zenno: stamina calculator first pass

zenno/src/lib/all.ts

@@ -49,6 +49,11 @@ export const PAGES = {
 			name: 'Carryover Calculator',
 			description: 'Calculate the importance of acceleration and speed carryover at the start of late race.',
 		},
+		{
+			route: resolve('/race/stam'),
+			name: 'Stamina Calculator',
+			description: 'Compute stamina requirements and recovery probability distributions.',
+		},
 	] satisfies Page[],
 	career: [
 		{

zenno/src/lib/race.ts

@@ -354,6 +354,17 @@ export function maxHP(raceLen: number, style: RunningStyle, stamStat: number): n
 	return 0.8 * hpStrategyCoeff[style] * stamStat + raceLen;
 }
 
+/**
+ * Compute the stamina stat that would produce a given effective HP
+ * @param raceLen Length of the race in meters
+ * @param style Horse's running style
+ * @param hp Effective HP, i.e. max HP plus recoveries minus debuffs
+ * @returns Stamina
+ */
+export function effectiveStam(raceLen: number, style: RunningStyle, hp: number): number {
+	return (hp - raceLen) / (0.8 * hpStrategyCoeff[style]);
+}
+
 const groundHPRateMod = {
 	[Surface.Turf]: {
 		[GroundConditions.Firm]: 1,

zenno/src/lib/racelib/recovery.spec.ts

@@ -0,0 +1,29 @@
+import { expect, test, describe } from 'vitest';
+import * as math from 'mathjs';
+import * as recovery from './recovery';
+
+describe.for<recovery.SkillCount[]>([
+	[],
+	[{ r: 100, n: 1 }],
+	[
+		{ r: 100, n: 2 },
+		{ r: 200, n: 2 },
+	],
+	[
+		{ r: 100, n: 3 },
+		{ r: 200, n: 3 },
+		{ r: -400, n: 3 },
+	],
+])('%j', (skills) => {
+	describe.for<number>([300, 1000, 2000])('base wit %i', (baseWit) => {
+		const base = recovery.distribution(baseWit, skills, []);
+		test('is a pmf', () => {
+			const p = math.sum([...base.values()]);
+			expect(p).toBeCloseTo(1, 8);
+		});
+		test('withRisky is a pmf', () => {
+			const p = math.sum([...recovery.withRisky(baseWit, base).values()]);
+			expect(p).toBeCloseTo(1, 8);
+		});
+	});
+});

zenno/src/lib/racelib/recovery.ts

@@ -0,0 +1,80 @@
+import * as race from '$lib/race';
+
+/**
+ * Count of skills activated at a given recovery rate.
+ */
+export interface SkillCount {
+	/** Recovery rate in ten thousandths. */
+	r: number;
+	/** Count of skills available. */
+	n: number;
+}
+
+/**
+ * Calculate the distribution of HP rates after skill activations.
+ * @param baseWit Uma's base wit stat
+ * @param skills Skills activated by the uma, both recovery and self-damaging
+ * @param debuffs Skills always applied to the uma
+ * @returns Map of HP rate to P(HP rate)
+ */
+export function distribution(baseWit: number, skills: SkillCount[], debuffs: SkillCount[]): Map<number, number> {
+	const debuff = debuffs.reduce((a, { r, n }) => a + r * n, 0);
+	if (skills.length == 0) {
+		return new Map([[debuff, 1]]);
+	}
+	const d = new Map<number, number>();
+	const nn = skills.map(() => 0);
+	while (true) {
+		// Calculate the current combination of skills.
+		const { r, p } = skills.reduce(
+			(a, s, i) => ({
+				r: a.r + s.r * nn[i],
+				p: a.p * race.skillWitCheck(baseWit, s.n, nn[i]),
+			}),
+			{ r: debuff, p: 1 },
+		);
+		// All events are mutually exclusive since they're combinations of skills,
+		// so we can combine by simple addition.
+		d.set(r, p + (d.get(r) ?? 0));
+		// Update counts for the next iteration.
+		let i = 0;
+		while (i < nn.length) {
+			nn[i]++;
+			if (nn[i] <= skills[i].n) {
+				break;
+			}
+			nn[i] = 0;
+			i++;
+		}
+		if (i >= nn.length) {
+			// All skills finished.
+			break;
+		}
+	}
+	return d;
+}
+
+/**
+ * Calculate the distribution of HP rates accounting for Risky Business
+ * @param baseWit Uma's base wit stat
+ * @param dist Map of HP rate to P(HP rate) as calculated by `distribution`
+ * @returns Map of HP rate to P(HP rate) accounting for Risky Business/Nothing Ventured
+ */
+export function withRisky(baseWit: number, dist: Map<number, number>): Map<number, number> {
+	// P(-0) = P(no activation OR activation AND -0) = (1-skillChance) + skillChance * 0.6,
+	// P(-200) = P(activation AND -200) = skillChance * 0.3,
+	// P(-400) = P(activation AND -400) = skillChance * 0.1.
+	// This is a single independent skill, so we combine with the existing pmf via
+	// P(r AND risky result) = P(r) * P(risky result).
+	const s = race.skillWitCheck(baseWit);
+	const p0 = 1 - s + s * 0.6;
+	const p200 = s * 0.3;
+	const p400 = s * 0.1;
+	const n = new Map<number, number>();
+	for (const [r, p] of dist.entries()) {
+		n.set(r, p * p0 + (n.get(r) ?? 0));
+		n.set(r - 200, p * p200 + (n.get(r - 200) ?? 0));
+		n.set(r - 400, p * p400 + (n.get(r - 400) ?? 0));
+	}
+	return n;
+}

