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

zenno/package-lock.json

@@ -8,7 +8,8 @@
 			"name": "zenno",
 			"version": "0.0.1",
 			"dependencies": {
-				"@observablehq/plot": "^0.6.17"
+				"@observablehq/plot": "^0.6.17",
+				"mathjs": "^15.2.0"
 			},
 			"devDependencies": {
 				"@eslint/compat": "^2.1.0",
@@ -40,6 +41,15 @@
 				"vitest-browser-svelte": "^2.1.1"
 			}
 		},
+		"node_modules/@babel/runtime": {
+			"version": "7.29.2",
+			"resolved": "https://registry.npmjs.org/@babel/runtime/-/runtime-7.29.2.tgz",
+			"integrity": "sha512-JiDShH45zKHWyGe4ZNVRrCjBz8Nh9TMmZG1kh4QTK8hCBTWBi8Da+i7s1fJw7/lYpM4ccepSNfqzZ/QvABBi5g==",
+			"license": "MIT",
+			"engines": {
+				"node": ">=6.9.0"
+			}
+		},
 		"node_modules/@blazediff/core": {
 			"version": "1.9.1",
 			"resolved": "https://registry.npmjs.org/@blazediff/core/-/core-1.9.1.tgz",
@@ -2416,6 +2426,19 @@
 				"node": ">= 10"
 			}
 		},
+		"node_modules/complex.js": {
+			"version": "2.4.3",
+			"resolved": "https://registry.npmjs.org/complex.js/-/complex.js-2.4.3.tgz",
+			"integrity": "sha512-UrQVSUur14tNX6tiP4y8T4w4FeJAX3bi2cIv0pu/DTLFNxoq7z2Yh83Vfzztj6Px3X/lubqQ9IrPp7Bpn6p4MQ==",
+			"license": "MIT",
+			"engines": {
+				"node": "*"
+			},
+			"funding": {
+				"type": "github",
+				"url": "https://github.com/sponsors/rawify"
+			}
+		},
 		"node_modules/convert-source-map": {
 			"version": "2.0.0",
 			"resolved": "https://registry.npmjs.org/convert-source-map/-/convert-source-map-2.0.0.tgz",
@@ -2880,6 +2903,12 @@
 				}
 			}
 		},
+		"node_modules/decimal.js": {
+			"version": "10.6.0",
+			"resolved": "https://registry.npmjs.org/decimal.js/-/decimal.js-10.6.0.tgz",
+			"integrity": "sha512-YpgQiITW3JXGntzdUmyUR1V812Hn8T1YVXhCu+wO3OpS4eU9l4YdD3qjyiKdV6mvV29zapkMeD390UVEf2lkUg==",
+			"license": "MIT"
+		},
 		"node_modules/deep-is": {
 			"version": "0.1.4",
 			"resolved": "https://registry.npmjs.org/deep-is/-/deep-is-0.1.4.tgz",
@@ -2986,6 +3015,12 @@
 				"@esbuild/win32-x64": "0.27.7"
 			}
 		},
+		"node_modules/escape-latex": {
+			"version": "1.2.0",
+			"resolved": "https://registry.npmjs.org/escape-latex/-/escape-latex-1.2.0.tgz",
+			"integrity": "sha512-nV5aVWW1K0wEiUIEdZ4erkGGH8mDxGyxSeqPzRNtWP7ataw+/olFObw7hujFWlVjNsaDFw5VZ5NzVSIqRgfTiw==",
+			"license": "MIT"
+		},
 		"node_modules/escape-string-regexp": {
 			"version": "4.0.0",
 			"resolved": "https://registry.npmjs.org/escape-string-regexp/-/escape-string-regexp-4.0.0.tgz",
@@ -3349,6 +3384,19 @@
 			"dev": true,
 			"license": "ISC"
 		},
+		"node_modules/fraction.js": {
+			"version": "5.3.4",
+			"resolved": "https://registry.npmjs.org/fraction.js/-/fraction.js-5.3.4.tgz",
+			"integrity": "sha512-1X1NTtiJphryn/uLQz3whtY6jK3fTqoE3ohKs0tT+Ujr1W59oopxmoEh7Lu5p6vBaPbgoM0bzveAW4Qi5RyWDQ==",
+			"license": "MIT",
+			"engines": {
+				"node": "*"
+			},
+			"funding": {
+				"type": "github",
+				"url": "https://github.com/sponsors/rawify"
+			}
+		},
 		"node_modules/fsevents": {
 			"version": "2.3.2",
 			"resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.2.tgz",
@@ -3493,6 +3541,12 @@
 			"integrity": "sha512-tFLRAygk9NqrRPhJSnNGh7g7oaVWDwR0wKh/GM2LgmPa50Eg4UfyaCO4I8k6EqJHl1/uh2RAD6g06n5ygEnrjQ==",
 			"license": "ISC"
 		},
+		"node_modules/javascript-natural-sort": {
+			"version": "0.7.1",
+			"resolved": "https://registry.npmjs.org/javascript-natural-sort/-/javascript-natural-sort-0.7.1.tgz",
+			"integrity": "sha512-nO6jcEfZWQXDhOiBtG2KvKyEptz7RVbpGP4vTD2hLBdmNQSsCiicO2Ioinv6UI4y9ukqnBpy+XZ9H6uLNgJTlw==",
+			"license": "MIT"
+		},
 		"node_modules/jiti": {
 			"version": "2.7.0",
 			"resolved": "https://registry.npmjs.org/jiti/-/jiti-2.7.0.tgz",
@@ -3869,6 +3923,29 @@
 				"@jridgewell/sourcemap-codec": "^1.5.5"
 			}
 		},
+		"node_modules/mathjs": {
+			"version": "15.2.0",
+			"resolved": "https://registry.npmjs.org/mathjs/-/mathjs-15.2.0.tgz",
+			"integrity": "sha512-UAQzSVob9rNLdGpqcFMYmSu9dkuLYy7Lr2hBEQS5SHQdknA9VppJz3cy2KkpMzTODunad6V6cNv+5kOLsePLow==",
+			"license": "Apache-2.0",
+			"dependencies": {
+				"@babel/runtime": "^7.26.10",
+				"complex.js": "^2.2.5",
+				"decimal.js": "^10.4.3",
+				"escape-latex": "^1.2.0",
+				"fraction.js": "^5.2.1",
+				"javascript-natural-sort": "^0.7.1",
+				"seedrandom": "^3.0.5",
+				"tiny-emitter": "^2.1.0",
+				"typed-function": "^4.2.1"
+			},
+			"bin": {
+				"mathjs": "bin/cli.js"
+			},
+			"engines": {
+				"node": ">= 18"
+			}
+		},
 		"node_modules/minimatch": {
 			"version": "10.2.5",
 			"resolved": "https://registry.npmjs.org/minimatch/-/minimatch-10.2.5.tgz",
@@ -4448,6 +4525,12 @@
 			"integrity": "sha512-YZo3K82SD7Riyi0E1EQPojLz7kpepnSQI9IyPbHHg1XXXevb5dJI7tpyN2ADxGcQbHG7vcyRHk0cbwqcQriUtg==",
 			"license": "MIT"
 		},
+		"node_modules/seedrandom": {
+			"version": "3.0.5",
+			"resolved": "https://registry.npmjs.org/seedrandom/-/seedrandom-3.0.5.tgz",
+			"integrity": "sha512-8OwmbklUNzwezjGInmZ+2clQmExQPvomqjL7LFqOYqtmuxRgQYqOD3mHaU+MvZn5FLUeVxVfQjwLZW/n/JFuqg==",
+			"license": "MIT"
+		},
 		"node_modules/semver": {
 			"version": "7.8.0",
 			"resolved": "https://registry.npmjs.org/semver/-/semver-7.8.0.tgz",
@@ -4689,6 +4772,12 @@
 				"url": "https://opencollective.com/webpack"
 			}
 		},
+		"node_modules/tiny-emitter": {
+			"version": "2.1.0",
+			"resolved": "https://registry.npmjs.org/tiny-emitter/-/tiny-emitter-2.1.0.tgz",
+			"integrity": "sha512-NB6Dk1A9xgQPMoGqC5CVXn123gWyte215ONT5Pp5a0yt4nlEoO1ZWeCwpncaekPHXO60i47ihFnZPiRPjRMq4Q==",
+			"license": "MIT"
+		},
 		"node_modules/tinybench": {
 			"version": "2.9.0",
 			"resolved": "https://registry.npmjs.org/tinybench/-/tinybench-2.9.0.tgz",
@@ -4769,6 +4858,15 @@
 				"node": ">= 0.8.0"
 			}
 		},
+		"node_modules/typed-function": {
+			"version": "4.2.2",
+			"resolved": "https://registry.npmjs.org/typed-function/-/typed-function-4.2.2.tgz",
+			"integrity": "sha512-VwaXim9Gp1bngi/q3do8hgttYn2uC3MoT/gfuMWylnj1IeZBUAyPddHZlo1K05BDoj8DYPpMdiHqH1dDYdJf2A==",
+			"license": "MIT",
+			"engines": {
+				"node": ">= 18"
+			}
+		},
 		"node_modules/typescript": {
 			"version": "5.9.3",
 			"resolved": "https://registry.npmjs.org/typescript/-/typescript-5.9.3.tgz",

zenno/package.json

@@ -45,6 +45,7 @@
 		"vitest-browser-svelte": "^2.1.1"
 	},
 	"dependencies": {
-		"@observablehq/plot": "^0.6.17"
+		"@observablehq/plot": "^0.6.17",
+		"mathjs": "^15.2.0"
 	}
 }

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/StatChart.svelte

@@ -2,32 +2,47 @@
 	import * as Plot from '@observablehq/plot';
 	import * as d3 from 'd3';
 	import { Stat } from './race';
-	import type { ComputedSeries } from './chart';
+	import type { ComputedSeries, HorizontalRule } from './chart';
 	import type { ClassValue } from 'svelte/elements';
 	import type { Attachment } from 'svelte/attachments';
 
 	interface Props {
+		/** The stat the chart shows. */
 		stat: Stat;
+		/** Series to show in the chart. */
 		y: ComputedSeries | Array<ComputedSeries | null>;
+		/** Label for the dependent variable. */
 		yLabel: string;
-		range?: [number, number];
+		/**
+		 * Range of the dependent variable to show.
+		 * If not given, the limits are the minimum and maximum values plotted.
+		 * If given as a triple, the second value is the default maximum and
+		 * the third is the maximum when the chart is expanded to 2000.
+		 */
+		range?: [number, number] | [number, number, number];
+		/** Range of the stat to plot. */
 		xRange?: [number, number] | null;
+		/**
+		 * Vertical rules to place on the graph.
+		 * Each rule gets a corresponding horizontal rule at the intersection
+		 * with each series.
+		 */
 		xRule?: number | number[];
+		/**
+		 * Horizontal rules to place on the graph.
+		 */
+		yRule?: HorizontalRule[];
 
 		class?: ClassValue | null;
 		plotOptions?: Omit<Plot.PlotOptions, 'marks' | 'x' | 'y'>;
 	}
 
