The Magical Probabilities


Right now there’s another debate on RPGNet about “50% is just too low a chance of success”. This time it’s about ORE, but it can involve Warhammer, Call of Cthulhu or Unknown Armies. It comes up a lot, and always goes the same way – a devolution into the question of exactly what a die roll is simulating. Is it doing an action under extreme success? Can it be boosted over time? Is that for a professional or just a non-amateur?

And this KIND OF misses the point.

And the point is that first of all, there’s another concern going on, and that’s the percentage that people like to succeed at dice rolls. I’ve always had an inclination that these numbers were about right, but I recently had it confirmed rather spectacularly when reading about the excellent MMORPG, City of Heroes. To wit: the game is configured so that, all else being equal, if a PC attacks an enemy of equal level, he has 75% of hitting (and if the same enemy attacks back, he has about 50% chance of hitting the same PC).

Now, you can trust computer game designers on getting the numbers right – they’re very very good at making things fun. And if you look at a lot of popular RPGs, they tend to use a fairly similar yardstick. People tend to like games where your general chance of succeeding when you’re using something you’re good at is about 70-80% (if you’re only average at it, 50-60% is okay).

Example: in D&D 2nd ed, you’ll probably start with a THAC0 of 19, your average kobold will have an AC of 7, so you need 12 or higher to hit – 45%.  However, in 3rd ed, a fighter probably has +4 to hit and his target probably has an AC of just 12, so he needs only an 8 to hit – 65%. In 4th ed D&D, your first level kobold has an AC of 15, and your tend to start off with around +7 to hit – again, 65% chance of hitting. White Wolf’s basic roll of say two in an attribute and two in a skill gives you four dice. The chance of rolling one success is 76%.

There are games which break that rule, like say Warhammer, which if you’re good starts you around 45% and if you suck around 25%. This helps reinforce some of Warhammer’s theme and style. Likewise, Call of Cthulhu’s average chance of hitting with a shotgun tends to be about 40%, 70 if you raised it because you’re a Great White Hunter – while most academic characters will have Archaeology and Library Use at 95%. In Savage Worlds, a character with d8 in a skill (above average) has 80% of hitting, rising to 85% if they have a d10. That little shift helps SW feel a bit pulpier than a game that sits around 65% – which is what SW would sit at if PCs lacked the “I’m a cool hero” Wild Die.

In my Famous Five RPG, I use 2d6. Originally I had the TNs being 5+, 7+, 9+ for easy, medium and hard, but that left me with a hard test being 27%, and a moderate only being 58%. In playtesting, that left the game feeling a bit gritty, so I slid it one place to the left, getting +4, +6, +8, for %s of 92%, 75% and 42%. I hit the magic number – 75% for a standard test. That left my kids feeling pretty safe, and the experts feeling unstoppable.

And here’s the take-home lesson: it doesn’t matter if you’re no good at stats, you can instinctively sense these percentages. They’re part of our psyche and your players will spot them. Casinos and slot machines are based around them (they usually pay something about 40% of the time, enough to keep you interested but not seem easy). So if you want to communicate genre, you should figure out your percentages. f you want your game to feel really high powered, your standard test should succeed about 85% of the time or more. If you want your game to be fun and not too challenging, aim for 75% on the nose. If you want your game to feel a bit harsh, aim for 50%

That’s for someone talented in the field, of course; by standard roll I mean the thing a player rolls most often, ie his specialty. Not necessarily “average difficulty” of a task, in simulation in-world speak. Because simulation ultimately doesn’t matter – what your players will notice first and foremost is how often they succeed on a roll during a session. If they’re keen for grit, they won’t complain if it’s 50% but if they’re NOT keen for that, you need to aim for around 75%.

If you don’t, you may have to give some sim-ish bullshit escape clause to explain it, as Wild Talents does, and you’ll end up with flame wars.

14 thoughts on “The Magical Probabilities

  1. Oh, and if you’re playing at home, you’ll have already noticed that the only stat in Daughters of Exile is rolled on 4d6, add the two highest, which gives you a mean of about 8 and a median of about 9 – so 40-45% chance of success, below the gritty line.. This means the PCs – like starting Warhammer PCs – will feel the world is harsh and against them, and thus making the “escape” of doing what a man says very tempting for them.

      • The video game design market in Brisbane is the largest in Australia, but that’s not really saying much. (Oh, and P.S. I put forward Daughters of Exile to go forward in Game Chef…a review to come soon).

      • My buddy was fired when said industry shrank to about 30% its size last year. My old roommate spent most of 2008 and 9 trying to get a job in same industry, and had to go back to Bulgaria, despite first rate qualifications. Meanwhile, I was offered a job on a MMORPG, but that was in the US, need a green card. It’s tough. (And woot, thanks! I admit, I haven’t read yours yet)

  2. OK Steve ‘t was understandable enough until the last sentence! Now would you please translate from non-professional-gamers-slang “If you don’t, you may have to give some sim-ish bullshit escape clause to explain it, as Wild Talents does, and you’ll end up with flame wars.”? What’s the bad thing with Wild Talents? 🙂

  3. Wild Talents is a great game, but like Greg Stolze’s other famous game, Unknown Armies, it tends to have a fairly low success rate – your standard roll is about 50%. To get around this it uses an in-game “simulationist” escape clause, saying that this reflects that you should only roll for tasks that are very hard or under gunfire or similar pressure. This deals with the problem by saying “we’re not simulating your idea of reality, we’re simulating our idea of reality” which ALWAYS missed the actual issue, which has nothing to DO with what’s being simulated, and everything to do with what’s being experienced.

    Don’t get me wrong, simulation is important – WFRP gets around this issue by saying straight up in its simulation “Your PC is pretty crap to start with, and life is hard, and this game thrives on that”. Wild Talents doesn’t say this, it just throws it in as an afterthought, and forces the GM to constantly adjust his rolling calls to only situations where it makes sense for trained professionals to have a hard time. WT passes the buck to the GM, which is never a good sign.

  4. Pingback: A Fiasco Replay | D-Constructions

  5. Hi,
    thanks for this fantastic article;
    it’s very interesting.
    Could you please tell me which mathematical formulas you used?
    I’d very much like to know which one it is so that I can use it myself in all the RPGs I use, either as a player or a DM.
    Thanks a lot !
    Keep on the good work !

      • Hi, thanks for your prompt response.

        For instance, in final fantasy RPG,
        to attack, we have to throw a d100 and then we have to take a look at the “chance of success” :
        namely character’s accuracy minus the target’s evasion;
        so let’s say we have 70 for the accuracy and 60 for the evasion.

        So the character should do 10 or less at the d100 dice to hit the target.

        Maybe the example I took was dumb since the rules already call that “chance of success or CoS”.

        Maybe I should have chosen another rpg lol.

        Have a nice sunday !

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s