zenno/doc/race: fix mobile

zenno: link up doc/race
Fixes #16.
2026-06-14 18:57:43 -04:00 · 2026-06-14 17:55:21 -04:00 · 2026-06-14 17:45:29 -04:00 · 2026-06-14 17:36:00 -04:00
5 changed files with 545 additions and 93 deletions
@@ -107,6 +107,42 @@ const speedStrategyPhaseCoeff = [

 const distanceProficiencyMod = [0.1, 0.2, 0.4, 0.6, 0.8, 0.9, 1.0, 1.05] as const;

+/**
+ * Get a horse's base target speed outside of late race.
+ * @param raceLen Length of the race in meters
+ * @param style Horse's running style
+ * @param phase Phase to calculate for
+ */
+export function baseTargetSpeed(raceLen: number, style: RunningStyle, phase: Exclude<Phase, Phase.LateRace>): number;
+/**
+ * Get a horse's base target speed when not spurting during late race.
+ * @param raceLen Length of the race in meters
+ * @param style Horse's running style
+ * @param phase Phase to calculate for
+ * @param speedStat Final speed stat
+ * @param distanceApt Horse's aptitude for the distance
+ */
+export function baseTargetSpeed(
+	raceLen: number,
+	style: RunningStyle,
+	phase: Phase.LateRace,
+	speedStat: number,
+	distanceApt: AptitudeLevel,
+): number;
+export function baseTargetSpeed(
+	raceLen: number,
+	style: RunningStyle,
+	phase: Phase,
+	speedStat?: number,
+	distanceApt?: number,
+): number {
+	const base = baseSpeed(raceLen);
+	const baseTarget = base * speedStrategyPhaseCoeff[style][phase];
+	const late =
+		phase === Phase.LateRace ? (math.sqrt(500 * speedStat!) as number) * distanceProficiencyMod[distanceApt!] * 0.002 : 0;
+	return baseTarget + late;
+}
+
 /**
 * Calculate the range of section speed values for a horse in early or mid race.
 * @param raceLen Length of the race in meters
@@ -224,6 +260,25 @@ export function inverseSpurtSpeed(
 	return Math.round(r);
 }

+const hpStrategyCoeff = {
+	[RunningStyle.FrontRunner]: 0.95,
+	[RunningStyle.PaceChaser]: 0.89,
+	[RunningStyle.LateSurger]: 1.0,
+	[RunningStyle.EndCloser]: 0.995,
+	[RunningStyle.GreatEscape]: 0.86,
+} as const;
+
+/**
+ * Calculate a horse's max HP (starting HP) for a race.
+ * @param raceLen Length of the race in meters
+ * @param style Horse's running style
+ * @param stamStat Final stamina stat
+ * @returns Max HP
+ */
+export function maxHP(raceLen: number, style: RunningStyle, stamStat: number): number {
+	return 0.8 * hpStrategyCoeff[style] * stamStat + raceLen;
+}
+
 /** Meters per horse length (馬身). */
 export const HORSE_LENGTH = 2.5;
 /** Meters per course width (a constant unit of measure). */
@@ -295,6 +350,57 @@ export function deceleration(phase: Phase, pdm?: boolean, dead?: boolean): numbe
 	return phaseDecel[phase];
 }

+/**
+ * Calculate a horse's lane change target speed before the first move lane point.
+ * @param powerStat Final power stat
+ * @param maxLane Max lane value on the race track in CW
+ * @param currentLane Current lane on the race track in CW
+ * @returns Lane change speed in CW/s
+ */
+export function laneChangeSpeed(powerStat: number, maxLane: number, currentLane: number): number;
+/**
+ * Calculate a horse's lane change target speed during late race and final spurt phase.
+ * @param powerStat Final power stat
+ * @param order Current order on the field
+ * @returns Lane change speed in CW/s
+ */
+export function laneChangeSpeed(powerStat: number, order: number): number;
+/**
+ * Calculate a horse's lane change target speed between the first move lane point and late race.
+ * @param powerStat Final power stat
+ * @returns Lane change speed in CW/s
+ */
+export function laneChangeSpeed(powerStat: number): number;
+export function laneChangeSpeed(powerStat: number, maxLaneOrOrder?: number, currentLane?: number): number {
+	const laneMod = currentLane != null ? 1 + (currentLane / maxLaneOrOrder!) * 0.05 : 1;
+	const orderMod = currentLane == null ? 1 + (maxLaneOrOrder ?? 0) * 0.05 : 1;
+	return 0.02 * (0.3 + 0.001 * powerStat) * laneMod * orderMod;
+}
+
+/**
+ * Acceleration of lane change (horizontal) current speed.
+ */
+export const LANE_CHANGE_ACCEL = 0.03;
+
+/**
+ * Calculate a horse's minimum speed for a race.