-	let { stat, y, yLabel, range, xRange, xRule = [], class: className, plotOptions = {} }: Props = $props();
+	let { stat, y, yLabel, range, xRange, xRule = [], yRule = [], class: className, plotOptions = {} }: Props = $props();
 
 	let width = $state(0);
 	let height = $state(0);
 
 	let expand = $state(false);
-	const expandIcon = $derived(expand ? '◀' : '▶');
-	function clickExpand() {
-		expand = !expand;
-	}
 
 	const xLabel = $derived(Stat[stat]);
 	const xLines = $derived([xRule].flat(1));
@@ -48,7 +63,10 @@
 	const vals = $derived(series.flatMap(({ y, label }) => xVal.map((x) => ({ x, y: y(x), label }))));
 	const yRange: [number, number] = $derived.by(() => {
 		if (range != null) {
-			return range;
+			if (range.length === 2) {
+				return range;
+			}
+			return [range[0], expand ? range[2] : range[1]];
 		}
 		const l = d3.min(vals, ({ y }) => y) ?? 0;
 		const r = d3.max(vals, ({ y }) => y) ?? 1;
@@ -63,6 +81,7 @@
 				Plot.plot({
 					width,
 					height,
+					clip: true,
 					...plotOptions,
 					x: {
 						domain: [xMin, xMax],
@@ -81,6 +100,8 @@
 						Plot.ruleX([thrX], { strokeOpacity: 0.25 }),
 						Plot.ruleX(xLines, { strokeOpacity: 0.5 }),
 						Plot.ruleY(yLines, { y: 'y', stroke: 'label', strokeOpacity: 0.5 }),
+						Plot.ruleY(yRule, { y: 'y', strokeOpacity: 0.75 }),
+						Plot.tip(yRule, { x: xMax, y: 'y', title: 'label', anchor: 'top-right', className: 'plot-tip' }),
 						Plot.frame(),
 						Plot.line(vals, { x: 'x', y: 'y', stroke: 'label', strokeWidth: 3 }),
 						Plot.tip(vals, Plot.pointerY({ x: 'x', y: 'y', stroke: 'label', className: 'plot-tip' })),
@@ -93,10 +114,7 @@
 
 <div bind:clientWidth={width} bind:clientHeight={height} class={['flex h-full w-full flex-col md:flex-row', className]}>
 	<div role="img" {@attach makeChart}>
-		<span>Loading chart!</span>
-	</div>
-	<div class="my-5 flex h-full flex-row place-content-end md:flex-col md:place-content-start">
-		<button class="h-8 rounded border px-2 pb-1 align-middle" onclick={clickExpand}>{expandIcon}</button>
+		<span>the chart seems to have didn't</span>
 	</div>
 </div>
 

zenno/src/lib/alpha123Umalator.ts

@@ -0,0 +1,78 @@
+import { AptitudeLevel, Mood, RunningStyle } from './race';
+import type { Runner } from './runner';
+
+const aptMap = {
+	G: AptitudeLevel.G,
+	F: AptitudeLevel.F,
+	E: AptitudeLevel.E,
+	D: AptitudeLevel.D,
+	C: AptitudeLevel.C,
+	B: AptitudeLevel.B,
+	A: AptitudeLevel.A,
+	S: AptitudeLevel.S,
+} as const;
+type AptitudeString = keyof typeof aptMap;
+
+const styleMap = {
+	Nige: RunningStyle.FrontRunner,
+	Sentou: RunningStyle.PaceChaser,
+	Sasi: RunningStyle.LateSurger,
+	Oikomi: RunningStyle.EndCloser,
+	Oonige: RunningStyle.GreatEscape,
+} as const;
+
+export interface ImportUma {
+	outfitId: string;
+	starCount: number;
+	speed: number;
+	stamina: number;
+	power: number;
+	guts: number;
+	wisdom: number;
+	strategy: keyof typeof styleMap;
+	distanceAptitude: AptitudeString;
+	surfaceAptitude: AptitudeString;
+	strategyAptitude: AptitudeString;
+	aptitudes: [
+		AptitudeString,
+		AptitudeString,
+		AptitudeString,
+		AptitudeString,
+		AptitudeString,
+		AptitudeString,
+		AptitudeString,
+		AptitudeString,
+		AptitudeString,
+		AptitudeString,
+	];
+	skills: string[];
+	uniqueLv: number;
+	mood: Mood;
+	popularity: number;
+}
+
+export function load(obj: ImportUma, name?: string): Runner {
+	return {
+		name: name ?? '',
+		chara_card_id: obj.outfitId !== '' ? parseInt(obj.outfitId) : 0,
+		style: styleMap[obj.strategy],
+		mood: obj.mood,
+		speed: obj.speed,
+		stamina: obj.stamina,
+		power: obj.power,
+		guts: obj.guts,
+		wit: obj.wisdom,
+		sprint: aptMap[obj.aptitudes[0]],
+		mile: aptMap[obj.aptitudes[1]],
+		medium: aptMap[obj.aptitudes[2]],
+		long: aptMap[obj.aptitudes[3]],
+		front: aptMap[obj.aptitudes[4]],
+		pace: aptMap[obj.aptitudes[5]],
+		late: aptMap[obj.aptitudes[6]],
+		end: aptMap[obj.aptitudes[7]],
+		turf: aptMap[obj.aptitudes[8]],
+		dirt: aptMap[obj.aptitudes[9]],
+		skills: obj.skills.map((s) => parseInt(s)),
+		unique_level: obj.uniqueLv,
+	};
+}

zenno/src/lib/chart.ts

@@ -2,3 +2,8 @@ export interface ComputedSeries {
 	y: (x: number) => number;
 	label: string;
 }
+
+export interface HorizontalRule {
+	y: number;
+	label: string;
+}

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

@@ -1,8 +1,11 @@
 // Umamusume race mechanics adapted from KuromiAK's doc:
 // https://docs.google.com/document/d/15VzW9W2tXBBTibBRbZ8IVpW6HaMX8H0RP03kq6Az7Xg/edit?usp=sharing
 
-import type { Uma } from './data/uma';
+import { binomPMF } from "./prob";
 
+/**
+ * Fundamental stats of umas.
+ */
 export enum Stat {
 	Speed,
 	Stamina,
@@ -11,63 +14,14 @@ export enum Stat {
 	Wit,
 }
 
+/**
+ * Stats as a list for easy iteration.
+ */
 export const StatList = [Stat.Speed, Stat.Stamina, Stat.Power, Stat.Guts, Stat.Wit] as const;
 
-export interface Runner {
-	name: string;
-
-	chara_card_id: number;
-	style: RunningStyle;
-	mood: Mood;
-
-	speed: number;
-	stamina: number;
-	power: number;
-	guts: number;
-	wit: number;
-
-	sprint: AptitudeLevel;
-	mile: AptitudeLevel;
-	medium: AptitudeLevel;
-	long: AptitudeLevel;
-	front: AptitudeLevel;
-	pace: AptitudeLevel;
-	late: AptitudeLevel;
-	end: AptitudeLevel;
-	turf: AptitudeLevel;
-	dirt: AptitudeLevel;
-
-	skills: number[];
-	unique_level: number;
-}
-
-export function new_runner(name?: string, base_uma?: Uma): Runner {
-	return {
-		name: name ?? '',
-		chara_card_id: base_uma?.chara_card_id ?? 0,
-		// TODO(zeph): default running style
-		style: RunningStyle.FrontRunner,
-		mood: Mood.Normal,
-		speed: 1200,
-		stamina: 1200,
-		power: 1200,
-		guts: 1200,
-		wit: 1200,
-		sprint: base_uma?.sprint ?? AptitudeLevel.A,
-		mile: base_uma?.mile ?? AptitudeLevel.A,
-		medium: base_uma?.medium ?? AptitudeLevel.A,
-		long: base_uma?.long ?? AptitudeLevel.A,
-		front: base_uma?.front ?? AptitudeLevel.A,
-		pace: base_uma?.pace ?? AptitudeLevel.A,
-		late: base_uma?.late ?? AptitudeLevel.A,
-		end: base_uma?.end ?? AptitudeLevel.A,
-		turf: base_uma?.turf ?? AptitudeLevel.A,
-		dirt: base_uma?.dirt ?? AptitudeLevel.A,
-		skills: base_uma != null ? [base_uma.unique] : [],
-		unique_level: 4,
-	};
-}
-
+/**
+ * Mood levels.
+ */
 export enum Mood {
 	Awful = -2,
 	Bad,
@@ -76,6 +30,11 @@ export enum Mood {
 	Great,
 }
 
+/**
+ * Running styles for strategy–phase coefficients.
+ * Great Escape is distinguished as a separate style even though it is
+ * mechanically identical to Front Runner.
+ */
 export enum RunningStyle {
 	FrontRunner,
 	PaceChaser,
@@ -84,6 +43,9 @@ export enum RunningStyle {
 	GreatEscape,
 }
 
+/**
+ * Aptitude or proficiency levels.
+ */
 export enum AptitudeLevel {
 	G,
 	F,
@@ -95,111 +57,35 @@ export enum AptitudeLevel {
 	S,
 }
 
+/**
+ * Aptitude levels as a descending list for easy iterating.
+ */
+export const APTITUDE_LEVELS = [
+	AptitudeLevel.S,
+	AptitudeLevel.A,
+	AptitudeLevel.B,
+	AptitudeLevel.C,
+	AptitudeLevel.D,
+	AptitudeLevel.E,
+	AptitudeLevel.F,
+	AptitudeLevel.G,
+] as const;
+
+/**
+ * Race phases.
+ * While last spurt phase is also a phase, it is not distinguished here.
+ */
 export enum Phase {
 	EarlyRace,
 	MidRace,
 	LateRace,
 }
 
-namespace Alpha123Umalator {
-	const aptitude_map = {
-		G: AptitudeLevel.G,
-		F: AptitudeLevel.F,
-		E: AptitudeLevel.E,
-		D: AptitudeLevel.D,
-		C: AptitudeLevel.C,
-		B: AptitudeLevel.B,
-		A: AptitudeLevel.A,
-		S: AptitudeLevel.S,
-	} as const;
-	type AptitudeString = keyof typeof aptitude_map;
-
-	const style_map = {
-		Nige: RunningStyle.FrontRunner,
-		Sentou: RunningStyle.PaceChaser,
-		Sasi: RunningStyle.LateSurger,
-		Oikomi: RunningStyle.EndCloser,
-		Oonige: RunningStyle.GreatEscape,
-	} as const;
-
-	export interface ImportUma {
-		outfitId: string;
-		starCount: number;
-		speed: number;
-		stamina: number;
-		power: number;
-		guts: number;
-		wisdom: number;
-		strategy: keyof typeof style_map;
-		distanceAptitude: AptitudeString;
-		surfaceAptitude: AptitudeString;
-		strategyAptitude: AptitudeString;
-		aptitudes: [
-			AptitudeString,
-			AptitudeString,
-			AptitudeString,
-			AptitudeString,
-			AptitudeString,
-			AptitudeString,
-			AptitudeString,
-			AptitudeString,
-			AptitudeString,
-			AptitudeString,
-		];
-		skills: string[];
-		uniqueLv: number;
-		mood: Mood;
-		popularity: number;
-	}
-
-	export function load(obj: ImportUma, name?: string): Runner {
-		return {
-			name: name ?? '',
-			chara_card_id: obj.outfitId !== '' ? parseInt(obj.outfitId) : 0,
-			style: style_map[obj.strategy],
-			mood: obj.mood,
-			speed: obj.speed,
-			stamina: obj.stamina,
-			power: obj.power,
-			guts: obj.guts,
-			wit: obj.wisdom,
-			sprint: aptitude_map[obj.aptitudes[0]],
-			mile: aptitude_map[obj.aptitudes[1]],
-			medium: aptitude_map[obj.aptitudes[2]],
-			long: aptitude_map[obj.aptitudes[3]],
-			front: aptitude_map[obj.aptitudes[4]],
-			pace: aptitude_map[obj.aptitudes[5]],
-			late: aptitude_map[obj.aptitudes[6]],
-			end: aptitude_map[obj.aptitudes[7]],
-			turf: aptitude_map[obj.aptitudes[8]],
-			dirt: aptitude_map[obj.aptitudes[9]],
-			skills: obj.skills.map((s) => parseInt(s)),
-			unique_level: obj.uniqueLv,
-		};
-	}
-}
-
-export function import_runner(obj: any, name?: string): Runner | null {
-	// TODO(zeph): check for keys that identify the uma source
-	if (typeof obj === 'object') {
-		try {
-			const r = Alpha123Umalator.load(obj as Alpha123Umalator.ImportUma, name);
-			// TODO(zeph): validate?
-			return r;
-		} catch (exc) {
-			console.warn('failed to import', obj, 'as alpha123 umalator:', exc);
-			return null;
-		}
-	}
-	console.warn('no guess on how to import', obj);
-	return null;
-}
-
 function baseSpeed(raceLen: number): number {
 	return 20 - (raceLen - 2000) / 1000;
 }
 
