Hi there!

As noted in my last post, one of the things I'm changing in v0.3 is Attack rolls keying off Armaments. I'm going to dive deeper into that here, think out loud about the balance involved, and see where that gets us in general. There's a bunch of math ahead. You've been warned! I promise it's going somewhere though.

Dice and Probability

I covered this a bit in my first devlog about v0.2's Attributes. The most important part, though, is the probability for each number of dice (0 and 4 won't come up much, but mostly for comparison):

• 0 dice is 55% fail with consequence, 33% succeed with consequence, 11% succeed without consequence (0 is roll two, take the lower).
• 1 die is 33% across the board for each outcome.
• 2 dice is 11% fail with consequence, 33% succeed with consequence, 55% succeed without consequence.
• 3 dice is 4% fail with consequence, 26% succeed with consequence, 70% succeed without consequence.
• 4 dice is 1% fail with consequence, 19% succeed with consequence, 80% succeed without consequence.
  

So now that we're differentiating between these on an Armament-by-Armament basis, I'm going to consider the two things we care about most here: the chance to deal Harm (that is, hit: to roll 3-6) and the chance to avoid a consequence when rolling (that is, roll 5-6). 

• 1 die to 2 dice gives ~22% higher chance to deal Harm, ~22% higher chance to avoid a consequence. (0 to 1 is the same.)
• 2 dice to 3 dice gives ~7% higher chance to deal Harm, ~15% higher chance to avoid a consequence.
• 3 dice to 4 dice gives ~3% higher chance to deal Harm, ~10% higher chance to avoid a consequence.
  

As you can see, the value of 1 die has very significant returns initially, but tapers off quickly for dealing Harm (less quickly for avoiding consequences). This is something we're going to keep in mind going forward.

Balancing against More or Less Dice

So let's think about balance for a second. These are a few Armaments from v0.2:

• Plasma Torch: 2 Harm, Close, Energy
• Assault Rifle: 2 Harm, Near, Burst
• Sniper Rifle: 2 Harm, Far, Stationary

These are pretty well balanced with each other, clearly! Each does the same Harm, has one Range where it operates, and has something that gives it a bit of an edge Harm-wise (ignores Armor, does 1 extra when a 6 is rolled, does 1 extra when staying still). As I've mentioned in previous devlogs, when writing Armaments, I kept a 3 Harm balance in mind (base Harm, plus each tag is roughly 0.5 Harm). They're not terribly distinct from one another - we'll get to that later - but there's a baseline.

Something to keep in mind while reading onward is the value of Harm. Typically light enemies will have 2 Vigor, medium enemies will have 3 Vigor, and heavy enemies will have 4 Vigor and either Armor or Shields. So baseline Armaments are balanced to very frequently take out light enemies, sometimes take out medium enemies, and need a few hits for heavy enemies. Prime enemies can have 6+ Vigor per Restoration, though, and Tyrants can have 10+, so high-Harm attacks aren't overkill against all enemies, just a lot of them.

Now, with this in mind, what's the value of a die? My first step is to boil those two datapoints (increased chance to harm and increased chance to avoid consequence) down to one. We need a basis and both of those are important so I'm just going to add those two percentages. This gives us:

• 1 to 2 dice: ~22% + ~22% = ~45% or so. (0 to 1 is the same.)
• 2 to 3 dice: ~7% + ~15% = ~22% or so.
• 3 to 4 dice: ~3% + ~10% = ~13% or so.

The game up until this point has been balanced around characters using 3 dice swinging with ~3 Harm equivalent. I'm going to fudge these upward a little (45% up to 50%, 22% up to 33%) and apply those percentages to our 3 Harm equivalence:

• Going from 3 dice to 2 dice is worth +1 Harm (33%), and
• Going from 2 dice to 1 die is worth +1.5 Harm (50%), so
• Going from 3 dice to 1 die is worth +2.5 Harm (83%)

This ends up a little skewed in favor of less dice because we fudged upward twice. If you were taking the original two values at face value and rounding to closest you'd get something like +0.6 Harm for 2 dice and +2 Harm for 1 die. But in my experience, it's way more interesting to give players an incentive to increase their level of risk. We're presumably playing to create interesting situations and risk is interesting.

This opens up a ton of options for Armament entries!

Armament Diversity

Let's look at those v0.2 Armaments again and think about how they distinguish:

• Plasma Torch: 2 Harm, Close, Energy.
  • Close-range weapon that ignores Armor.
• Assault Rifle: 2 Harm, Near, Burst.
  • Near-range weapon that does more Harm if you roll well.
• Sniper Rifle: 2 Harm, Far, Stationary.
  • Far-range weapon that does more Harm if targets come to you.

They certainly are balanced...probably to a fault. When balancing in this manner, you're going to get two Harm-equivalent entries:

• 1 Harm, 4 tags
• 2 Harm, 2 tags

Of the v0.2 weapons, 2 are the first and 10 are the second. This has been a sticking point with me while watching playtesting: they kind of all look the same, even if the various tags correspond better or worse to various playstyles, enemies, etc. so it's harder for players to scan the list and see what they want out of an Armament.

Now let's look at what those 3 Armaments look like with our changes:

• Plasma Blade: 1 die, 4 Harm, Close, Energy, Piercing
  • Feels like a mech sword now! Will reliably one-shot the majority of Standard enemies, Energy and Piercing let it ignore any non-Vigor defense. That said, it has to hit to deal that Harm, and consequences will add up.
• Assault Rifle: 3 dice, 2 Harm, Near, Burst
  • This is the same as the v0.2 entry, but now reliability and accuracy are a featured quality instead of the presumed default.
• Sniper Rifle: 2 dice, 3 Harm, Far, Stationary
  • Enough damage to one-shot medium enemies if it hits, but less accuracy if you're moving around - a few tags now add +1 die instead of +1 Harm when their condition is met and Stationary is one of them.

These are much more distinct from each other! And if our balance metric holds, they're fairly comparable. I'll have to playtest this to see how it goes, of course - the one thing that immediately strikes me is that effects that add dice are worth more when you're at less dice, so keeping an eye on those is a good plan, but that's also true of effects that remove dice (like Sensor damage). From initial eyeballing, though, it doesn't look too far off. Our Harm-equivalence list now looks like:

• 3 dice, 1 Harm, 4 tags
• 3 dice, 2 Harm, 2 tags
• 2 dice, 2 Harm, 4 tags
• 2 dice, 3 Harm, 2 tags
• 1 die, 4 Harm, 3 tags
• 1 die, 5 Harm, 1 tags (won't use this one, 1 tag is going to just be a single range tag and that's boring)

Thanks to this increased diversity of options, I can reasonably increase the Stock Model Armament roster to a list of 18 instead of 12. This means that every stock Frame will now come standard with two Armaments that no other Frame comes with.

And that's mostly that for now. I'll probably be thinking about adding Ammo and System changes next.

Until next time!