+ * @param raceLen Length of the race in meters
+ * @param gutsStat Final guts stat
+ * @returns Minimum speed in m/s
+ */
+export function minSpeed(raceLen: number, gutsStat: number): number {
+	return 0.85 * baseSpeed(raceLen) + Math.sqrt(200 * gutsStat) * 0.001;
+}
+
+/**
+ * Calculate a horse's HP consumption multiplier for late race and last spurt phase.
+ * @param gutsStat Final guts stat
+ * @returns HP consumption multiplier
+ */
+export function spurtHPRateMod(gutsStat: number): number {
+	return 1 + 200 / Math.sqrt(600 * gutsStat);
+}
+
 /**
 * Calculate the speed boost gained from spot struggle.
 * @param gutsStat Final guts stat
@@ -319,6 +425,24 @@ export function spotStruggleDuration(gutsStat: number, frontAptitude: AptitudeLe
 	return Math.sqrt(700 * gutsStat) * 0.012 * strategyProficiencyMod[frontAptitude];
 }

+/**
+ * Calculate the target speed bonus of dueling.
+ * @param gutsStat Final guts stat
+ * @returns Modifier to target speed while dueling in m/s
+ */
+export function duelSpeedMod(gutsStat: number): number {
+	return Math.pow(200 * gutsStat, 0.708) * 0.0001;
+}
+
+/**
+ * Calculate the acceleration bonus of dueling.
+ * @param gutsStat Final guts stat
+ * @returns Modifier to acceleration while dueling in m/s²
+ */
+export function duelAccelMod(gutsStat: number): number {
+	return Math.pow(160 * gutsStat, 0.59) * 0.0001;
+}
+
 /**
 * Calculate the speed modifier for running uphill.
 * Contrary to the race mechanics document, this is expressed as a negative number.
@@ -348,7 +472,7 @@ export function moveLaneModifier(powerStat: number): number {
 * @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);
+	const p = Math.ceil(Math.max(20, 100 - 9000 / baseWit)) / 100;
 	return binomPMF(p, N ?? 1, n ?? 1);
 }

@@ -389,13 +513,22 @@ export function speedGain(speedBonus: number, dur: number, accel: number | null,
 	return speedBonus * (dur + 0.5 * (decelTime - accelTime));
 }

+/**
+ * Calculate the probability of accepting a reduced spurt candidate.
+ * @param witStat Final wit stat
+ * @returns Probability per candidate to accept
+ */
+export function reducedSpurtChance(witStat: number): number {
+	return Math.ceil(15 + 0.05 * witStat) / 100;
+}
+
 /**
 * 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;
+	return Math.ceil(witStat * 0.04) / 100;
 }

 /**
@@ -415,3 +548,13 @@ export function frontModeEnterChance(witStat: number): number {
 export function paceUpEnterChance(witStat: number): number {
 	return 0.15 * math.log10(witStat) - 0.15;
 }
+
+/**
+ * Calculate the chance for a horse to become rushed during a given race.
+ * @param witStat Final wit stat, including style aptitude modifier
+ * @returns Probability to become rushed during the race
+ */
+export function rushedChance(witStat: number): number {
+	const r = 6.5 / Math.log10(0.1 * witStat + 1);
+	return Math.ceil(r * r) / 100;
+}
@@ -43,6 +43,14 @@
 		<a href="https://lanecalc.hf-uma.net/" target="_blank" rel="noopener noreferrer">危険回避シミュ</a>, or Lanecalc, for precise
 		lane combo simulation.
 	</li>
+	<li>
+		<a href={resolve('/doc/race')}>Race Mechanics Charts</a> &mdash; Interactive adaptation of
+		<a
+			href="https://docs.google.com/document/d/15VzW9W2tXBBTibBRbZ8IVpW6HaMX8H0RP03kq6Az7Xg/edit"
+			target="_blank"
+			rel="noopener noreferrer">KuromiAK's race mechanics documentation</a
+		> for easier visualization of how mechanics scale.
+	</li>
 </ul>

 <h2 class="my-4 text-4xl">About</h2>
@@ -14,4 +14,12 @@
 		<a href="https://lanecalc.hf-uma.net/" target="_blank" rel="noopener noreferrer">危険回避シミュ</a>, or Lanecalc, for precise
 		lane combo simulation.
 	</li>
+	<li>
+		<a href={resolve('/doc/race')}>Race Mechanics Charts</a> &mdash; Interactive adaptation of
+		<a
+			href="https://docs.google.com/document/d/15VzW9W2tXBBTibBRbZ8IVpW6HaMX8H0RP03kq6Az7Xg/edit"
+			target="_blank"
+			rel="noopener noreferrer">KuromiAK's race mechanics documentation</a
+		> for easier visualization of how mechanics scale.