-const strategyPhaseCoeff = [
+const speedStrategyPhaseCoeff = [
 	[1.0, 0.98, 0.962],
 	[0.978, 0.991, 0.975],
 	[0.938, 0.998, 0.994],
@@ -211,22 +97,21 @@ const distanceProficiencyMod = [0.1, 0.2, 0.4, 0.6, 0.8, 0.9, 1.0, 1.05] as cons
 
 /**
  * Calculate an Uma's last spurt target speed.
- * @param rawSpeed Uma's speed stat. No accounting for mood lol.
- * @param gutsStat Uma's guts stat.
+ * @param speedStat Adjusted speed stat
+ * @param gutsStat Adjusted guts stat
  * @param style Running style
  * @param distance Distance aptitude
  * @param raceLen Length of the race
  * @returns Target speed in the last spurt in m/s
  */
 export function spurtSpeed(
-	rawSpeed: number,
+	speedStat: number,
 	gutsStat: number,
 	style: RunningStyle,
 	distance: AptitudeLevel,
 	raceLen: number,
 ): number {
-	const speedStat = rawSpeed <= 1200 ? rawSpeed : 1200 + (rawSpeed - 1200) * 0.5;
-	const spc = strategyPhaseCoeff[style][Phase.LateRace];
+	const spc = speedStrategyPhaseCoeff[style][Phase.LateRace];
 	const dpm = distanceProficiencyMod[distance];
 	const base = baseSpeed(raceLen);
 	// Expand and rearrange terms from the doccy to make solving for the inverse easier.
@@ -260,13 +145,184 @@ export function inverseSpurtSpeed(
 	// spurtSpeed - base * (1.05*spc + 0.0105) - pow(450*gutsStat, 0.597)*0.0001 = 0.0041*sqrt(500*speedStat)*dpm
 	// (spurtSpeed - base * (1.05*spc + 0.0105) - pow(450*gutsStat, 0.597)*0.0001)²/(0.0041²*dpm²*500) = speedStat
 	// (spurtSpeed - base * (1.05*spc + 0.0105) - pow(450*gutsStat, 0.597)*0.0001)²/(0.008405*dpm²) = speedStat
-	const spc = strategyPhaseCoeff[style][Phase.LateRace];
+	const spc = speedStrategyPhaseCoeff[style][Phase.LateRace];
 	const dpm = distanceProficiencyMod[distance];
 	const base = baseSpeed(raceLen);
 	const nr = spurtSpeed - base * (1.05 * spc + 0.0105) - Math.pow(450 * gutsStat, 0.597) * 0.0001;
 	const r = (nr * nr) / (0.008405 * dpm * dpm);
-	if (r > 1200) {
-		return Math.round(2 * r - 1200);
-	}
 	return Math.round(r);
 }
+
+/** Meters per horse length (馬身). */
+export const HORSE_LENGTH = 2.5;
+/** Meters per course width (a constant unit of measure). */
+export const COURSE_WIDTH = 11.25;
+/** Meters per lane width. */
+export const LANE_WIDTH = COURSE_WIDTH / 18;
+
+const accelStrategyPhaseCoeff = {
+	[RunningStyle.FrontRunner]: [1.0, 1.0, 0.996],
+	[RunningStyle.PaceChaser]: [0.985, 1.0, 0.996],
+	[RunningStyle.LateSurger]: [0.975, 1.0, 1.0],
+	[RunningStyle.EndCloser]: [0.945, 1.0, 0.997],
+	[RunningStyle.GreatEscape]: [1.17, 0.94, 0.956],
+} as const;
+
+const surfaceProficiencyMod = [0.1, 0.3, 0.5, 0.7, 0.8, 0.9, 1.0, 1.05] as const;
+const accelDistanceProficiencyMod = [0.4, 0.5, 0.6, 1, 1, 1, 1, 1] as const;
+
+/**
+ * Calculate a horse's instantaneous acceleration value.
+ * @param powerStat Final power stat
+ * @param style Running style
+ * @param phase Current race phase for this frame
+ * @param surfaceAptitude Surface aptitude
+ * @param distanceAptitude Distance aptitude; no effect if not given
+ * @param uphill Whether this frame has a positive SlopePer value
+ * @param startDash Whether this frame is in the start dash period, i.e. current speed has not yet reached 85% of the race's base speed
+ * @returns Acceleration in m/s²
+ */
+export function acceleration(
+	powerStat: number,
+	style: RunningStyle,
+	surfaceAptitude: AptitudeLevel,
+	phase: Phase,
+	distanceAptitude?: AptitudeLevel,
+	uphill?: boolean,
+	startDash?: boolean,
+): number {
+	const baseAccel = uphill ? 0.0004 : 0.0006;
+	const startDashMod = startDash ? 24.0 : 0;
+	const spc = accelStrategyPhaseCoeff[style][phase];
+	const spm = surfaceProficiencyMod[surfaceAptitude];
+	const dpm = accelDistanceProficiencyMod[distanceAptitude ?? AptitudeLevel.A];
+	return baseAccel * Math.sqrt(500 * powerStat) * spc * spm * dpm + startDashMod;
+}
+
+const phaseDecel = {
+	[Phase.EarlyRace]: -1.2,
+	[Phase.MidRace]: -0.8,
+	[Phase.LateRace]: -1.0,
+} as const;
+
+/**
+ * Get the phase-based deceleration value.
+ * @param phase Race phase that the horse is running this frame
+ * @param pdm Whether the horse is currently running in pace-down mode
+ * @param dead Whether the horse has zero or less HP
+ * @returns Current deceleration value in m/s², a negative value
+ */
+export function deceleration(phase: Phase, pdm?: boolean, dead?: boolean): number {
+	if (dead) {
+		return -1.2;
+	}
+	if (pdm) {
+		// This isn't until 1.5anni.
+		// return -0.5;
+		return phaseDecel[phase];
+	}
+	return phaseDecel[phase];
+}
+
+/**
+ * Calculate the speed boost gained from spot struggle.
+ * @param gutsStat Final guts stat
+ * @returns Spot struggle speed boost in m/s
+ */
+export function spotStruggleSpeed(gutsStat: number): number {
+	return Math.pow(500 * gutsStat, 0.6) * 0.0001;
+}
+
+const strategyProficiencyMod = [0.1, 0.2, 0.4, 0.6, 0.75, 0.85, 1.0, 1.1] as const;
+
+/**
+ * Calculate the max duration of spot struggle.
+ * Note that spot struggle ends early if the frontmost horse in it reaches a 5m lead,
+ * or at the start of section 9.
+ * @param gutsStat Final guts stat
+ * @param frontAptitude Front runner aptitude level
+ * @returns Spot struggle duration in s
+ */
+export function spotStruggleDuration(gutsStat: number, frontAptitude: AptitudeLevel): number {
+	// https://hakuraku.moe/notes/spot-struggle
+	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.
+ * @param powerStat Final power stat
+ * @returns Move-lane speed modifier in m/s
+ */
+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
+ * @param raceLen Length of the race in m
+ * @returns Actual skill duration in s
+ */
+export function skillDuration(baseDur: number, raceLen: number): number {
+	return baseDur * raceLen * 0.001;
+}
+
+/**
+ * Calculate the distance gained from a target speed boost, including
+ * acceleration to the boosted target speed and deceleration back to baseline.
+ * @param speedBonus Difference between baseline and boosted speed in m/s
+ * @param accel Current acceleration value in m/s², or null for instant acceleration
+ * @param decel Current phase-based deceleration value in m/s², a negative value; or null for instant deceleration
+ * @param dur Duration of the boosted speed
+ * @returns Distance gained from the speed boost in m
+ */
+export function speedGain(speedBonus: number, dur: number, accel: number | null, decel: number | null): number {
+	// Actual effect of a target speed bonus looks like
+	// 	speed: __/-----\__
+	// 	bonus:   ======
+	// I.e., the speed bonus duration includes acceleration to the new speed
+	// and does not include the acceleration back to baseline after it ends.
+	const accelTime = accel !== null ? speedBonus / accel : 0;
+	const decelTime = decel !== null ? -speedBonus / decel : 0;
+	if (accelTime >= dur) {
+		// Acceleration is so low that the horse won't reach the boosted target
+		// speed before the effect ends. E.g., G surface aptitude.
+		const peakSpeed = (accel ?? 0) * dur;
+		return 0.5 * (peakSpeed * dur - peakSpeed / (decel ?? 0));
+	}
+	// 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;
+}

