Natural Game Behaviors with Dice Rolls

Making MMO Systems Feel “Right” In Combat, Crafting, and Everything Else

Years ago I was visiting the Beijing studio of an up and coming MMO developer for a sit-down with their design team. The topic was combat: it wasn’t fun.

It wasn’t an unusual MMO combat system either; in fact, it was based on very solid game design principles common to the level grinders of its day (i.e. World of Warcraft) with a heavy focus on fantasy melee combat with a Romance of the Three Kingdoms vibe to it.

We sat down as a team at a table with a big screen on the wall, and, after instantiating a new character holding onto a crescent blade went to find a few mobs to fight.

I watched a few fights and saw what I could see: damage output seemed all over the place, character model animations lacked fluidity, lighting was off, effects and sound mismatches?—?all the hallmarks of trying to get a general solution off the ground without any time on polish.

As a designer I knew I could involve the Art team to solve many of the “delightful” issues (things that make you feel good about watching/engaging in combat). The damage output bothered me at a deeper level, though, so I took over the controls.

(Base Damage * Level) / Modifier

Auto-attacking made it obvious that there was something very strange happening. Every successful hit on the attacking wolf seemed like it ranged all over the place from 5 to 20 points of damage.

I asked what the damage output for my blade was, and the answer was: 5 to 20.

What was the base damage for my weapon? 5 to 20.

Oh.

I put down the controls and went to the whiteboard and started sketching up some numbers. I queried the designers again about the base damage vs. actual damage output. It was a class based game so I expected some modifications of the base damage depending on level, but they let me know that levels only affected special abilities.

So now I had two very different design issues, one of which was a fundamental lacking in applying leveling to auto-attack weapon damage, and the other was the actual way damage was being dealt.

What I wanted to understand, right then, was how they were deciding on how to deal the damage.

Really Random is Really Bad

The designers seemed a little cowed at my question, and one rushed off to fetch a senior engineer.

Together, they explained that they had a random number generator where they set the range of damage for the weapon, and the designers could specify the bottom and top of the range. After all, in every game guide out there it displays weapon stats in that manner.

I understood, certainly, but began my diagnosis with a simple fact: just because the result has a bottom and top in a range, doesn’t mean that other game actually implemented the underlying mechanics that way.

The confusion was palpable so I continued at the whiteboard, simplifying the example. I made a weapon with base damage 1 to 5. I asked them all what the chances of doing 1 point of damage should be.

“20%” they responded. And yes, mathematically that would be correct. In a random number generator using the range 1 to 5 you would expect that 20% of the time you end up with 1 point of damage.

I asked about doing 5 points of damage: “20%” as expected.

“Is that fun?” I asked.

No one could answer definitively one way or another.

Understanding How Skills Work

“Does anyone here play darts?” and this time I got some nods. “When you throw a dart at the board, would you say that most of time you don’t really hit exactly where you aimed, but get somewhat close?”

“Sure,” I heard.

“Do you sometimes totally screw up? Do you sometimes hit exactly where you wanted?”

Everyone understood that, and so the follow-up:

“Do you miss the board completely about one in five times you throw?”

No. No, an average darts player doesn’t consistently and predictably miss the dart board every few throws. Even just a few nights out of practice can help someone generally hit the board and not fail catastrophically.

“That’d suck,” someone pointed out.

I nodded: “That’s how players feel when they see their damage output land all over the place instead of ‘mostly’ in the middle of the range.”

Average Chance vs. Bell Curves

“But on average they do hit in the middle! The calculations all check out!”

No they don’t. Your stats are lying to your face.

Let’s take a dice roll, for instance, and upgrade our weapon to do a base damage of 1 to 6 points.

On average, you would expect damage output to be 3.5 points. (1 + 2 + 3 + 4 + 5 + 6) / 6 or (1 + 6) / 2.

Sure, over enough time that is statistically true, but long runs of statistical averages have nothing to do with the realities of game combat. In most combat scenarios you have a limited number of opportunities to wear your opponent down or outright kill them before they kill you.

If you have a 16.67% chance to roll a 1 or 2 then you have a 33.34% chance of rolling very low damage on every swing.

If you’re not lucky, you’re already dead by the time the chances turn in your favor.

And you’re going to be unlucky a lot.

What you really want is most of the time to be doing around 3 or 4 points of damage, with the occasional critical hit or failure?—?a probability curve that looks more like this:

With a straight up random number picker between “low” and “high” you end up with a probability curve that looks like this:

That’s right. Flat.

Flat is boring. Flat is not fun.

Rolling Dice (or just using Normal Curves)

Ultima Online based most of its gameplay behaviors on dice rolls in one way or another, just like many other RPGs inheriting the D&D mode of game design.

Weapon damage, monster hitpoints, armor ratings?—?a lot of it all boiled down to dice rolls.

The most surprising thing when examining those dice roll definitions though was seeing a dice notation like this: 3d6+32.

What this effectively did was roll 3 dice with 6 sides, and then add 32 to the result (to have a higher starting point). In this case, the range was 35 to 50 but 25% of the time the result would be 42 or 43, and only 0.5% of the time would it be 35 or 50.

Here’s how it works:

Take one dice with six sides and roll it. The curve is flat as mentioned before:

Now take two dice with six sides and roll them, the curve is now quite different:

If you’ve ever played Craps at the casino then rolling two dice and looking at the probabilities should look pretty familiar.

What happens if you roll three dice with six sides?

What you’ll see in the bell curve above is a predictable behavior: most of the damage would be in the middle, with the lower and higher damages being naturally rarer events.

How would you take that 3d6 calculation and still get a bell curve for a target damage range of 1 to 6?

Just divide the result by 3 (three dice), and round to the nearest whole. When you do that, you end up with one of the first charts you saw in this article:

Great Expectations

The wonderful thing about using curves of probability in your game is that, whether it’s dice or another method, you can create a variety of naturalistic behaviors where “average damage output” feels “right.”

When you focus on providing “centered” output your players feel more confident in not being sacrificed to the random number generator gods, and are more likely not to die immediately after successive streaks of bad luck.

It gives you a great starting point (you don’t have to stop with dice rolls, you can use ranks, promotions, and event modifiers!) for any skill or stat-based behavior.

Want to see how it’ll apply in Shards Online? Join our Alpha! https://www.shardsonline.com