+	</li>
 </ul>
@@ -1278,97 +1278,11 @@
 		</li>
 	</ul>

-	<Sec h={2} id="stats">Stat Reference</Sec>
-	<p>
-		This chapter is an extremely brief reference of what front runner race mechanics each stat and aptitude applies to and how
-		they scale.
-	</p>
-	<p>There are four types of each stat.</p>
-	<ol class="mb-4 list-decimal pl-4">
-		<li>
-			<i>Raw stat</i> is the number displayed in the horse's info. Once stat caps are raised, any portion of raw stats above 1200 is
-			halved.
-		</li>
-		<li><i>Base stat</i> is raw stat modified by mood.</li>
-		<li>
-			<i>Adjusted stat</i> is base stat modified by surface conditions (for speed and power), track stat thresholds (for speed), and
-			style proficiency (for wit).
-		</li>
-		<li><i>Final stat</i> or just <i>stat</i> is adjusted stat plus the effects of green skills.</li>
-	</ol>
-	<p>
-		For example, a 1200 wit style S horse in great mood with the corresponding savvy skill at level 1 has 1200 raw wit, 1248 base
-		wit, 1372 adjusted wit, and 1412 (final) wit.
-	</p>
-	<p>
-		<i>Linear scaling</i> means that a given increase to a stat produces the same change in the mechanical value regardless of the
-		stat value.
-		<i>Root scaling</i> means that the mechanical value scales with the square root, 0.6 power, or 0.7 power of the stat, which
-		means the increase becomes smaller as the stat grows.
-		<i>Log scaling</i> means it scales with the logarithm of the stat; this is the fastest diminishing scaling type.
-		<i>Log-linear scaling</i> means it scales with the stat value multiplied by its logarithm.
-		<i>Negative scaling</i> of any type means that the mechanic instead decreases as the stat increases.
-		<i>Inverse scaling</i> means it scales with the multiplicative inverse of the stat, i.e. <span class="font-mono">1/x</span>.
-		Inverse scaling is negative scaling by definition, which means that negative inverse scaling (e.g. skill activation chance)
-		flips back to positive.
-	</p>
-
-	<Sec h={3} id="stats-speed">Speed</Sec>
-	<ul class="mb-4 list-disc pl-4">
-		<li>Spurt speed, root scaling</li>
-		<li>Late race speed when not spurting, root scaling</li>
-	</ul>
-
-	<Sec h={3} id="stats-stamina">Stamina</Sec>
-	<ul class="mb-4 list-disc pl-4">
-		<li>HP, linear scaling</li>
-	</ul>
-
-	<Sec h={3} id="stats-power">Power</Sec>
-	<ul class="mb-4 list-disc pl-4">
-		<li>Move lane modifier (<a href="#lane-combo">lane combo</a>), root scaling</li>
-		<li><a href="#uphills">Uphill target speed loss</a>, negative inverse scaling</li>
-		<li>Acceleration, root scaling</li>
-		<li>Lane change target speed (i.e. the horizontal rather than forward speed of changing lanes), linear</li>
-	</ul>
-
-	<Sec h={3} id="stats-guts">Guts</Sec>
-	<ul class="mb-4 list-disc pl-4">
-		<li>Spurt speed, root scaling (roughly 5% of the effect of the speed stat)</li>
-		<li>Minimum speed, root scaling</li>
-		<li>HP consumption multiplier during last spurt, inverse root scaling</li>
-		<li>Target speed gain from spot struggle, root scaling</li>
-		<li>Duration of spot struggle, root scaling</li>
-		<li>Target speed gain from dueling, root scaling</li>
-		<li>Acceleration gain from dueling, root scaling</li>
-	</ul>
-
-	<Sec h={3} id="stats-wit">Wit</Sec>
-	<ul class="mb-4 list-disc pl-4">
-		<li><a href="#section-speed">Section speed</a>, log-linear scaling</li>
-		<li>Chance to enter <a href="#downhills">downhill accel mode</a>, linear scaling</li>
-		<li>Chance to accept a spurt speed and delay when not full spurting, linear scaling</li>
-		<li>Chance to activate skills, negative inverse scaling, base stat</li>
-		<li>Chance to enter <a href="#front-modes">speed-up and overtake modes</a> during position keep, log scaling</li>
-		<li>
-			For non-fronts, chance to enter pace-up mode, log scaling; but no effect on <a href="#pdm">pace-down mode</a>, which is
-			purely controlled by distance to the pacemaker
-		</li>
-		<li>Chance to become rushed, inverse log-squared scaling</li>
-	</ul>
-
-	<Sec h={3} id="stats-surface">Surface (Turf/Dirt) Aptitude</Sec>
-	<p>Surface aptitude is a multiplier on acceleration. (Not the power stat, for the purposes of other mechanics using power.)</p>
-
-	<Sec h={3} id="stats-distance">Distance Aptitude</Sec>
-	<p>Distance aptitude is a multiplier on spurt speed. At distance E and below, it is also a multiplier on acceleration.</p>
-
-	<Sec h={3} id="stats-style">Style Aptitude</Sec>
-	<p>
-		Style aptitude directly multiplies wit in the computation of the wit stat, which means it affects everything in <a
-			href="#stats-wit">the wit section</a
-		> except for mechanics that use base wit.