zenno/src/lib/runner.ts

@@ -0,0 +1,89 @@
+import type { Uma } from './data/uma';
+import { AptitudeLevel, Mood, RunningStyle } from './race';
+import * as alpha123Umalator from './alpha123Umalator';
+
+/**
+ * Race runner, i.e. a trained horse.
+ */
+export interface Runner {
+	name: string;
+
+	chara_card_id: number;
+	style: RunningStyle;
+	mood: Mood;
+
+	speed: number;
+	stamina: number;
+	power: number;
+	guts: number;
+	wit: number;
+
+	sprint: AptitudeLevel;
+	mile: AptitudeLevel;
+	medium: AptitudeLevel;
+	long: AptitudeLevel;
+	front: AptitudeLevel;
+	pace: AptitudeLevel;
+	late: AptitudeLevel;
+	end: AptitudeLevel;
+	turf: AptitudeLevel;
+	dirt: AptitudeLevel;
+
+	skills: number[];
+	unique_level: number;
+}
+
+/**
+ * Create a new runner with baseline stats.
+ * @param name Name to apply to the runner
+ * @param base_uma Character card (trainee or uma) to use for aptitudes; otherwise all aptitudes are A
+ * @returns Baseline runner
+ */
+export function newRunner(name?: string, base_uma?: Uma): Runner {
+	return {
+		name: name ?? '',
+		chara_card_id: base_uma?.chara_card_id ?? 0,
+		// TODO(zeph): default running style
+		style: RunningStyle.FrontRunner,
+		mood: Mood.Normal,
+		speed: 1200,
+		stamina: 1200,
+		power: 1200,
+		guts: 1200,
+		wit: 1200,
+		sprint: base_uma?.sprint ?? AptitudeLevel.A,
+		mile: base_uma?.mile ?? AptitudeLevel.A,
+		medium: base_uma?.medium ?? AptitudeLevel.A,
+		long: base_uma?.long ?? AptitudeLevel.A,
+		front: base_uma?.front ?? AptitudeLevel.A,
+		pace: base_uma?.pace ?? AptitudeLevel.A,
+		late: base_uma?.late ?? AptitudeLevel.A,
+		end: base_uma?.end ?? AptitudeLevel.A,
+		turf: base_uma?.turf ?? AptitudeLevel.A,
+		dirt: base_uma?.dirt ?? AptitudeLevel.A,
+		skills: base_uma != null ? [base_uma.unique] : [],
+		unique_level: 4,
+	};
+}
+
+/**
+ * Import a runner from an external source.
+ * @param obj Decoded object to import
+ * @param name Name or memo to apply to the runner
+ * @returns Imported runner, or null if import was not possible
+ */
+export function importRunner(obj: unknown, name?: string): Runner | null {
+	// TODO(zeph): check for keys that identify the uma source
+	if (typeof obj === 'object') {
+		try {
+			const r = alpha123Umalator.load(obj as alpha123Umalator.ImportUma, name);
+			// TODO(zeph): validate?
+			return r;
+		} catch (exc) {
+			console.warn('failed to import', obj, 'as alpha123 umalator:', exc);
+			return null;
+		}
+	}
+	console.warn('no guess on how to import', obj);
+	return null;
+}

zenno/src/routes/+layout.svelte

@@ -19,6 +19,7 @@
 		<span class="flex-1 text-center">
 			<a href={resolve('/')} class="mx-8 my-1 block font-semibold md:hidden">Zenno Rob Roy</a>
 			<a href={resolve('/spurt')} class="mx-8 my-1 inline-block">Spurt Speed</a>
+			<a href={resolve('/mspeed')} class="mx-8 my-1 inline-block">Mechanical Speed</a>
 			<a href={resolve('/convo')} class="mx-8 my-1 inline-block">Lobby Conversations</a>
 		</span>
 	</nav>

zenno/src/routes/+page.svelte

@@ -10,6 +10,10 @@
 		<a href={resolve('/spurt')}>Spurt Speed</a> — Calculate a horse's target speed in the last spurt and compare to other distance aptitudes
 		and running styles.
 	</li>
+	<li>
+		<a href={resolve('/mspeed')}>Front Runner Mechanical Speed Comparator</a> &mdash; Compare spot struggle and lane combo to the effects
+		of individual skills.
+	</li>
 	<li>
 		<a href={resolve('/convo')}>Lobby Conversations</a> — Check participants in lobby conversations and get recommendations on unlocking
 		them quickly.

zenno/src/routes/doc/frbm/+page.svelte

@@ -1,6 +1,38 @@
 <script lang="ts">
 	import { resolve } from '$app/paths';
+	import type { ComputedSeries, HorizontalRule } from '$lib/chart';
+	import { AptitudeLevel, downhillAccelEnterChance, moveLaneModifier, skillWitCheck, spotStruggleDuration, spotStruggleSpeed, Stat, uphillMod } from '$lib/race';
+	import Skill from '$lib/Skill.svelte';
+	import StatChart from '$lib/StatChart.svelte';
 	import Sec from '../Sec.svelte';
+
+	const witCheckSeries: ComputedSeries[] = [
+		{ label: "1/1", y: (x) => 100*skillWitCheck(x, 1, 1) },
+		{ label: "1/2 or 2/2", y: (x) => 100*(skillWitCheck(x, 2, 1) + skillWitCheck(x, 2, 2)) },
+		{ label: "2/2", y: (x) => 100*skillWitCheck(x, 2, 2) },
+	];
+	const ssBoostSeries: ComputedSeries = { label: "Target Speed Boost", y: (x) => spotStruggleSpeed(x) };
+	const ssDurSeries: ComputedSeries[] = [
+		{ label: "Front Runner S", y: (x) => spotStruggleDuration(x, AptitudeLevel.S) },
+		{ label: "Front Runner A", y: (x) => spotStruggleDuration(x, AptitudeLevel.A) },
+	];
+	const laneComboSeries: ComputedSeries = {label: "Target Speed Boost", y: (x) => moveLaneModifier(x) };
+	const lcYRule: HorizontalRule[] = [
+		{ label: "+0.35", y: 0.35 },
+		{ label: "+0.45", y: 0.45 },
+	];
+	const uphillSeries: ComputedSeries[] = [
+		{ label: "+2 Hill", y: (x) => uphillMod(x, 2.0) },
+		{ label: "+1.5 Hill", y: (x) => uphillMod(x, 1.5) },
+		{ label: "+1 Hill", y: (x) => uphillMod(x, 1.0) },
+	];
+	const uphillYRule: HorizontalRule[] = [
+		{ label: "Dominator", y: -0.25 },
+	];
+	const downhillSeries: ComputedSeries[] = [
+		{ label: "Style S", y: (x) => downhillAccelEnterChance(x * 1.1) * 100 },
+		{ label: "Style A", y: (x) => downhillAccelEnterChance(x) * 100 },
+	];
 </script>
 
