zenno/doc/frbm: update with charts &c.

zenno/src/lib/Skill.svelte

@@ -0,0 +1,27 @@
+<script lang="ts">
+	import { skills, ZERO_SKILL, type Skill } from "./data/skill";
+
+    interface CommonProps {
+        hint?: string;
+        mention?: boolean;
+    }
+
+    type Props = CommonProps & ({skill: number, name?: never} | {name: string, skill?: never});
+
+    let {hint, mention, skill, name}: Props = $props();
+
+    const s: Readonly<Skill> = $derived.by(() => {
+        const l = skill != null ? skills.global.filter((s) => s.skill_id === skill) : skills.global.filter((s) => s.name.includes(name!));
+        if (name != null) {
+            console.warn(`skills specified as ${name} (${hint}):`, l);
+        }
+        if (l.length === 0) {
+            return ZERO_SKILL;
+        }
+        return l[0];
+    });
+
+    const spanClass = $derived(mention ? 'italic' : 'font-bold')
+</script>
+
+<span class={spanClass}>{s.name}</span>

zenno/src/lib/data/skill.ts

@@ -0,0 +1,173 @@
+import skillGlobal from '../../../../global/skill.json'
+import groupGlobal from '../../../../global/skill-group.json'
+
+/**
+ * Skill data.
+ */
+export interface Skill {
+	/**
+	 * Skill ID.
+	 */
+	skill_id: number;
+	/**
+	 * Regional skill name.
+	 */
+	name: string;
+	/**
+	 * Regional skil description.
+	 */
+	description: string;
+	/**
+	 * Skill group ID.
+	 */
+	group: number;
+	/**
+	 * Skill rarity. 3-5 are uniques for various star levels.
+	 */
+	rarity: 1 | 2 | 3 | 4 | 5;
+	/**
+	 * Upgrade position within the skill's group.
+	 * -1 is for negative (purple) skills.
+	 */
+	group_rate: 1 | 2 | 3 | -1;
+	/**
+	 * Grade value, or the amount of rating gained for having the skill with
+	 * appropriate aptitude.
+	 */
+	grade_value?: number;
+	/**
+	 * Whether the skill requires a wit check.
+	 */
+	wit_check: boolean;
+	/**
+	 * Conditions and results of skill activation.
+	 */
+	activations: Activation[];
+	/**
+	 * Name of the Uma which owns this skill as a unique, if applicable.
+	 */
+	unique_owner?: string;
+	/**
+	 * SP cost to purchase the skill, if applicable.
+	 */
+	sp_cost?: number;
+	/**
+	 * Skill icon ID.
+	 */
+	icon_id: number;
+}
+
+/**
+ * Conditions and results of skill activation.
+ */
+export interface Activation {
+	/**
+	 * Precondition which must be satisfied before the condition is checked.
+	 */
+	precondition?: string;
+	/**
+	 * Activation conditions.
+	 */
+	condition: string;
+	/**
+	 * Skill duration in ten thousandths of a second.
+	 * Generally undefined for activations which only affect HP.
+	 */
+	duration?: number;
+	/**
+	 * Special skill duration scaling mode.
+	 */
+	dur_scale: 1 | 2 | 3 | 4 | 5 | 7;
+	/**
+	 * Skill cooldown in ten thousandths of a second.
+	 * A value of 5000000 indicates that the cooldown is forever.
+	 * Generally undefined for passive skills.
+	 */
+	cooldown?: number;
+	/**
+	 * Results applied when the skill's conditions are met.
+	 */
+	abilities: Ability[];
+}
+
+/**
+ * Effects applied when a skill activates.
+ */
+export interface Ability {
+	/**
+	 * Race mechanic affected by the ability.
+	 */
+	type: 1 | 2 | 3 | 4 | 5 | 6 | 8 | 9 | 10 | 13 | 21 | 27 | 28 | 31 | 35;
+	/**
+	 * Special scaling type of the skill value.
+	 */
+	value_usage: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 13 | 14 | 19 | 20 | 22 | 23 | 24 | 25;
+	/**
+	 * Amount that the skill modifies the race mechanic in ten thousandths of
+	 * whatever is the appropriate unit.
+	 */
+	value: number;
+	/**
+	 * Selector for horses targeted by the ability.
+	 */
+	target: 1 | 2 | 4 | 7 | 9 | 10 | 11 | 18 | 19 | 20 | 21 | 22 | 23;
+	/**
+	 * Argument value for the ability target, when appropriate.
+	 */
+	target_value?: number;
+}
+
+/**
+ * Skill groups.
+ * Skills in a skill group replace each other when purchased.
+ * 
+ * As a special case, horsegen lists both unique skills and their inherited
+ * versions in the skill groups for both.
+ */
+export interface SkillGroup {
+	/**
+	 * Skill group ID.
+	 */
+	skill_group: number;
+	/**
+	 * Base skill in the skill group, if any.
+	 * Either a common (white) skill or an Uma's own unique.
+	 * 
+	 * Some skill groups, e.g. for G1 Averseness, have no base skill.
+	 */
+	skill1?: number;
+	/**
+	 * First upgraded version of a skill, if any.
+	 * A rare (gold) skill, double circle skill, or an inherited unique skill.
+	 */
+	skill2?: number;
+	/**
+	 * Highest upgraded version of a skill, if any.
+	 * Gold version of a skill with a double circle version.
+	 */
+	skill3?: number;
+	/**
+	 * Negative (purple) version of a skill, if any.
+	 */
+	skill_bad?: number;
+}
+
+export const skills = {
+    global: skillGlobal as Skill[],
+} as const;
+
+export const skillGroups = {
+	global: groupGlobal as SkillGroup[],
+} as const;
+
+export const ZERO_SKILL: Readonly<Skill> = {
+	skill_id: 0,
+	name: "invalid skill",
+	description: "an invalid skill was specified",
+	group: 0,
+	rarity: 1,
+	group_rate: 1,
+	wit_check: false,
+	activations: [],
+	icon_id: 0,
+} as const;