-	</p>
+	{#each ['stats', 'stats-speed', 'stats-stamina', 'stats-power', 'stats-guts', 'stats-wit', 'stats-surface', 'stats-style'] as id (id)}
+		<h2 class="hidden target:block target:py-32" {id}>
+			Stat Reference: This chapter moved to <a href={resolve('/doc/race')}>its own article</a>.
+		</h2>
+	{/each}

 	<Sec h={2} id="cm">My CM Teams</Sec>

@@ -0,0 +1,379 @@
+<script lang="ts">
+	import type { ComputedAreas, ComputedSeries } from '$lib/chart';
+	import Article from '../Article.svelte';
+	import Sec from '../Sec.svelte';
+	import * as race from '$lib/race';
+	import StatChart from '$lib/StatChart.svelte';
+	import { resolve } from '$app/paths';
+
+	function modemean(x: number, bonus: number, p: number): number {
+		return x * (1 - p) + x * bonus * p;
+	}
+
+	let style = $state(race.RunningStyle.FrontRunner);
+	let surfaceApt = $state(race.AptitudeLevel.A);
+	let distanceApt = $state(race.AptitudeLevel.A);
+	let raceLen = $state(2000);
+	const raceLenType = $derived.by(() => {
+		if (raceLen < 1500) {
+			return 'Sprint';
+		}
+		if (raceLen < 1900) {
+			return 'Mile';
+		}
+		if (raceLen < 2500) {
+			return 'Medium';
+		}
+		return 'Long';
+	});
+
+	const spurtSpeed: Array<ComputedSeries | null> = $derived([
+		{ label: `Guts 1200`, y: (x) => race.spurtSpeed(x, 1200, style, distanceApt, raceLen) },
+		{ label: `Guts 600`, y: (x) => race.spurtSpeed(x, 600, style, distanceApt, raceLen) },
+		distanceApt !== race.AptitudeLevel.A
+			? { label: `${raceLenType} A, Guts 1200`, y: (x) => race.spurtSpeed(x, 1200, style, race.AptitudeLevel.A, raceLen) }
+			: null,
+	]);
+	const nonSpurtSpeed: Array<ComputedSeries | null> = $derived([
+		{ label: `Base Target Speed`, y: (x) => race.baseTargetSpeed(raceLen, style, race.Phase.LateRace, x, distanceApt) },
+		distanceApt !== race.AptitudeLevel.A
+			? {
+					label: `${raceLenType} A`,
+					y: (x) => race.baseTargetSpeed(raceLen, style, race.Phase.LateRace, x, race.AptitudeLevel.A),
+				}
+			: null,
+	]);
+	const hp: ComputedSeries[] = $derived([
+		{ label: 'Front Runner', y: (x) => race.maxHP(raceLen, race.RunningStyle.FrontRunner, x) },
+		{ label: 'Pace Chaser', y: (x) => race.maxHP(raceLen, race.RunningStyle.PaceChaser, x) },
+		{ label: 'Late Surger', y: (x) => race.maxHP(raceLen, race.RunningStyle.LateSurger, x) },
+		{ label: 'End Closer', y: (x) => race.maxHP(raceLen, race.RunningStyle.EndCloser, x) },
+		{ label: 'Runaway', y: (x) => race.maxHP(raceLen, race.RunningStyle.GreatEscape, x) },
+	]);
+	const moveLane: ComputedSeries[] = [{ label: 'Move Lane Modifier', y: (x) => race.moveLaneModifier(x) }];
+	const uphill: ComputedSeries[] = [
+		{ label: '+2 Hill', y: (x) => race.uphillMod(x, 2.0) },
+		{ label: '+1.5 Hill', y: (x) => race.uphillMod(x, 1.5) },
+		{ label: '+1 Hill', y: (x) => race.uphillMod(x, 1.0) },
+	];
+	const accel: Array<ComputedSeries | null> = $derived([
+		{ label: 'Early Race', y: (x) => race.acceleration(x, style, surfaceApt, race.Phase.EarlyRace) },
+		{ label: 'Mid Race', y: (x) => race.acceleration(x, style, surfaceApt, race.Phase.MidRace) },
+		{ label: 'Late Race', y: (x) => race.acceleration(x, style, surfaceApt, race.Phase.LateRace) },
+		{
+			label: 'Early Race Uphill',
+			y: (x) => race.acceleration(x, style, surfaceApt, race.Phase.EarlyRace, race.AptitudeLevel.A, true),
+		},
+	]);
+	const laneChange: ComputedSeries[] = [{ label: 'Lane Change Target Speed', y: (x) => race.laneChangeSpeed(x) }];
+	const gutsSpurt: Array<ComputedSeries | null> = $derived([
+		{ label: `Speed 1200`, y: (x) => race.spurtSpeed(1200, x, style, distanceApt, raceLen) },
+		{ label: `Speed 600`, y: (x) => race.spurtSpeed(600, x, style, distanceApt, raceLen) },