 <article class="mx-auto max-w-4xl text-justify">
@@ -12,9 +44,10 @@
 	<p>
 		This document is advanced material. The target audience intends to win Champions Meet Group A Finals and either wants to use
 		front runners to do it or wants to understand what front runners they need to beat. This is meant for players who are already
-		strong at training: players who can take a target stat line and skill set and turn it into a horse. This is about what those
-		stat lines and skill sets should be, along with <i>why</i>.
+		strong at training: players who can take a target stat line and skill set and turn it into a horse. This document is about the
+		mechanics that determine what those stat lines and skill sets should be.
 	</p>
+
 	<Sec h="2" id="me">About Me</Sec>
 	<p>
 		About three weeks after Global launched, my friend told me to get a job, so I sent him a screenshot of me clicking the install
@@ -39,6 +72,7 @@
 		rationalize running triple fronts for every CM even though it's not actually very good and most of my favorite horses are late
 		surgers.
 	</p>
+
 	<Sec h="2" id="mechanics">Race Mechanics</Sec>
 	<p>
 		Very quick gloss of race fundamentals. Races are divided into four phases: early race, mid race, late race, and last spurt
@@ -49,68 +83,78 @@
 	<p>
 		The numeric value of acceleration depends on the Power stat, dueling, surface aptitude, uphills, race phase, running style. At
 		the start of early race, horses accelerate from 3 m/s to the early race <i>base target speed</i>, which varies by race
-		distance and running style. At the start of late race, if they have enough HP remaining for their last spurt, horses
-		accelerate from the mid race base target speed to their spurt speed, which varies by speed stat, distance aptitude, race
-		distance, running style, and guts stat, in decreasing order of effect. "Last spurt" and "last spurt phase" are different and
-		unrelated things; the latter is only used in the condition for Homestretch Haste.
+		distance and running style but is generally on the order of 20 m/s. At the start of late race, if they have enough HP remaining for their last spurt, horses
+		accelerate from the mid race base target speed to their spurt speed, which varies by speed stat, distance aptitude, running style, race
+		distance, and guts stat, in decreasing order of effect. "Last spurt" and "last spurt phase" are different and
+		unrelated things; the latter is only used in the condition for <Skill skill={200512} hint="homestretch haste" mention />.
 	</p>
 	<p>
 		Speed skills add a flat amount of target speed, generally +0.15 m/s for white skills, +0.25 m/s for double circle skills and
 		some inherited uniques, +0.35 m/s for gold skills and most speed uniques, and +0.45 m/s for a handful of speed uniques. Accel
-		skills similarly add a flat amount of acceleration, either +0.1 or +0.2 m/s² for white skills and inherited uniques, or +0.3
+		skills similarly add a flat amount of acceleration, typically +0.1 or +0.2 m/s² for white skills and inherited uniques, or +0.3
 		or +0.4 m/s² for gold skills and uniques.
 	</p>
-	<p>
-		Generally speaking, competitive races are won by the horse who gets the most acceleration at the start of late race. The
-		consistency of front runner accel skills is what makes it a viable running style.
-	</p>
+
 	<Sec h="3" id="runaway">Runaway</Sec>
 	<p>
-		The skill <b>Runaway</b> converts front runners into the <i>Great Escape</i> running style. However, no player has ever uttered
+		The skill <Skill skill={202051} hint="runaway" /> converts front runners into the <i>Great Escape</i> running style. However, no player has ever uttered
 		the words "Great Escape" when talking about Umamusume, presumably because Runaway is a much cooler name.
+		("Great Escape" is a direct translation of Japanese 大逃げ <i>oonige</i>, whereas "Front Runner" is a more liberal localization of 逃げ <i>nige</i> that technically just means "escape.")
 	</p>
 	<p>
-		Runaways are still front runners for most purposes, the main difference just being different base target speeds per phase.
+		Runaways are still front runners for all purposes.
+		The main difference is just different numbers for things like base speed and acceleration, stamina to HP conversion, and distance thresholds for running modes.
 		Other mechanics that are specific to front runners also apply to runaways.
 	</p>
-	<Sec h="3" id="spot-struggle">Spot Struggle</Sec>
+
+	<Sec h="2" id="win-cons">Win Conditions</Sec>
 	<p>
-		For each of runaways and non-runaways, there is at most one spot struggle per race. Runaways will not spot struggle with
-		non-runaways, nor vice-versa. When a spot struggle triggers, all front runnners of that type within range participate; I've
-		had a horse join while in 6th.
+		On Global today, competitive horses usually have stat lines that are pretty similar to each other.
+		Races, therefore, are more often won by skills – typically acceleration skills that activate at the start of late race.
+		Front runners have strong options.
+	</p>
+	<ul class="list-disc pl-4 mb-4">
+		<li>
+			<Skill skill={900201} hint="angling" />, sometimes called Rod, is the second best skill in the game.
+			Because only the horse in first place gets it, everything about training front runners becomes a matter of being in front at the start of late race, true to name.
+		</li>
+		<li>
+			On long distance tracks, <Skill skill={900681} hint="vc" /> takes that role instead.
+			The front two horses get it, which opens the opportunity for multi-front builds using <Skill skill={200492} hint="nn" mention />/<Skill skill={200491} hint="nsm" mention /> &ndash;
+			especially because VC tracks aren't subject to the final corner spread that makes those skills worse on sprints and miles &ndash;
+			but otherwise the function is the same.
+		</li>
+		<li>
+			On those sprints where Angling is dead, the front-specific options include <Skill skill={900141} hint="pasta" /> (VPP, or Pasta) and <Skill skill={910451} hint="mummy creek" /> (HCreek),
+			It takes both of them to equal Angling, so such sprints may be better served gambling on <Skill skill={200651} hint="turbo sprint" mention />, <Skill skill={200371} hint="rushing gale" mention />, and possibly <Skill skill={200551} hint="unrestrained" mention /> instead.
+			Front runners are especially strong on sprints for <a href="#spot-struggle">other reasons</a> anyway.
+		</li>
+	</ul>
+	<p>
+		<Skill skill={200491} hint="nsm" /> is the best skill in the game.
+		Unfortunately, for the most part, it's bad on front runners; generally not a win condition.
+		Activating NSM requires not being in first, which means whoever <i>was</i> used Angling and is pulling away from you before you accumulate the blocked time to activate it.
+		Again, VC tracks may be an exception if you specifically build for it.
+	</p>
+
+	<Sec h="2" id="pdm">Pace Down Mode</Sec>
+	<p>
+		During the first 41.67% of the race, <i>position keep</i> is busy arranging each running style into their respective packs.
+		The primary mechanism for this is pace down mode (PDM), which activates whenever a horse gets what their style defines as too close to first place.
 	</p>
 	<p>
-		Spot struggle provides a target speed bonus that scales with the guts stat. If it isn't cut short, which will approximately
-		never happen, its duration scales with the guts stat. Unlike skills, its duration <i>does not</i> scale with race distance.
+		Watch a MANT late surger with 1000+ power and wit in a daily legend race.
+		As long as they don't get blocked, they should <a href="#section-speed">slide forward</a> throughout the early race.
+		Then, around when they reach the pace chaser pack, they'll suddenly start moonwalking back to the rest of the late surgers, often near the back of the group.
+		That's PDM.
 	</p>
 	<p>
-		Spot struggle also greatly increases HP consumption. For normal front runners, the rate is slightly less than Rushed. For
-		runaways, it's more than double Rushed. (This is the reason people say you can't get enough stamina for runaways on Global.)
-		Actually getting Rushed during spot struggle dramatically increases HP consumption, much more than just adding them together;
-		red-light green-light pretty much guarantees that horse won't spurt.
+		On lesser running styles, early race and sometimes mid race speed skills are effectively converted from distance gain into HP conservation via PDM.
+		The thing that really makes front runners good is that they don't have to worry about that &ndash; they aren't subject to PDM at all.
+		Their mid race speed skills always gain distance.
 	</p>
-	<Sec h="3" id="position-keep">Position Keep</Sec>
-	<p>Position Keep is the process by which pace chasers don't pass front runners in the mid race.</p>
-	<p>
-		During Position Keep, the frontmost front runner of each type uses <i>speed up mode</i> to try to stay at least 4.5m (a length
-		is 2.5m) ahead of second place, and other front runners use <i>overtake mode</i> to try to become the frontmost. Both of these modes
-		take wit checks to enter and apply a target speed bonus for their duration; overtake mode is slightly better than speed up mode.
-	</p>
-	<p>
-		Lesser running styles instead have <i>pace up mode</i> and <i>pace down mode</i>. Whether horses enter these is based on their
-		distance from the frontmost horse. Pace up also requires a wit check, but PDM doesn't – if a non-front horse gets too close to
-		the frontmost runner in the first 41.67% of the race, they are guaranteed to switch into PDM, which converts distance into HP.
-	</p>
-	<p>
-		Watch a MANT late surger with 1000+ power and wit in a solo practice match. When you see her advance forward early but then
-		moonwalk for two seconds to the back of the pack, that's PDM.
-	</p>
-	<p>
-		Converting distance into HP is quite a lot worse than just having enough HP. The fact that front runners don't have to worry
-		about PDM is one of their major strengths. In particular, it means that early race speed skills always gain distance for front
-		runners, which is not the case for the inferior styles.
-	</p>
-	<Sec h="3" id="skill-timing">Skill Timing</Sec>
+
+	<Sec h="2" id="skill-timing">Skill Timing</Sec>
 	<p>Thought experiment.</p>
 	<p>
 		Picture two cars driving on a straight freeway, both at exactly 59 mph because I am American, adjacent lanes, keeping exactly
@@ -143,37 +187,163 @@
 		This thought experiment shows that speed skills are actually more valuable before late race than during it. Thus, front
 		runners not having to worry about PDM is even more of an advantage.
 	</p>
-	<Sec h="3" id="skill-stacking">Skill Stacking</Sec>
+
+	<Sec h="2" id="gate-skills">Gate Skills</Sec>
 	<p>
-		In a void, the fact that skill effects stack doesn't change the total distance you get from them. However, getting multiple to
-		activate at the same time drastically improves a front runner's ability to overtake.
+		Gate skills are <Skill skill={201601} hint="gw" /> (GW), <Skill skill={200531} hint="ttl" /> (TTL), and <Skill skill={200431} hint="conc" /> (Conc), as well as all green skills including <Skill skill={202051} hint="runaway" mention />.
+		These skills activate the moment the race starts.
 	</p>
 	<p>
-		The practical consequence of this is that <b>Tail Held High</b> and, for multi-front builds, <b>Ramp Up</b> are extremely good skills
-		for front runners. THH has a long duration and will pretty much always trigger off another speed skill, pushing your horse far forward.
-		Ramp activates upon overtake mid-race, which can turn a lucky order change into a full pass.
+		GW is an absolutely mandatory skill for all front runners.
+		Even runaway blockers should have it, otherwise they will be passed by the normal fronts they're trying to block.
+		It requires three other gate skills, which should be active greens to avoid overreliance on wit checks.
+		For reference, the chart below shows proc chances of one of one, one of two, or two of two skills with wit checks.
 	</p>
-	<Sec h="3" id="duels">Duels</Sec>
+	<div class="w-full h-60 md:h-96 mb-4">
+		<StatChart class="h-full w-full max-w-3xl mx-auto" stat={Stat.Wit} y={witCheckSeries} yLabel="% Chance" range={[50, 100]} xRule={1000} />
+	</div>
 	<p>
-		Aside from spot struggle, the other mechanic that tries to make guts a stat that matters is dueling. This requires two horses
-		on the final straight to sustain a certain distance both along and across the track, and to be close in actual speed. There is
-		some evidence that three horses might be able to enter a single duel, although I am not certain this is confirmed.
+		TTL must be combined with GW if they want any chance of being first out of early race.
+		Since the main source of it is the Mihono Bourbon Wit SSR from the first Halloween event, VBourbon can suffice with its white version <Skill skill={200532} hint="early lead" mention /> and get to the front with her unique instead.
+		(Her other option is the Twin Turbo SSR that does generate a lot of stats but requires winning three 50/50s to get the gold skill.)
 	</p>
 	<p>
-		Duels give a substantial bonus to target speed, a gold speed skill's worth at only 500 guts, for the entire duration of the
-		final straight. (Also a bit of acceleration, but this rarely matters.)
+		Conc is less critical.
+		It's worth taking on horses who have it, but it isn't worth using support card slots just to get it.
