This is a re-post of an article I wrote for Muse on Minis. I really love the content on OzBall and when Sean offered me the opportunity to contribute here, I leapt at the opportunity. Enjoy!

It’s been a long time since I’ve written for Muse on Minis. I could give the ‘I’ve been busy’ excuse. The truth is, when you’re passionate about something, you make time. I haven’t been THIS passionate about a miniature game for close to two years now. That said, the thrill is back, and with it another article on applied statistics. This article is a light intro to a different style of dice mechanics vs. my previous articles. I’m going to go over statistics implied by that new system and give a few support pieces to help gamers make smarter in-game decisions.

So. What’s got me falling in love with miniature gaming again? If you haven’t guessed already by the title, it’s Guild Ball!

I love the game. It’s as simple as that. However, their dice system is slightly different than previous games I’ve played. Here’s the scoop so we can get into the numbers. Most actions a model may make in Guild Ball are resolved using a dice-pool and a Target Number (TN) test. For attacks, the dice-pool equals the attacking model’s Tactical Ability (TAC) and the Target Number is based on the defending model’s Defensive Ability (DEF). Each die rolled that equals or exceeds the target number generates a successful hit. Let’s see how this works in action.

For the balance of this article, I’m going to use Tapper attacking Calculus as an example. Tapper is a Brewer. I play Brewers. Calculus is an Alchemist. My best friend and nemesis plays Alchemists. BONUS: I get additional points for cleverly mentioning *Calculus* in a math article. Feels like a good choice all around.

Tapper is a TAC of 6. Calculus is a DEF of 4+.

Here’s how I interpret these numbers. Each die has a 50% probability of being a 4 or greater, yielding me a successful hit. I’ve got 6d6 in my dice-pool, so my expected net-hit is 3. (6 dice * 50% probability for each die)

That’s the basic stuff. Now let’s get into the interesting part. After you successfully hit a target model with an attack, the attacking player applies the net-hits to the attacking model’s Playbook to determine the result of the attack. Beyond being the Playbook being a fun mechanic for the game (allowing you to choose from damage, spells, or in-game effects) this choice is strategically interesting.

Let’s go back to Tapper and that derivative Alchemist Jezebel.

Tapper is close enough to either charge Calculus, or walk up and start swinging. So there’s a decision there. Additionally, Tapper has Knock-Down (KD) on his playbook. I could choose to knock down Calculus to reduce her to DEF 3+ for subsequent bashing. That’s another decision we’ll assess.

**Example 1: Tapper has four influence (4 INF). He uses it to charge and attack twice.** Since I called the Calculus player my best friend AND nemesis, I’m going to assume he annoyingly and appropriately uses Defensive Stance. Defensive Stance makes Calculus DEF 5+ for resolving the charge attack.

**Charge:**

Dice-pool = 10. TAC 6 plus 4d6 for the charge.

TN = 5+. DEF4+ plus Defensive Stance.

Probability of Knock-down: 61.0% (I’ll give you a graph for these shortly)

**Attack x2 (if knocked down):**

Dice-pool = 6. TAC 6.

TN = 3+. DEF4+ plus Knock Down.

Probability of 2 damage: 91.8%

Probability of 3 damage: 39.9%

Expected Damage: 4

**Attack x2 (on the 39.0% chance you missed the KD):**

Dice-pool = 6. TAC 6.

TN = 4+. DEF4+.

Probability of 2 damage: 65.7%

Probability of 3 damage: 9.4%

Expected Damage: 3

**Example 2: Tapper has four influence (4 INF). He uses it to attack four times.**

Attack x4:

Dice-pool = 6. TAC 6.

TN = 4+. DEF4+.

Probability of 2 damage: 65.7%

Probability of 3 damage: 9.4%

Expected Damage: 6

In this example, charging and applying KD is questionable. First off, the charge opened up vulnerability to Defensive Stance. Additionally, the yield from INF to damage wasn’t high enough to invest the INF in KD for Tapper’s sake alone. Of course, the Brewers love going ‘Bash Bros’-mode and that KD spread across multiple players would create additional value. This exercise was simplified to introduce the statistics at hand, but creative players certainly understand the overall value KD has on the pitch.

As for my promise to share something interesting; I’ve put together some graphs shown below on the cumulative probabilities for several TAC/DEF combinations to help developing in-game intuition for the critical cut-points. I’ll include the link to the full set below. To read this, each series represents the desired number of net-hits. The vertical axis is the cumulative probability. The horizontal axis is the DEF of the defending model. In Example 2 above, I would use the Dice-Pool = 6d6 graph. At the time, I was hunting for 3 damage. Tapper’s Playbook requires 5 net-hits to do that because it’s on column 4 of his Playbook and one net-hit is nullified by the 1 ARM for Calculus. The 5 net-hit line is light blue below. In Example 2, Calculus was DEF 4+. The cumulative probability of me getting that result is 9.4%.

Here’s the link: http://museonminis.com/the-statisticians-guild-graphs/