+		distanceApt !== race.AptitudeLevel.A
+			? { label: `${raceLenType} A, Speed 1200`, y: (x) => race.spurtSpeed(1200, x, style, race.AptitudeLevel.A, raceLen) }
+			: null,
+	]);
+	const minSpeed: ComputedSeries[] = $derived([{ label: 'Minimum Speed', y: (x) => race.minSpeed(raceLen, x) }]);
+	const gutsHPRate: ComputedSeries[] = [{ label: 'HP Consumption Rate Multiplier', y: (x) => race.spurtHPRateMod(x) }];
+	const ssBoost: ComputedSeries[] = [{ label: 'Target Speed Boost', y: (x) => race.spotStruggleSpeed(x) }];
+	const ssDur: ComputedSeries[] = [
+		{ label: 'Front Runner S', y: (x) => race.spotStruggleDuration(x, race.AptitudeLevel.S) },
+		{ label: 'Front Runner A', y: (x) => race.spotStruggleDuration(x, race.AptitudeLevel.A) },
+	];
+	const duelSpeed: ComputedSeries[] = [{ label: 'Dueling Speed Boost', y: (x) => race.duelSpeedMod(x) }];
+	const duelAccel: ComputedSeries[] = [{ label: 'Dueling Acceleration Boost', y: (x) => race.duelAccelMod(x) }];
+	const styleIsFront = $derived(style === race.RunningStyle.FrontRunner || style === race.RunningStyle.GreatEscape);
+	const secSpeed: Array<ComputedAreas | null> = $derived([
+		{
+			label: 'Early Race',
+			y1: (x) => race.sectionSpeed(raceLen, x, x, style, race.Phase.EarlyRace)[0],
+			y2: (x) => race.sectionSpeed(raceLen, x, x, style, race.Phase.EarlyRace)[1],
+		},
+		{
+			label: 'Mid Race',
+			y1: (x) => race.sectionSpeed(raceLen, x, x, style, race.Phase.MidRace)[0],
+			y2: (x) => race.sectionSpeed(raceLen, x, x, style, race.Phase.MidRace)[1],
+		},
+		styleIsFront
+			? {
+					label: 'Early Race + Mean Speed-Up Mode',
+					y1: (x) =>
+						modemean(race.sectionSpeed(raceLen, x, x, style, race.Phase.EarlyRace)[0], 1.04, race.frontModeEnterChance(x)),
+					y2: (x) =>
+						modemean(race.sectionSpeed(raceLen, x, x, style, race.Phase.EarlyRace)[1], 1.04, race.frontModeEnterChance(x)),
+				}
+			: {
+					label: 'Early Race + Mean Pace-Up Mode',
+					y1: (x) => modemean(race.sectionSpeed(raceLen, x, x, style, race.Phase.EarlyRace)[0], 1.04, race.paceUpEnterChance(x)),
+					y2: (x) => modemean(race.sectionSpeed(raceLen, x, x, style, race.Phase.EarlyRace)[1], 1.04, race.paceUpEnterChance(x)),
+				},
+		styleIsFront
+			? {
+					label: 'Mid Race + Mean Speed-Up Mode',
+					y1: (x) => modemean(race.sectionSpeed(raceLen, x, x, style, race.Phase.MidRace)[0], 1.04, race.frontModeEnterChance(x)),
+					y2: (x) => modemean(race.sectionSpeed(raceLen, x, x, style, race.Phase.MidRace)[1], 1.04, race.frontModeEnterChance(x)),
+				}
+			: {
+					label: 'Mid Race + Mean Pace-Up Mode',
+					y1: (x) => modemean(race.sectionSpeed(raceLen, x, x, style, race.Phase.MidRace)[0], 1.04, race.paceUpEnterChance(x)),
+					y2: (x) => modemean(race.sectionSpeed(raceLen, x, x, style, race.Phase.MidRace)[1], 1.04, race.paceUpEnterChance(x)),
+				},
+	]);
+	const downhill: ComputedSeries[] = [
+		{ label: 'Style S', y: (x) => race.downhillAccelEnterChance(x * 1.1) * 100 },
+		{ label: 'Style A', y: (x) => race.downhillAccelEnterChance(x) * 100 },
+	];
+	const reducedSpurt: ComputedSeries[] = [
+		{ label: 'Style S', y: (x) => race.reducedSpurtChance(x * 1.1) * 100 },
+		{ label: 'Style A', y: (x) => race.reducedSpurtChance(x) * 100 },
+	];
+	const skillChance: ComputedSeries[] = [
+		{ label: 'Per Skill', y: (x) => race.skillWitCheck(x) * 100 },
+		{ label: '1 of 2 or 2 of 2', y: (x) => (race.skillWitCheck(x, 2, 1) + race.skillWitCheck(x, 2, 2)) * 100 },
+		{ label: '2 of 2', y: (x) => race.skillWitCheck(x, 2, 2) * 100 },
+		{ label: '3 of 3', y: (x) => race.skillWitCheck(x, 3, 3) * 100 },
+		// TODO(zeph): why is this wrong?