+		On the other hand, its white version <Skill skill={200432} hint="focus" /> is bad; its only real use is as a backup gate skill for GW when you don't have enough greens available.
+	</p>
+
+	<Sec h="2" id="spot-struggle">Spot Struggle</Sec>
+	<p>
+		For each of runaways and non-runaways, there is at most one spot struggle per race. Runaways will not spot struggle with
+		non-runaways, nor vice-versa. When a spot struggle triggers, all front runnners of that type within range participate; I've
+		had a horse join while in 6th a couple times.
 	</p>
 	<p>
-		Unfortunately, winning front runners almost never get duels. After Angling, no one else will be nearly close enough to
-		trigger; other fronts are left behind, and other styles are still catching up. On tracks like Tokyo 1600 where Angling is
-		right before the final straight, the problem instead becomes width, since horses spread out on the final corner.
+		Spot struggle provides a target speed bonus that scales with the guts stat. If it isn't cut short, which will approximately
+		never happen, its duration also scales with the guts stat. Unlike skills, its duration <i>does not</i> scale with race distance.
+	</p>
+	<div class="grid w-full h-60 md:h-96 grid-cols-2 mb-4">
+		<StatChart stat={Stat.Guts} y={ssBoostSeries} yLabel="Speed Bonus (m/s)" range={[0, 0.3]} />
+		<StatChart stat={Stat.Guts} y={ssDurSeries} yLabel="Duration (s)" range={[0, 12]} />
+	</div>
+    <p>
+        Spot struggle also greatly increases HP consumption.
+        For normal front runners, the rate is slightly less than Rushed.
+        For runaways, it's more than double Rushed. (This is the reason people say you can't get enough stamina for runaways on Global.)
+        Actually getting Rushed during spot struggle dramatically increases HP consumption, much more than just adding them together; red-light green-light pretty much guarantees that horse won't spurt.
+    </p>
+	<p>
+		In medium+ races, the extra HP consumption is a serious consideration; front runners need more stamina and recoveries than other styles.
+		At 1600m and shorter, the fact that Spot Struggle doesn't scale with race distance means that it can be worth multiple gold speed skills in total distance gained.
+		See the <a href={resolve('/mspeed')}>mechanical speed calculator</a> for precise analysis.
+	</p>
+
+	<Sec h="2" id="lane-combo">Lane Combo</Sec>
+	<p>
+		While under the influence of a skill that increases lane movement speed (shoe icon skills), and while actively changing lanes (i.e. moving sideways), horses gain a (forward) target speed boost that scales with power.
+		This was a change Global received with the Unity Cup scenario.
+	</p>
+	<div class="w-full h-60 md:h-96 mb-4">
+		<StatChart class="h-full w-full max-w-3xl mx-auto" stat={Stat.Power} y={laneComboSeries} yLabel="Speed Boost" yRule={lcYRule} range={[0.2, 0.5]} />
+	</div>
+	<p>
+		Front runners have access to the skill <Skill skill={201262} hint="dd" />, which forces a horse who uses it to move outward to a specific distance from the rail.
+		DD almost always ends shortly before the horse has finished accelerating to early race speed, so it does not convert the move lane speed modifier into distance.
 	</p>
 	<p>
-		For CM12 Aries Cup (Satsuki Sho), I used a guts/wit NSM Suzuka whose goal was to be in third place at late race start, trigger
-		NSM to stick with the Angling user, and duel with high guts to finish out the race. This plan never materialized. I did get
-		one win off the duel itself when it enabled Suzuka to pass back a pace chaser in the closest win I had in the whole event; but
-		one win in eighty races is not a great record.
+		We get advantage from move lane speed modifier by following DD with <Skill skill={200452} hint="pp" /> or <Skill skill={210052} hint="ignited wit" />.
+		DD created an opportunity for those return skills to convert into huge forward speed.
+		This setup is called <i>lane combo</i>.
 	</p>
+	<p>
+		Lane combo is only viable on tracks where early race ends before or at most very early into the first corner.
+		Since PP and Ignited WIT are <span class="font-mono">phase_random==0</span> skills, they can activate at the very end of late race.
+		If there's a corner there, and your horse is still on the outside from DD, you are now physically running a longer distance than those on the inside.
+		That can more than undo the gain from the lane combo itself.
+	</p>
+	<p>
+		The <a href={resolve('/mspeed')}>mechanical speed calculator</a> has an approximation of lane combo's benefit.
+		A more precise lane combo simulator <a href="https://lanecalc.hf-uma.net/" target="_blank" rel="noopener noreferrer">exists</a>,
+		but I am not sufficiently confident in my Japanese to try to guide readers through it.
+		<!-- TODO(zeph): i could totally annotate a picture though -->
+	</p>
+
+	<Sec h="2" id="slopes">Slopes</Sec>
+	<p>
+		Different slopes can be of different angles; the <i>SlopePer</i> parameter is positive for uphills and negative for downhills.
+		SlopePer values that currently exist on tracks include 1, 1.5, and 2, positive or negative.
+	</p>
+
+	<Sec h="3" id="uphills">Uphills</Sec>
+	<p>
+		Running uphill carries a penalty to target speed.
+		This penalty scales negatively with the power stat; that is, higher power means faster uphill running.
+		It scales positively with slope angle.
+	</p>
+	<div class="w-full h-60 md:h-96 mb-4">
+		<StatChart class="w-full max-w-3xl h-full mx-auto" stat={Stat.Power} y={uphillSeries} yLabel="Speed Modifier (m/s)" yRule={uphillYRule} range={[-2, 0]} />
+	</div>
+	<p>
+		Note that surface aptitude <i>does not</i> affect uphill speed, nor power generally.
+		It only affects acceleration.
+	</p>
+	<p>
+		The practical impact is that steep early- and mid-race hills filter out front runners with low power.
+		Even with an otherwise perfect build, an 800 power VBourbon is likely to be passed by a 1280 power (<Skill skill={200152} hint="firm" mention /> + <Skill skill={200282} hint="comp spirit" mention />) Seiun Sky.
+	</p>
+	
+	<Sec h="3" id="downhills">Downhills</Sec>
+	<p>
+		Running downhill allows horses to enter <i>downhill accel mode</i>.
+		Contrary to its name, downhill accel mode does not affect acceleration at all;
+		it gives horses a target speed boost that scales with the slope angle, plus lowered HP consumption via a flat multiplier.
+	</p>
+	<p>
+		Entering downhill accel mode requires passing a wit check.
+		The success rate scales linearly with wit.
+		Style aptitude <i>does</i> affect the chance to pass the check.
+		Its duration is random with a geometric distribution; it does not scale with stats.
+	</p>
+	<div class="w-full h-60 md:h-96 mb-4">
+		<StatChart class="w-full max-w-3xl h-full mx-auto" stat={Stat.Wit} y={downhillSeries} yLabel="Entry Chance (% each second)" range={[0, 60]} />
+	</div>
+	<p>
+		Similar to uphills disproportionately rewarding front runners with higher power, downhills tend to reward high wit.
+		However, the random elements of downhill accel mode mean that lower wit horses may still keep up on downhills, depending on luck.
+		Conversely, the HP savings on long downhills can be enough to drop a recovery skill or two on some tracks.
+	</p>
+
+	<Sec h="2" id="section-speed">Section Speed</Sec>
+	<p>
+		Each section, each horse gets a random modifier to target speed.
+		The modifier's range is determined by the wit stat.
+		(Curiously, the calculation uses both wit as modified by style proficiency and green skills as well as base wit.)
+	</p>
+	<p>
+		Section speed is generally very small; at 1200 wit with style S, it has a range of about -0.15% to 0.5% of race base speed.
+		At 2000m, that translates to an actual speed range of 19.97 to 20.10 m/s.
+	</p>
+	<p>
+		Unlike anything affected by the speed stat, though, it applies during the early and mid race, where front runners are trying to become frontest runners.
+		Wit difference alone can 
+	</p>
+
+	<Sec h="2" id="phase-speed">Phase Speed</Sec>
+	<p>
+		Race base speed is multiplied by the strategy–phase coefficient for each horse.
+		As the name suggests, SPC is different per running style and per race phase.
+		It's the thing that makes runaways take off in early race, and the thing that makes pace chaser promotion scary in late race (for those not using any of the correct running style).
+	</p>
+	<p>
+		Front runners, and even moreso runaways, have particularly punishing SPC for late race.
+		This makes sense; if they weren't forced to be substantially slower than the late surgers they're thirty meters ahead of at late race start, then they would be guaranteed to win every time.
+	</p>
+	<p>
+		Late race, or more precisely the last spurt, is also the only place where the speed stat and distance aptitude apply.
+		In terms of lengths gained, distance S actually does more for front runners than any other style due to SPC.
+	</p>
+
 	<Sec h="2" id="stats">Stats</Sec>
 	<Sec h="3" id="speed">Speed</Sec>
 	<!-- speed matters less than for other styles; corollary: distance S matters less -->
@@ -184,39 +354,6 @@
 	<Sec h="3" id="wit">Wit</Sec>
 	<!-- position keep; front S -->
 	<Sec h="2" id="skills">Skills</Sec>
-	<Sec h="3" id="win-cons">Win Conditions</Sec>
-	<p>
-		On all medium races, almost every mile, many sprints, and some longs, <b>Angling and Scheming</b> is the second strongest single
-		skill currently in the game. Any time late race starts on (or, in the case of Nakayama 2500, very shortly before) a corner, Angling
-		is how front runners win. This means that Seiun Sky is the most important horse to front runner trainers. Everything about training
-		a front runner is for the sake of improving the odds of being the horse to trigger Angling – because only the horse in first gets
-		it.
-	</p>
-	<p>
-		Long races get a different primary win condition: <b>Victory Cheer!</b> from Kitasan Black. VC is more forgiving than Angling, activating
-		for both first and second place, but it's also weaker.
-	</p>
-	<p>
-		The sprints where Angling is dead can try to work with <b>Victoria por plancha ☆</b> (Pasta) and <b>Give Mummy a Hug ♡</b>
-		(Mummy Creek) instead. These skills are also on the weaker side, so front running becomes more of a matter of gambling with skills
-		like Turbo Sprint, Rushing Gale, and Unrestrained. The closest anyone has to not-gambling on such sprints is Nishino Flower's unique,
-		though, and front runners are especially strong in sprints for <a href="#spot-struggle">other reasons</a>.
-	</p>
-	<p>
-		If Angling is the second strongest skill, then the strongest is <b>No Stopping Me!</b>
-		Unfortunately, in most races, it is generally not a front runner skill. Because only one horse gets Angling, they will pull away
-		from whoever is in second, not giving a chance to activate NSM. For NSM to win on a front, the horse who got Angling has to not
-		be Seiun Sky (since Sei's own Angling is equal to NSM in strength), and there has to be no gap in the front pack so that it can
-		trigger. As I write this, I am 80 races into CM12 using a Silence Suzuka who has NSM, and it has been involved in exactly one win
-		where she leapfrogged off (my) Sei to pass (my) VBourbon (who placed second). It was cool, but she would have been better off in
-		the event if she hadn't had Yukino Wit in her deck.
-	</p>
-	<p>
-		The above paragraph notwithstanding, NSM and even its white version, <b>Nimble Navigator</b>, are a decent choice for
-		multi-front builds on VC races. Since the top two horses both get VC, and the accel from it is weaker, having an extra push
-		for your second front is strong. VC maps also don't suffer from the final corner spread that makes NN/NSM hard to trigger on
-		sprints and miles.
-	</p>
 	<Sec h="3" id="gate-skills">Gate Skills</Sec>
 	<!-- gw, ttl, conc -->
 	<Sec h="3" id="lane-combo">Lane Combo</Sec>
@@ -365,131 +502,159 @@
 		Kitasan benefits a lot from running as a Pace Chaser early on, just for the higher effective speed. Rivals are best defeated
 		with your intended style, but in career, winning is more important than front running.
 	</p>
-	<Sec h="2" id="cm">My CM Teams</Sec>
+    <Sec h="2" id="cm">My CM Teams</Sec>
 	<Sec h="3" id="cm13">CM13 – Taurus Cup (Tokyo Derby)</Sec>
 	<p>
-		Maruzensky's unique is live as an order&le;5 for approximately everyone. Filling the ranks with front runners should be a
-		strong means to delay it for later positions, especially COC.
+		Maruzensky's unique is live as an order&le;5 for approximately everyone.
+		Filling the ranks with front runners should be a strong means to delay it for later positions, especially COC.
 	</p>
 	<p>
-		I even considered using Maruzensky herself, since she's a front runner. That line of thought led me to some interesting
-		experiments in Umalator. Redshift hits 25m into the start of late race, as a 0.4 accel on Maruzen and 0.2 inherited, just like
-		Angling. It turns out that that delay has a substantial impact. Sei with Redshift beats Maruzen with Angling by about 0.4
-		lengths.
+		I even considered using Maruzensky herself, since she's a front runner.
+		That line of thought led me to some interesting experiments in Umalator.
+		Redshift hits 25m into the start of late race, as a 0.4 accel on Maruzen and 0.2 inherited, just like Angling.
+		It turns out that that delay has a substantial impact.
+		Sei with Redshift beats Maruzen with Angling by about 0.4 lengths.
 	</p>
 	<p>
-		The story doesn't end there, either. As it turns out, Redshift gains less than half a length for Sei. Ines Fujin's unique