zenno/src/lib/prob.ts

@@ -0,0 +1,9 @@
+import * as math from "mathjs";
+
+export function binomPMF(p: number, n: number, k: number): number {
+    // Operate in log domain for precision.
+    const lc = math.lgamma(n+1) - math.lgamma(k+1) - math.lgamma(n-k+1);
+    const lpk = k * math.log(p);
+    const lr = (n - k) * math.log(1 - p);
+    return math.exp(lc + lpk + lr);
+}

zenno/src/lib/race.ts

@@ -1,6 +1,8 @@
 // Umamusume race mechanics adapted from KuromiAK's doc:
 // https://docs.google.com/document/d/15VzW9W2tXBBTibBRbZ8IVpW6HaMX8H0RP03kq6Az7Xg/edit?usp=sharing
 
+import { binomPMF } from "./prob";
+
 /**
  * Fundamental stats of umas.
  */
@@ -246,6 +248,17 @@ export function spotStruggleDuration(gutsStat: number, frontAptitude: AptitudeLe
 	return Math.sqrt(700 * gutsStat) * 0.012 * strategyProficiencyMod[frontAptitude];
 }
 
+/**
+ * Calculate the speed modifier for running uphill.
+ * Contrary to the race mechanics document, this is expressed as a negative number.
+ * @param powerStat Final power stat
+ * @param slopePer Slope percentage, generally one of 0.5, 1.0, 1.5, or 2.0
+ * @returns Speed modifier for running uphill, a negative value
+ */
+export function uphillMod(powerStat: number, slopePer: number): number {
+	return slopePer * -200/powerStat;
+}
+
 /**
  * Calculate the forward speed boost given when moving lanewise while a skill
  * that grants a lane change speed boost is active.
@@ -256,6 +269,18 @@ export function moveLaneModifier(powerStat: number): number {
 	return Math.sqrt(0.0002 * powerStat);
 }
 
+/**
+ * Calculate the probability of n of N skills activating.
+ * @param baseWit Base wit stat
+ * @param N Number of skills available, default 1
+ * @param n Number of skills activating, default 1
+ * @returns Probability of exactly n skills out of N passing wit checks
+ */
+export function skillWitCheck(baseWit: number, N?: number, n?: number): number {
+	const p = Math.max(0.2, 1 - 90/baseWit);
+	return binomPMF(p, N ?? 1, n ?? 1);
+}
+
 /**
  * Calculate a skill's actual duration scaled to race length.
  * @param baseDur Skill's listed duration in s
@@ -292,3 +317,12 @@ export function speedGain(speedBonus: number, dur: number, accel: number | null,
 	// speedBonus*(dur-accelTime) + speedBonus*accelTime/2 + speedBonus*decelTime/2
 	return speedBonus * (dur + 0.5 * (decelTime - accelTime));
 }
+
+/**
+ * Calculate the chance to enter downhill accel mode each second while running downhill.
+ * @param witStat Final wit stat, including style aptitude modifier
+ * @returns Probability each eligible tick to enter downhill accel mode
+ */
+export function downhillAccelEnterChance(witStat: number): number {
+	return witStat * 0.0004;
+}