+		{ label: '3 of 3 or 3 of 4', y: (x) => (race.skillWitCheck(x, 4, 3) + race.skillWitCheck(x, 3, 3)) * 100 },
+	];
+	const poskeep: ComputedSeries[] = [
+		{ label: 'Front Runner S', y: (x) => 100 * race.frontModeEnterChance(x * 1.1) },
+		{ label: 'Front Runner A', y: (x) => 100 * race.frontModeEnterChance(x) },
+		{ label: 'Style S', y: (x) => 100 * race.paceUpEnterChance(x * 1.1) },
+		{ label: 'Style A', y: (x) => 100 * race.paceUpEnterChance(x) },
+	];
+	const rushed: ComputedSeries[] = [
+		{ label: 'Style S', y: (x) => race.rushedChance(x * 1.1) * 100 },
+		{ label: 'Style A', y: (x) => race.rushedChance(x) * 100 },
+	];
+</script>
+
+{#snippet statChart(
+	stat: race.Stat,
+	y: Array<ComputedSeries | null>,
+	yLabel: string,
+	range?: [number, number],
+	pick?: { len?: boolean; style?: boolean; dist?: boolean; surf?: boolean },
+)}
+	{#if !pick?.len && !pick?.style && !pick?.dist && !pick?.surf}
+		<div class="mb-12 h-60 w-full md:mb-20 md:h-96">
+			<StatChart
+				class="mx-auto mb-12 h-full w-full max-w-3xl md:mb-10"
+				{stat}
+				{y}
+				{yLabel}
+				{range}
+				plotOptions={{ color: { legend: true } }}
+			/>
+		</div>
+	{:else}
+		<div class="mb-36 h-60 w-full md:mb-28 md:h-96">
+			<StatChart
+				class="mx-auto mb-12 h-full w-full max-w-3xl md:mb-10"
+				{stat}
+				{y}
+				{yLabel}
+				{range}
+				plotOptions={{ color: { legend: true } }}
+			/>
+			<div class="mx-auto grid w-full grid-cols-3 gap-y-6 md:max-w-2xl md:grid-cols-7">
+				{#if pick?.len}
+					<input
+						class="col-span-2 my-auto w-full justify-self-center-safe"
+						type="range"
+						id="raceLen"
+						min="1000"
+						max="3600"
+						step="100"
+						bind:value={raceLen}
+					/>
+					<span class="col-span-1 my-auto pl-2 text-sm">{raceLen}m</span>
+				{/if}
+				{#if pick?.style}
+					<select class="col-span-1 my-auto text-sm md:col-span-2" id="stylePick" bind:value={style}>
+						{#each race.RUNNING_STYLES as [name, style] (style)}
+							<option value={style}>{name}</option>
+						{/each}
+					</select>
+				{/if}
+				{#if pick?.dist}
+					<label class="col-span-1 my-auto pr-2 text-right text-sm md:inline" for="distPick">{raceLenType}</label>
+					<select class="col-span-1 my-auto text-sm" id="distPick" bind:value={distanceApt}>
+						{#each race.APTITUDE_LEVELS as l (l)}
+							<option value={l}>{race.AptitudeLevel[l]}</option>
+						{/each}
+					</select>
+				{/if}
+				{#if pick?.surf}
+					<label class="col-span-1 my-auto pr-2 text-right text-sm md:inline" for="surfPick">Surface</label>
+					<select class="col-span-1 my-auto text-sm" id="surfPick" bind:value={surfaceApt}>
+						{#each race.APTITUDE_LEVELS as l (l)}
+							<option value={l}>{l}</option>
+						{/each}
+					</select>
+				{/if}
+			</div>
+		</div>
+	{/if}
+{/snippet}
+
+<Article>
+	{#snippet head()}
+		<Sec h={1} id="top" class="text-center">Race Mechanics Charts</Sec>
+		<p>
+			This article is an interactive version of <a
+				href="https://docs.google.com/document/d/15VzW9W2tXBBTibBRbZ8IVpW6HaMX8H0RP03kq6Az7Xg/edit"
+				target="_blank"
+				rel="noopener noreferrer">KuromiAK's race mechanics documentation</a
+			>
+			to give a better sense of how mechanics scale with stats and aptitudes.