-		(which has a strong version on Tokyo turf specifically) is worth about 0.2 lengths more! So, for Sei specifically, Ines Fujin
-		is the ideal inherit, not Maruzensky.
+		The story doesn't end there, either.
+		As it turns out, Redshift gains less than half a length for Sei.
+		Ines Fujin's unique (which has a strong version on Tokyo turf specifically) is worth about 0.2 lengths more!
+		So, for Sei specifically, Ines Fujin is the ideal inherit, not Maruzensky.
 	</p>
 	<p>
-		Realistically, my team comp probably should be Seiun Sky, VBourbon, and Maruzensky. However, we run our oshis, and Silence
-		Suzuka is my favorite front runner, so she's going in. The question then becomes whether to run VBourbon or Maruzen.
+		Realistically, my team comp probably should be Seiun Sky, VBourbon, and Maruzensky.
+		However, we run our oshis, and Silence Suzuka is my favorite front runner, so she's going in.
+		The question then becomes whether to run VBourbon or Maruzen.
 	</p>
 	<p>
-		Maruzensky has the advantage of working even as far back as 5th place. However, what does that actually beat? She's a front
-		runner, so she can only outrun another front runner, and only if she has a significantly higher spurt speed than whoever got
-		Angling. That basically means she needs to be a guts horse hoping for duels, which in turn means probably both of Professor
-		and Escape Artist aren't happening. That's tough.
+		Maruzensky has the advantage of working even as far back as 5th place.
+		However, what does that actually beat?
+		She's a front runner, so she can only outrun another front runner, and only if she has a significantly higher spurt speed than whoever got Angling.
+		That basically means she needs to be a guts horse hoping for duels, which in turn means probably both of Professor and Escape Artist aren't happening. That's tough.
 	</p>
 	<p>
-		On the other hand, Maruzen isn't relying on a wit check for her big accel. She's also free to take VBourbon or Ines Fujin as
-		her non-Angling inherit, whereas VBourbon is forced into Sei and Maruzen parents. So, basically, what Maruzen would be trying
-		to beat is a VBourbon who hits both Angling and Redshift (&gt;80% chance), matching 0.4 accels but winning in spurt speed.
+		On the other hand, Maruzen isn't relying on a wit check for her big accel.
+		She's also free to take VBourbon or Ines Fujin as her non-Angling inherit, whereas VBourbon is forced into Sei and Maruzen parents.
+		So, basically, what Maruzen would be trying to beat is a VBourbon who hits both Angling and Redshift (&gt;80% chance), matching 0.4 accels but winning in spurt speed.
 	</p>
 	<p>
-		I'm not convinced that's good for my comp. I'd rather just be that VBourbon, having approximately every good front runner
-		skill built in. So, final team comp:
+		I'm not convinced that's good for my comp.
+		I'd rather just be that VBourbon, having approximately every good front runner skill built in.
+		So, final team comp:
 	</p>
-	<ol class="mb-4 list-decimal pl-4">
-		<li>Seiun Sky as a gambler, where the gamble is getting into first in midrace.</li>
+	<ol class="list-decimal pl-4 mb-4">
 		<li>
-			VBourbon as an ace. 1200 wit is basically mandatory thanks to the requirement of double accels. Final Push won't be a bad
-			take as a gamble-y backup.
+			Seiun Sky as a gambler, where the gamble is getting into first in midrace.
 		</li>
 		<li>
-			Silence Suzuka as Silence Suzuka. If you prefer winning over running your favorites, this should be Maruzensky instead.
+			VBourbon as an ace.
+			1200 wit is basically mandatory thanks to the requirement of double accels.
+			Final Push won't be a bad take as a gamble-y backup.
+		</li>
+		<li>
+			Silence Suzuka as Silence Suzuka.
+			If you prefer winning over running your favorites, this should be Maruzensky instead.
 		</li>
 	</ol>
-	<Sec h="3" id="cm12">CM12 – Aries Cup (Satsuki Sho)</Sec>
-	<p>
-		One of COC's best tracks, because U=ma2 is at worst only slightly less good than 777 as a trigger. If there is any other front
-		runner, triple front pushes pace COC out of range for U=ma2, making her at best as reliable as the usual.
-	</p>
-	<ol class="mb-4 list-decimal pl-4">
+    <Sec h="3" id="cm12">CM12 – Aries Cup (Satsuki Sho)</Sec>
+    <p>
+        One of COC's best tracks, because U=ma2 is at worst only slightly less good than 777 as a trigger.
+		If there is any other front runner, triple front pushes pace COC out of range for U=ma2, making her at best as reliable as the usual.
+    </p>
+	<ol class="list-decimal pl-4 mb-4">
 		<li>
-			Seiun Sky's Angling is a 0.4 accel that lasts for the entire accel period, better than COC's 0.3 that's only up for 2/3 of
-			it. I want her to be my ace in front, so capped wit, high power, strong spot struggles, huge mid-race skills. Didn't get a
-			guts build to come together after three weeks of attempts, so switched to a standard speed/power/wit build and got a high
-			roll on the first try. 1181/786/1185/474/1185 A/A/S.
+			Seiun Sky's Angling is a 0.4 accel that lasts for the entire accel period, better than COC's 0.3 that's only up for 2/3 of it.
+			I want her to be my ace in front, so capped wit, high power, strong spot struggles, huge mid-race skills.
+			Didn't get a guts build to come together after three weeks of attempts, so switched to a standard speed/power/wit build and got a high roll on the first try.
+			1181/786/1185/474/1185 A/A/S.
 		</li>
 		<li>
-			VBourbon is a horse that exists. She can beat other people's front runners, so great as a backup. Ideally she lets Sei in
-			front, but it's better to let this happen naturally off the lack of TTL than to force low stats. Second attempt got charming
-			and fast learner for free, medium S, and manageable stats. Skill hints were a bit sparse, but not worth rolling more.
+			VBourbon is a horse that exists. She can beat other people's front runners, so great as a backup.
+			Ideally she lets Sei in front, but it's better to let this happen naturally off the lack of TTL than to force low stats.
+			Second attempt got charming and fast learner for free, medium S, and manageable stats. Skill hints were a bit sparse, but not worth rolling more.
 			1164/662/1010/599/1167 A/S/A.
 		</li>
 		<li>
-			Silence Suzuka is my favorite front runner, so I will run her. Her primary task is to be in third or fourth so COC can't be,
-			so I don't need amazing stats. To maximize her effectiveness, there are two possible plans: I could make her a debuffer,
-			which needs 1200 power and wit but no other stats matter, or I could experiment with something wacky like NSM into duels.
-			The latter sounds more fun, even if it is obviously bad. First attempt didn't get aptitudes but did get Lone Wolf to disable
-			it for everyone else and surprisingly decent stats, which is good enough for me; her job isn't to win anyway.
+			Silence Suzuka is my favorite front runner, so I will run her.
+			Her primary task is to be in third or fourth so COC can't be, so I don't need amazing stats.
+			To maximize her effectiveness, there are two possible plans:
+			I could make her a debuffer, which needs 1200 power and wit but no other stats matter,
+			or I could experiment with something wacky like NSM into duels.
+			The latter sounds more fun, even if it is obviously bad.
+			First attempt didn't get aptitudes but did get Lone Wolf to disable it for everyone else and surprisingly decent stats, which is good enough for me;
+			her job isn't to win anyway.
 			<!-- TODO: stat line -->
 		</li>
 	</ol>
-	<p>Win rates after 40: VBourbon 35%, Sei 17.5%, Suzuka 15%. Not quite executing the plan, but I'll take the wins.</p>
 	<p>
-		Win rates after 80: VBourbon 30%, Sei 22.5%, Suzuka 12.5%. I believe this is my best round 2 performance ever. I lose more to
-		other fronts than to COC. "Most dominant racing horse for a year" continues to get trounced by the wacky triple front build.
+		Win rates after 40: VBourbon 35%, Sei 17.5%, Suzuka 15%. Not quite executing the plan, but I'll take the wins.
+	</p>
+	<p>
+		Win rates after 80: VBourbon 30%, Sei 22.5%, Suzuka 12.5%. I believe this is my best round 2 performance ever.
+		I lose more to other fronts than to COC. "Most dominant racing horse for a year" continues to get trounced by the wacky triple front build.
 	</p>
 	<Sec h="3" id="cm11">CM11 – Pisces Cup (Hanshin 3200 Heavy Rain)</Sec>
-	<p>N.B. This CM was before I started writing this document, so henceforth, there is much less info.</p>
-	<p>Late race starts on the back stretch, which means the end closers are out to play.</p>
-	<ol class="mb-4 list-decimal pl-4">
+	<p>
+		N.B. This CM was before I started writing this document, so henceforth, there is much less info.
+	</p>
+	<p>
+		Late race starts on the back stretch, which means the end closers are out to play.
+	</p>
+	<ol class="list-decimal pl-4 mb-4">
 		<li>
-			Kitasan Black is a snap take. Her unique is the only reliable accel outside of Straightaway Spurt, and it's quite a lot
-			better. 1200/1200/816/777/742 A/S/A.
+			Kitasan Black is a snap take.
+			Her unique is the only reliable accel outside of Straightaway Spurt, and it's quite a lot better.
+			1200/1200/816/777/742 A/S/A.
 		</li>
 		<li>
 			VBourbon's unique has a built-in recovery, which makes her the perfect choice as the survivor if stamina debuffers show up.
 			<!-- TODO: stat line -->
 		</li>
-		<li>Silence Suzuka is coming. 1200/1145/653/608/1000 A/A/A.</li>
+		<li>
+			Silence Suzuka is coming.
+			1200/1145/653/608/1000 A/A/A.
+		</li>
 	</ol>
 	<p>
-		I floundered on parenting and ended up with not enough time to make runners. Suzuka had more wit than Kitasan could handle, so
-		I rarely got Kitasan uniques.
+		I floundered on parenting and ended up with not enough time to make runners.
+		Suzuka had more wit than Kitasan could handle, so I rarely got Kitasan uniques.
+	</p>
+	<p>
+		Win rates after 80: VBourbon 31.25%, Kitasan 21.25%, Suzuka 2.5%.
+	</p>
+	<p>
+		Extremely unlucky finals gave me third place for the first time ever.
 	</p>
-	<p>Win rates after 80: VBourbon 31.25%, Kitasan 21.25%, Suzuka 2.5%.</p>
-	<p>Extremely unlucky finals gave me third place for the first time ever.</p>
 	<Sec h="3" id="cm10">CM10 – Aquarius Cup (February Stakes)</Sec>
 	<p>
-		Everyone is terrified of Taiki Shuttle, who has a 3-4 ult. Triple fronts would like to have a word. It's a dirt track, but
-		every horse can run dirt if you're brave enough.
+		Everyone is terrified of Taiki Shuttle, who has a 3-4 ult.
+		Triple fronts would like to have a word.
+		It's a dirt track, but every horse can run dirt if you're brave enough.
 	</p>
-	<ol class="mb-4 list-decimal pl-4">
+	<ol class="list-decimal pl-4 mb-4">
 		<li>
-			Smart Falcon is the obvious choice, being the only actual dirt front runner to exist. Her unique isn't terribly strong for
-			this track, but her gold skills are – Trending makes it extremely difficult for others to overtake her. 1200/467/920/410/930
-			A/S/A.
+			Smart Falcon is the obvious choice, being the only actual dirt front runner to exist.
+			Her unique isn't terribly strong for this track, but her gold skills are – Trending makes it extremely difficult for others to overtake her.
+			1200/467/920/410/930 A/S/A.
 		</li>
 		<li>
-			Silence Suzuka in runaway mode will make positioning much easier. I don't have to think about Unrestrained on my other
-			horses because they won't be able to get in position for it anyway. Other Suzukas will be rare because she has G dirt and
-			people don't realize distance aptitude hardly matters for runaways. 1200/674/820/470/774 B/A/A.
+			Silence Suzuka in runaway mode will make positioning much easier.
+			I don't have to think about Unrestrained on my other horses because they won't be able to get in position for it anyway.
+			Other Suzukas will be rare because she has G dirt and people don't realize distance aptitude hardly matters for runaways.
+			1200/674/820/470/774 B/A/A.
 		</li>
 		<li>
-			Taiki Shuttle is a front runner now. She has B dirt and C front at base. Very easy to fix. Falco's mid-race is probably
-			stronger than Taiki's between her unique and Trending, so Taiki should often be in position for her ult in this build.
+			Taiki Shuttle is a front runner now.
+			She has B dirt and C front at base. Very easy to fix.
+			Falco's mid-race is probably stronger than Taiki's between her unique and Trending, so Taiki should often be in position for her ult in this build.
 			<!-- TODO: stat line -->
 		</li>
 	</ol>
 	<p>
-		This is probably the strongest gameplan I've been able to use, but I failed to execute it properly. In particular, this was
-		the CM that taught me through experience how important mid race speed skills are for front runners. Final win rate was a bit
-		over 50%, including my first ever five win round 2 entry. Insane luck with Unrestrained at the same time as Angling made
-		Suzuka the champion of the Aquarius Cup.
+		This is probably the strongest gameplan I've been able to use, but I failed to execute it properly.
+		In particular, this was the CM that taught me through experience how important mid race speed skills are for front runners.
+		Final win rate was a bit over 50%, including my first ever five win round 2 entry.
+		Insane luck with Unrestrained at the same time as Angling made Suzuka the champion of the Aquarius Cup.
 	</p>
 	<Sec h="2" id="history">Version History</Sec>
 	<ul class="list-disc pl-4">

