zenno/spurt: calculator for last spurt speed

zenno/src/lib/race.ts

@@ -0,0 +1,103 @@
+// Umamusume race mechanics adapted from KuromiAK's doc:
+// https://docs.google.com/document/d/15VzW9W2tXBBTibBRbZ8IVpW6HaMX8H0RP03kq6Az7Xg/edit?usp=sharing
+
+export enum RunningStyle {
+	FrontRunner,
+	PaceChaser,
+	LateSurger,
+	EndCloser,
+	GreatEscape,
+}
+
+export enum AptitudeLevel {
+	G,
+	F,
+	E,
+	D,
+	C,
+	B,
+	A,
+	S,
+}
+
+export enum Phase {
+	EarlyRace,
+	MidRace,
+	LateRace,
+}
+
+function baseSpeed(raceLen: number): number {
+	return 20 - (raceLen - 2000) / 1000;
+}
+
+const strategyPhaseCoeff = [
+	[1.0, 0.98, 0.962],
+	[0.978, 0.991, 0.975],
+	[0.938, 0.998, 0.994],
+	[0.931, 1.0, 1.0],
+	[1.063, 0.962, 0.95],
+] as const;
+
+const distanceProficiencyMod = [0.1, 0.2, 0.4, 0.6, 0.8, 0.9, 1.0, 1.05] as const;
+
+/**
+ * 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 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,
+	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 dpm = distanceProficiencyMod[distance];
+	const base = baseSpeed(raceLen);
+	// Expand and rearrange terms from the doccy to make solving for the inverse easier.
+	// (lateBaseTarget + 0.01*base) * 1.05 + sqrt(500*speedStat) * dpm * 0.002
+	// = (base * spc + sqrt(500*speedStat) * dpm * 0.002 + 0.01 * base) * 1.05 + sqrt(500*speedStat) * dpm * 0.002
+	// = 1.05*base*spc + 1.05*sqrt(500*speedStat)*dpm*0.002 + 0.0105*base + sqrt(500*speedStat)*dpm*0.002
+	// = base * (1.05*spc + 0.0105) + 0.0041 * sqrt(500*speedStat) * dpm
+	// plus the guts component.
+	// TODO(zephyr): numerical precision?
+	return base * (1.05 * spc + 0.0105) + 0.0041 * Math.sqrt(500 * speedStat) * dpm + Math.pow(450 * gutsStat, 0.597) * 0.0001;
+}
+
+/**
+ * Calculate the speed stat which produces a given target speed in the last spurt.
+ * Inverse of spurtSpeed.
+ * @param spurtSpeed Target speed in the last spurt in m/s
+ * @param gutsStat Uma's guts stat. No accounting for mood or stat thresholds.
+ * @param style Running style
+ * @param distance Distance aptitude
+ * @param raceLen Length of the race in meters
+ * @returns Speed stat which produces the target speed
+ */
+export function inverseSpurtSpeed(
+	spurtSpeed: number,
+	gutsStat: number,
+	style: RunningStyle,
+	distance: AptitudeLevel,
+	raceLen: number,
+): number {
+	// spurtSpeed = base * (1.05*spc + 0.0105) + 0.0041*sqrt(500*speedStat)*dpm + pow(450*gutsStat, 0.597)*0.0001
+	// 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 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);
+}

zenno/src/routes/+layout.svelte

@@ -21,6 +21,7 @@
 			<a href={resolve('/inherit')} class="mx-8 my-1 inline-block">Inheritance Chance</a>
 			<a href={resolve('/spark')} class="mx-8 my-1 inline-block">Spark Chance</a>
 			<a href={resolve('/vet')} class="mx-8 my-1 inline-block">My Veterans</a>
+			<a href={resolve('/spurt')} class="mx-8 my-1 inline-block">Spurt Speed</a>
 			<a href={resolve('/convo')} class="mx-8 my-1 inline-block">Lobby Conversations</a>
 		</span>
 	</nav>

zenno/src/routes/+page.svelte

@@ -18,6 +18,10 @@
 		<a href={resolve('/vet')}>My Veterans</a> — <i>Not yet implemented</i> — Set up and track your veterans for Zenno Rob Roy's inspiration
 		and spark calculators.
 	</li>
+	<li>
+		<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('/convo')}>Lobby Conversations</a> — Check participants in lobby conversations and get recommendations on unlocking
 		them quickly.

zenno/src/routes/layout.css

@@ -38,5 +38,15 @@ a:hover {
 
 select {
 	background-color: light-dark(var(--color-mist-300), var(--color-mist-900));
-	padding: 0.5rem 0.75rem;
+	padding: 0 0.75rem;
+	min-height: 1.5lh;
+}
+
+input {
+	background-color: light-dark(var(--color-mist-300), var(--color-mist-900));
+	padding: 0 0.75rem;
+}
+
+input[type='number'] {
+	min-height: 1.5lh;
 }