+		</p>
+		<p>
+			Mechanics are organized in this article according to the stats that determine them. Those that vary with multiple stats,
+			e.g. spurt speed, appear in all relevant sections with differing horizontal axes. Mechanics that vary with race distance,
+			distance aptitudes, and surface aptitudes have controls to change each by their charts.
+		</p>
+		<p>
+			Only numeric mechanics that vary with stats and aptitudes are shown. Descriptions of concepts and conditions are left to the
+			original source.
+		</p>
+		<p>
+			Given the recent discovery that rushed chance uses integer RNG, I am assuming that all wit check mechanics use integer RNG
+			until shown otherwise.
+		</p>
+	{/snippet}
+
+	<Sec h={2} id="speed">Speed</Sec>
+
+	<Sec h={3} id="spurt-speed">Spurt Speed</Sec>
+	<p>Target speed during the Uma's last spurt. See also <a href="#spurt-speed-guts">the effect of Guts</a>.</p>
+	{@render statChart(race.Stat.Speed, spurtSpeed, 'Spurt Speed (m/s)', [20, 26], { len: true, style: true, dist: true })}
+
+	<Sec h={3} id="late-race-speed">Late Race Speed</Sec>
+	<p>Base target speed during late race when the Uma is not spurting (but not dead yet).</p>
+	{@render statChart(race.Stat.Speed, nonSpurtSpeed, 'Base Target Speed (m/s)', [18, 23], { len: true, style: true, dist: true })}
+
+	<Sec h={2} id="stamina">Stamina</Sec>
+
+	<Sec h={3} id="hp">HP</Sec>
+	<p>Max HP, i.e. starting HP.</p>
+	{@render statChart(race.Stat.Stamina, hp, 'HP', [1000, 5000])}
+
+	<Sec h={2} id="power">Power</Sec>
+
+	<Sec h={3} id="move-lane-mod">Move Lane Modifier</Sec>
+	<p>
+		Target speed bonus when changing lanes while under the effect of a lane change speed skill. See <a
+			href={resolve('/doc/frbm#lane-combo')}>lane combo</a
+		>.
+	</p>
+	{@render statChart(race.Stat.Power, moveLane, 'Target Speed Modifier (m/s)', [0.2, 0.5])}
+
+	<Sec h={3} id="uphill">Uphill Target Speed Loss</Sec>
+	<p>Target speed modifier while running uphill.</p>
+	{@render statChart(race.Stat.Power, uphill, 'Target Speed Modifier (m/s)', [-2, 0])}
+
+	<Sec h={3} id="acceleration">Acceleration</Sec>
+	<p>Acceleration.</p>
+	{@render statChart(race.Stat.Power, accel, 'Acceleration (m/s²)', [0.1, 0.5])}
+
+	<Sec h={3} id="lane-change-target-speed">Lane Change Target Speed</Sec>
+	<p>Horizontal (rather than forward) target speed of changing lanes.</p>
+	<div class="mb-4 h-60 w-full md:h-96">
+		<StatChart
+			class="mx-auto mb-12 h-full w-full max-w-3xl md:mb-10"
+			stat={race.Stat.Power}
+			y={laneChange}
+			yLabel="Lane Change Target Speed (CW/s)"
+			range={[0.01, 0.03]}
+		/>
+	</div>
+
+	<Sec h={2} id="guts">Guts</Sec>
+
+	<Sec h={3} id="spurt-speed-guts">Spurt Speed</Sec>
+	<p>Target speed during the Uma's last spurt. See also <a href="#spurt-speed">the effect of Speed</a>.</p>
+	{@render statChart(race.Stat.Guts, gutsSpurt, 'Spurt Speed (m/s)', [20, 26], { len: true, style: true, dist: true })}
+
+	<Sec h={3} id="min-speed">Minimum Speed</Sec>
+	<p>Forced minimum speed, as well as target speed when out of HP.</p>
+	{@render statChart(race.Stat.Guts, minSpeed, 'Target Speed (m/s)', [15.8, 18.4], { len: true })}
+
+	<Sec h={3} id="hp-rate-mod">Late Race HP Consumption Rate Modifier</Sec>
+	<p>Multiplier on HP consumption rate during late race and last spurt phase.</p>
+	{@render statChart(race.Stat.Guts, gutsHPRate, 'HP Consumption Multiplier', [1.2, 1.6])}
+
+	<Sec h={3} id="spot-struggle">Spot Struggle</Sec>
+	<p>Speed boost and duration of spot struggle.</p>
+	<div class="mb-4 grid h-96 w-full md:grid-cols-2">