zenno/src/routes/mspeed/+page.svelte

@@ -0,0 +1,181 @@
+<script lang="ts">
+	import type { ComputedSeries, HorizontalRule } from '$lib/chart';
+	import {
+		acceleration,
+		APTITUDE_LEVELS,
+		AptitudeLevel,
+		deceleration,
+		HORSE_LENGTH,
+		moveLaneModifier,
+		Phase,
+		RunningStyle,
+		skillDuration,
+		speedGain,
+		spotStruggleDuration,
+		spotStruggleSpeed,
+		Stat,
+	} from '$lib/race';
+	import StatChart from '$lib/StatChart.svelte';
+	import SpeedDur from './SpeedDur.svelte';
+
+	let rawPower = $state(1200);
+	let rawGuts = $state(1200);
+	let raceLen = $state(1600);
+	let surfApt = $state(AptitudeLevel.A);
+	let frontApt = $state(AptitudeLevel.A);
+	let isRunaway = $state(false);
+	let isCareer = $state(false);
+
+	const careerMod = $derived(isCareer ? 400 : 0);
+	const powerStat = $derived(rawPower + careerMod);
+	const gutsStat = $derived(rawGuts + careerMod);
+	const style = $derived(isRunaway ? RunningStyle.GreatEscape : RunningStyle.FrontRunner);
+
+	const phases = [Phase.EarlyRace, Phase.MidRace, Phase.LateRace] as const;
+	const accel = $derived(phases.map((p) => acceleration(powerStat, style, surfApt, p)));
+	const decel = phases.map((p) => deceleration(p));
+
+	const ssBoost = $derived(spotStruggleSpeed(gutsStat));
+	const ssDur = $derived(spotStruggleDuration(gutsStat, frontApt));
+
+	const lcBoost = $derived(moveLaneModifier(powerStat));
+	const lcDur = $derived(Math.min(skillDuration(3, raceLen), 6));
+
+	const uniques = [
+		['Operation Cacao', 0.35, 5, Phase.MidRace],
+		["All Charged! It's Go Time! (Tokyo turf)", 0.45, 5, Phase.LateRace],
+	] as const;
+	const skills = [
+		['Fast-Paced', 0.15, 3, Phase.MidRace],
+		['Professor of Curvature (mid race)', 0.35, 2.4, Phase.MidRace],
+		["All Charged! It's Go Time! (inherited)", 0.25, 3, Phase.LateRace],
+	] as const;
+
+	const ssY: Array<ComputedSeries | null> = $derived([
+		{
+			label: 'Aptitude S',
+			y: (x) => speedGain(spotStruggleSpeed(x), spotStruggleDuration(x, AptitudeLevel.S), accel[0], decel[0]) / HORSE_LENGTH,
+		},
+		{
+			label: 'Aptitude A',
+			y: (x) => speedGain(spotStruggleSpeed(x), spotStruggleDuration(x, AptitudeLevel.A), accel[0], decel[0]) / HORSE_LENGTH,
+		},
+		frontApt < AptitudeLevel.A
+			? {
+					label: `Aptitude ${AptitudeLevel[frontApt]}`,
+					y: (x) => speedGain(spotStruggleSpeed(x), spotStruggleDuration(x, frontApt), accel[0], decel[0]) / HORSE_LENGTH,
+				}
+			: null,
+	]);
+	const lcY: Array<ComputedSeries | null> = $derived([
+		{ label: 'Ideal Lane Combo', y: (x) => speedGain(moveLaneModifier(x), lcDur, accel[0], decel[0]) / HORSE_LENGTH },
+	]);
+	const pcRuler = $derived({ y: speedGain(0.35, skillDuration(2.4, raceLen), accel[1], decel[1]) / HORSE_LENGTH, label: 'Professor of Curvature' });
+    const ssYRule = $derived([
+        pcRuler,
+        { y: speedGain(lcBoost, lcDur, accel[0], decel[0]) / HORSE_LENGTH, label: 'Lane Combo' },
+    ]);
+    const lcYRule = $derived([
+        pcRuler,
+        { y: speedGain(ssBoost, ssDur, accel[0], decel[1]) / HORSE_LENGTH, label: 'Spot Struggle' },
+    ]);
+</script>
+
+<h1 class="text-4xl">Front Runner Mechanical Speed Comparator</h1>
+<div class="mx-auto mt-8 grid max-w-4xl grid-cols-1 rounded-md text-center shadow-md ring md:grid-cols-8">
+	<div class="m-4 md:col-span-2">
+		<label for="powerStat">Power Stat</label>
+		<input type="number" id="powerStat" bind:value={rawPower} class="w-full" />
+	</div>
+	<div class="m-4 md:col-span-2">
+		<label for="gutsStat">Guts Stat</label>
+		<input type="number" id="gutsStat" bind:value={rawGuts} class="w-full" />
+	</div>
+	<div class="m-4 md:col-span-2">
+		<label for="surfaceApt">Surface Aptitude</label>
+		<select id="surfaceApt" required bind:value={surfApt} class="w-full">
+			{#each APTITUDE_LEVELS as apt (apt)}
+				<option value={apt}>{AptitudeLevel[apt]}</option>
+			{/each}
+		</select>
+	</div>
+	<div class="m-4 md:col-span-2">
+		<label for="frontApt">Front Runner Aptitude</label>
+		<select id="frontApt" required bind:value={frontApt} class="w-full">
+			{#each APTITUDE_LEVELS as apt (apt)}
+				<option value={apt}>{AptitudeLevel[apt]}</option>
+			{/each}
+		</select>
+	</div>
+	<div class="m-4 md:col-span-2 md:col-start-2">
+		<label for="raceLen">Race Distance</label>
+		<input type="number" id="raceLen" required min="1000" max="3600" step="100" bind:value={raceLen} class="w-full" />
+	</div>
+	<div class="m-4 self-center md:col-span-2">
+		<label for="isRunaway" class="mr-1 align-middle">Runaway</label>
+		<input type="checkbox" id="isRunaway" role="switch" bind:checked={isRunaway} class="min-h-6 min-w-6 align-middle" />
+	</div>
+	<div class="m-4 self-center md:col-span-2">
+		<label for="isCareer" class="mr-1 align-middle">In Career</label>
+		<input type="checkbox" id="isCareer" role="switch" bind:checked={isCareer} class="min-h-6 min-w-6 align-middle" />
+	</div>
+</div>
+<span class="mt-8 block w-full text-center text-lg">Mechanics</span>
+<div class="mx-auto flex w-full flex-col md:flex-row md:justify-center">
+	<SpeedDur speed={ssBoost} dur={ssDur} accel={accel[0]} decel={[decel[0], decel[1]]}>Spot Struggle</SpeedDur>
+	<SpeedDur speed={lcBoost} dur={lcDur} accel={accel[0]} decel={decel[0]}>Idealized Lane Combo (DDPP)</SpeedDur>
+</div>
+<span class="mt-8 block w-full text-center text-lg">Unique Skills</span>
+<div class="mx-auto flex flex-col md:flex-row md:justify-center">
+	{#each uniques as [name, boost, dur, phase] (name)}
+		<SpeedDur speed={boost} dur={skillDuration(dur, raceLen)} accel={accel[phase]} decel={decel[phase]}>{name}</SpeedDur>
+	{/each}
+</div>
+<span class="mt-8 block w-full text-center text-lg">Inherited Uniques &amp; Other Skills</span>
+<div class="mx-auto flex flex-col md:flex-row md:justify-center">
+	{#each skills as [name, boost, dur, phase] (name)}
+		<SpeedDur speed={boost} dur={skillDuration(dur, raceLen)} accel={accel[phase]} decel={decel[phase]}>{name}</SpeedDur>
+	{/each}
+</div>
+<div class="mx-auto h-60 py-4 md:h-96 md:w-3xl">
+	<StatChart class="flex-1" stat={Stat.Guts} y={ssY} yLabel="Lengths Gained" range={[0, 1.5, 2.5]} xRule={gutsStat} yRule={ssYRule} />
+</div>
+<div class="mx-auto mt-4 h-60 py-4 md:mt-0 md:h-96 md:w-3xl">
+	<StatChart class="flex-1" stat={Stat.Power} y={lcY} yLabel="Lengths Gained" range={[0, 1.5, 2.5]} xRule={powerStat} yRule={lcYRule} />
+</div>
+<div class="mx-auto mt-12 w-full max-w-4xl border-t md:mt-8">
+	<ul class="ml-4 list-disc">
+		<li>All lengths gained include acceleration at the beginning of each speed boost and deceleration after its end.</li>
+		<li>Each effect is assumed to be isolated and executed on level ground.</li>
+		<li>
+			Spot struggle has two numbers to distinguish ending in early race versus ending in mid race, which gives different
+			deceleration values. Since spot struggle duration does not scale with race length, it is more likely to end in mid race on
+			shorter races.
+		</li>
+		<li>
+			Lane combo is idealized in the sense of assuming second lane change speed skill executes immediately after Dodging Danger
+			completes, the horse is never blocked, and the horse returns to the rail in early race before the first corner.
+			<ul class="ml-8 list-[revert]">
+				<li>
+					The move lane modifier is capped to 6 seconds, which is the approximate observed time to move from the Dodging Danger
+					fixed lane back to the rail under the effect of Prudent Positioning.
+				</li>
+				<li>
+					On medium+ tracks, with a proper gate acceleration build, Dodging Danger should realize some lane movement speed
+					modifier, so the actual benefit will be more than the idealized number.
+				</li>
+				<li>
+					Ignited Spirit WIT has a longer duration and lower lane change speed boost than Prudent Positioning, so it is likely to
+					give more benefit than the idealized number.
+				</li>
+				<li>
+					For full simulated analysis of lane combo, see <a
+						href="https://lanecalc.hf-uma.net/"
+						target="_blank"
+						rel="noopener noreferrer">危険回避シミュ</a
+					>.
+				</li>
+			</ul>
+		</li>
+	</ul>
+</div>

zenno/src/routes/mspeed/SpeedDur.svelte

@@ -0,0 +1,33 @@
+<script lang="ts">
+	import { HORSE_LENGTH, speedGain } from '$lib/race';
+	import type { Snippet } from 'svelte';
+
+	interface Props {
+		children: Snippet;
+		speed: number;
+		dur: number;
+		accel: number;
+		decel: number | number[];
+	}
+
+	function fmtp(x: number): string {
+		return x >= 0 ? '+' + x.toFixed(3) : x.toFixed(3);
+	}
+
+	const { children, speed, dur, accel, decel }: Props = $props();
+	const decels = $derived([decel].flat(1));
+
+	const gain = $derived(decels.map((d) => speedGain(speed, dur, accel, d) / HORSE_LENGTH));
+	const text = $derived(gain.map(fmtp).join(' – '));
+</script>
+
+<div
+	class="m-2 flex h-full w-full max-w-80 flex-1 flex-col rounded-md border p-2 text-center shadow-sm transition-shadow hover:shadow-md"
+>
+	<div class="block">{@render children()}</div>
+	<span class="block text-xl">{text} L</span>
+	<div class="flex flex-row">
+		<span class="flex-1 text-xs">{fmtp(speed)} m/s</span>
+		<span class="flex-1 text-xs">{dur.toFixed(3)} s</span>
+	</div>
+</div>

zenno/src/routes/spurt/+page.svelte

@@ -86,7 +86,7 @@
 	</div>
 	<div class="m-4 md:col-start-2">
 		<label for="raceLen">Race Distance</label>
-		<input type="number" id="raceLen" required bind:value={raceLen} class="w-full" />
+		<input type="number" id="raceLen" required min="1000" max="3600" step="100" bind:value={raceLen} class="w-full" />
 	</div>
 	<div class="m-4 self-center">
 		<label for="isCareer" class="mr-1 align-middle">In Career</label>