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

@@ -0,0 +1,97 @@
+<script lang="ts">
+	import { AptitudeLevel, inverseSpurtSpeed, RunningStyle, spurtSpeed } from '$lib/race';
+
+	const aptsList = Object.entries(AptitudeLevel).filter(([_name, val]) => typeof val === 'number');
+	const stylesList = [
+		['Front Runner', RunningStyle.FrontRunner],
+		['Pace Chaser', RunningStyle.PaceChaser],
+		['Late Surger', RunningStyle.LateSurger],
+		['End Closer', RunningStyle.EndCloser],
+		['Great Escape', RunningStyle.GreatEscape],
+	] as const;
+
+	let rawSpeed: number = $state(1200);
+	let rawGuts: number = $state(1200);
+	let style: RunningStyle = $state(RunningStyle.FrontRunner);
+	let distanceApt: AptitudeLevel = $state(AptitudeLevel.S);
+	let raceLen: number = $state(2000);
+	let isCareer: boolean = $state(false);
+
+	const careerMod = $derived(isCareer ? 400 : 0);
+	const speedStat = $derived(rawSpeed + careerMod);
+	const gutsStat = $derived(rawGuts + careerMod);
+	const speed = $derived(spurtSpeed(speedStat, gutsStat, style, distanceApt, raceLen));
+
+	const sProf = $derived([
+		inverseSpurtSpeed(speed, gutsStat, RunningStyle.FrontRunner, AptitudeLevel.S, raceLen) - careerMod,
+		inverseSpurtSpeed(speed, gutsStat, RunningStyle.PaceChaser, AptitudeLevel.S, raceLen) - careerMod,
+		inverseSpurtSpeed(speed, gutsStat, RunningStyle.LateSurger, AptitudeLevel.S, raceLen) - careerMod,
+		inverseSpurtSpeed(speed, gutsStat, RunningStyle.EndCloser, AptitudeLevel.S, raceLen) - careerMod,
+		inverseSpurtSpeed(speed, gutsStat, RunningStyle.GreatEscape, AptitudeLevel.S, raceLen) - careerMod,
+	]);
+	const aProf = $derived([
+		inverseSpurtSpeed(speed, gutsStat, RunningStyle.FrontRunner, AptitudeLevel.A, raceLen) - careerMod,
+		inverseSpurtSpeed(speed, gutsStat, RunningStyle.PaceChaser, AptitudeLevel.A, raceLen) - careerMod,
+		inverseSpurtSpeed(speed, gutsStat, RunningStyle.LateSurger, AptitudeLevel.A, raceLen) - careerMod,
+		inverseSpurtSpeed(speed, gutsStat, RunningStyle.EndCloser, AptitudeLevel.A, raceLen) - careerMod,
+		inverseSpurtSpeed(speed, gutsStat, RunningStyle.GreatEscape, AptitudeLevel.A, raceLen) - careerMod,
+	]);
+</script>
+
+<h1 class="text-4xl">Spurt Speed Calculator</h1>
+<div class="mx-auto mt-8 grid max-w-4xl grid-cols-1 rounded-md text-center shadow-md ring md:grid-cols-4">
+	<div class="m-4">
+		<label for="speedStat">Speed Stat</label>
+		<input type="number" id="speedStat" required bind:value={rawSpeed} class="w-full" />
+	</div>
+	<div class="m-4">
+		<label for="gutsStat">Guts Stat</label>
+		<input type="number" id="gutsStat" required bind:value={rawGuts} class="w-full" />
+	</div>
+	<div class="m-4">
+		<label for="style">Style</label>
+		<select id="style" required bind:value={style} class="w-full">
+			{#each stylesList as [name, style]}
+				<option value={style}>{style === RunningStyle.GreatEscape ? 'Great Escape (Runaway)' : name}</option>
+			{/each}
+		</select>
+	</div>
+	<div class="m-4">
+		<label for="distanceApt">Distance Aptitude</label>
+		<select id="distanceApt" required bind:value={distanceApt} class="w-full">
+			{#each aptsList.toReversed() as [name, val] (val)}
+				<option value={val}>{name}</option>
+			{/each}
+		</select>
+	</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" />
+	</div>
+	<div class="m-4 self-center">
+		<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">
+	Target spurt speed: {speed.toFixed(3)} m/s
+</span>
+{#each [[AptitudeLevel.A, aProf] as const, [AptitudeLevel.S, sProf] as const] as [level, inv] (level)}
+	<div class="mx-auto max-w-3xl">
+		<span class="mt-8 block w-full">
+			With {AptitudeLevel[level]} proficiency, the equivalent speed is
+		</span>
+		<div class="flex flex-col md:flex-row">
+			{#each stylesList as [styleName, s] (s)}
+				<div
+					class={['m-2 flex-1 rounded-md border shadow-sm transition-shadow hover:shadow-md', s === style ? 'border-2' : null]}
+				>
+					<div class="h-full w-full flex-col text-center">
+						<span class="block text-lg">{styleName}</span>
+						<span class="block text-2xl">{inv[s]}</span>
+					</div>
+				</div>
+			{/each}
+		</div>
+	</div>
+{/each}