+		<StatChart stat={race.Stat.Guts} y={ssBoost} yLabel="Speed Bonus (m/s)" range={[0, 0.3]} />
+		<StatChart stat={race.Stat.Guts} y={ssDur} yLabel="Duration (s)" range={[0, 12]} />
+	</div>
+
+	<Sec h={3} id="dueling">Dueling</Sec>
+	<p>Speed boost and acceleration boost of dueling.</p>
+	<div class="mb-4 grid h-96 w-full md:grid-cols-2">
+		<StatChart stat={race.Stat.Guts} y={duelSpeed} yLabel="Speed Bonus (m/s)" range={[0, 0.65]} />
+		<StatChart stat={race.Stat.Guts} y={duelAccel} yLabel="Acceleration Bonus (m/s²)" range={[0, 0.14]} />
+	</div>
+
+	<Sec h={2} id="wit">Wit</Sec>
+
+	<Sec h={3} id="section-speed">Section Speed</Sec>
+	<p>Random variance in target speed per race section.</p>
+	<div class="mb-24 h-60 w-full md:mb-20 md:h-96">
+		<StatChart
+			class="mx-auto mb-12 h-full w-full max-w-3xl md:mb-10"
+			stat={race.Stat.Wit}
+			yArea={secSpeed}
+			yLabel="Section Speed (m/s)"
+			range={[17.5, 22.5]}
+			plotOptions={{ color: { legend: true } }}
+		/>
+		<div class="mx-auto flex w-full md:max-w-2xl">
+			<label class="my-auto hidden flex-1 pr-2 text-right text-sm md:inline" for="secSpeedRaceLen">Race Length</label>
+			<input
+				class="my-auto max-w-40 flex-1 md:flex-2"
+				type="range"
+				id="secSpeedRaceLen"
+				min="1000"
+				max="3600"
+				step="100"
+				bind:value={raceLen}
+			/>
+			<span class="my-auto flex-1 pl-2 text-sm">{raceLen}m</span>
+			<label class="my-auto hidden flex-1 pr-2 text-right text-sm md:inline" for="secSpeedStyle">Style</label>
+			<select class="my-auto flex-1 text-sm" id="secSpeedStyle" bind:value={style}>
+				{#each race.RUNNING_STYLES as [name, style] (style)}
+					<option value={style}>{name}</option>
+				{/each}
+			</select>
+		</div>
+	</div>
+
+	<Sec h={3} id="downhill">Downhill Accel Mode Chance</Sec>
+	<p>Chance each second to enter downhill accel mode when eligible.</p>
+	{@render statChart(race.Stat.Wit, downhill, 'Entry Chance (% each second)', [0, 60])}
+
+	<Sec h={3} id="spurt-accept">Reduced Spurt Accept Chance</Sec>
+	<p>Chance to accept each checked spurt delay and speed when not full spurting.</p>
+	{@render statChart(race.Stat.Wit, reducedSpurt, 'Accept Chance (% each candidate)', [0, 100])}
+
+	<Sec h={3} id="skill">Skill Activation Chance</Sec>
+	<p>
+		Chance that each skill that has a wit check will be eligible to activate. This uses base wit, so style aptitude and passive
+		wit skills do not affect the chance, although mood does.
+	</p>
+	<p>TODO(zeph): Why is the 3 of 4 series getting values over 100%? Is it not just binom(3, 4, p) + binom(4, 4, p)?</p>
+	{@render statChart(race.Stat.Wit, skillChance, 'Skill Activation Chance (%)', [0, 100])}
+
+	<Sec h={3} id="poskeep">Position Keep Mode Chance</Sec>
+	<p>
+		Chance for front runners to enter speed-up or overtake mode, or for non-front runners to enter pace-up mode (but no effect on
+		pace-down mode), each 2 seconds when eligible.
+	</p>
+	{@render statChart(race.Stat.Wit, poskeep, 'Mode Entry Chance (%)', [0, 50])}
+
+	<Sec h={3} id="rushed">Rushed Chance</Sec>
+	<p>Chance for runners to become rushed at some point during the race.</p>
+	{@render statChart(race.Stat.Wit, rushed, 'Rushed Chance (%)', [0, 30])}
+</Article>
Author	SHA1	Message	Date
zephyr	8ef3936be5	zenno/doc/race: fix mobile	2026-06-14 18:57:43 -04:00
zephyr	b06e4b537b	zenno: link up doc/race Fixes #16.	2026-06-14 17:55:21 -04:00
zephyr	7b4cd41d3b	zenno/doc/frbm: remove stat summaries For #16.	2026-06-14 17:45:29 -04:00
zephyr	2c9434729a	zenno/doc/race: interactive graphs for race mechanics For #16.	2026-06-14 17:36:00 -04:00