your base success chance up over 2/3 and it doubles your chances of a raise over the d8 level. Plus you would have 2 points left to raise other stats to a d6 - no sense in sucking at everything else if you can avoid it.  Adding +1's to a d12 roll seems very inefficient but at higher experience levels that may be your only option.

Let's look at it in the context of combat. The target in melee is Parry, which is 2 + half of Fighting. Damage is compared to Toughness, which is 2+ half of Vigor. Meeting or beating these is a success, beating by 4 is a raise, and each additional increment of 4 is another raise.

Average human stats are d6's so assuming getting in a fight have a d6 in Fighting then most people's average Parry & Toughness = 5. Effectively what this does is shift everyone down one notch on the chart, roughly. Due to the way exploding dice work, certain target numbers do not change the odds. If you're rolling a d4, the odds of rolling a 5 are the same as rolling a 4 (d4 + d4). For d6's a 7 is as likely as a 6, for d8's a 9 is as common as an 8, etc. It does impact the Wild Die so there is an effect overall even for the d4 roller, but the base odds on your "main" die don't change.

You could go d12 in Strength, d6 in Vigor, then d4's in Smarts, Spirit, and Agility.  Given the presence of the d6 Wild Die you actually still have pretty decent capabilities with your other stats and be pretty nasty in hand to hand combat.

So the baseline for Savage Worlds - the d6 - will succeed about half of the time on a normal test. That's a pretty solid base but could be unsatisfying in play because it also means that the average character fails at the average task half the time too. The Wild Die bumps the success chance up to 75% in this case which makes for a much more satisfying game for the players without breaking the universe for everyone else. As skill (die types) increases this has less and less impact, so it nicely expands the "middle ground" for the system and then takes a lower profile as things ramp up. I think it's a very well-done mechanic.

There are of course various edges that can affect certain kinds of rolls and hindrances that will let one buy stats up another point or two but those are not universally available. Also, even with a little more crunch than ICONS, I'm not sure that SW is worth much agonizing over the math. Higher dice = better chance of success in every case (even if raises have that one kink) so most of the time the higher die type should win, though SW's other cinematic mechanics (Wild Die, Bennies) can be used to overcome this.

Anyway there's my math homework for the week. I do like the d20 systems out there but they are kind of plain probability-wise as everything is so simple: +/-1 = +/-5% chance of success, regardless. Efficient but boring math-wise!  Thank goodness for the multitude of choices out there that still try out other approaches and let us flex our brains in slightly different ways from time to time! Each individual approach may not be better than a particular standard but having options is always preferable to a boring uniformity.

Some other time (some other website if you care about it right now): GURPS, Hero, and those dice pool games.


kelvingreen said...

I've played and run Savage Worlds quite a bit, and I find that the maths fade into the background in play. With TN4 as your baseline, and modifiers being limited -- at least the way I play, where I tend to use +/-2 and +/-4 and nothing else -- it's all rather intuitive and fast. Since it is something of a crunchy system, and I don't tend to enjoy crunch, this has been a pleasant surprise for me.

Simon Forster said...

Normally I find breakdowns like this a bore, but I found yours quite interesting. Probably because I keep messing with RPG design and was looking at SW the other day; or maybe it's because you write up the maths well :) Looking forward to more.

Blacksteel said...

I do like limiting the modifiers - I think I got hooked on that after moving from D&D 3E to 4E and working through some Saga edition Star Wars - +/-2, +/-5, +/- 10 works just fine in those games and is easier to keep track of than tables and tables of modifiers. I think the 2 levels of modifier you describe is perfectly fine for Savage Worlds and I agree that the math drops out of sight pretty quickly.

Thanks for the hat-tip - I don't like to over-analyze these things but after playing them again recently it was on my mind. I like to check the numbers sometimes and see if "average" is truly average or how the mechanics work out when looked at apart from the descriptions. I find keeping it short helps too - let's look at the main part of the game and not worry so much about the ends of the spectrum.

It's also interesting as a player because some systems demand specialized characters to be good at anything, while others allow a character with a broader competence to be viable and fun too. Savage Worlds especially seems to allow for this and I like it a little more because of that.