zenno/src/routes/race/stam/+page.svelte

@@ -1,6 +1,9 @@
 <script lang="ts">
 	import * as course from '$lib/course';
 	import * as race from '$lib/race';
+	import * as recovery from '$lib/racelib/recovery';
+	import HPChart from './HPChart.svelte';
+	import InfoPanels from './InfoPanels.svelte';
 
 	let rawStats = $state({
 		[race.Stat.Speed]: 1200,
@@ -23,6 +26,19 @@
 		[race.Stat.Wit]: 0,
 	});
 
+	const recovRates = [35, 50, 150, 350, 550, 750, 950];
+	const debuffRates = [-25, -50, -100, -200, -300];
+	const selfDebuffRates = [-200, -400];
+	let recovCounts = $state(recovRates.map((v) => ({ r: v, n: 0 })));
+	let debuffCounts = $state(debuffRates.map((v) => ({ r: v, n: 0 })));
+	let selfDebuffCounts = $state(selfDebuffRates.map((v) => ({ r: v, n: 0 })));
+	let risky = $state(false);
+	const skills = $derived([...recovCounts, ...selfDebuffCounts].filter(({ n }) => n > 0));
+
+	function rate(r: number): string {
+		return `${r / 100}%`;
+	}
+
 	let raceLen = $state(2000);
 	let slopesRaw: course.Slope[] = $state([]);
 	let surface = $state(race.Surface.Turf);
@@ -99,6 +115,23 @@
 
 	const maxHP = $derived(race.maxHP(raceLen, style, stats[race.Stat.Stamina]));
 
+	const baseDistribution = $derived(recovery.distribution(baseStats[race.Stat.Wit], skills, debuffCounts));
+	const distribution = $derived(risky ? recovery.withRisky(baseStats[race.Stat.Wit], baseDistribution) : baseDistribution);
+	const statistics = $derived.by(() => {
+		let mp = 0,
+			mr = 0,
+			mean = 0;
+		for (const [r, p] of distribution) {
+			mean += (r * p * maxHP) / 10000;
+			if (p > mp) {
+				mp = p;
+				mr = r;
+			}
+		}
+		return { mode: (mr * maxHP) / 10000, modePer: mp * 100, mean };
+	});
+	const effStam = $derived(race.effectiveStam(raceLen, style, maxHP + statistics.mode));
+
 	const sections = $derived.by(() => {
 		const r = course.splitSectionSlopes(raceLen, slopesRaw).map((s) => {
 			const uphillMod = s.slope > 0 ? race.uphillMod(stats[race.Stat.Power], s.slope) : 0;
@@ -129,7 +162,6 @@
 		),
 	);
 	const needHP = $derived(race.fullSpurtHP(raceLen, phaseSpeed[race.Phase.LateRace][0], spurtHPRate));
-	const needHPPer = $derived((100 * needHP) / maxHP);
 	const spurtStartHP = $derived(sections.findLast((s) => s.phase !== race.Phase.LateRace)?.remain);
 
 	let slopeAddParams: course.Slope = $state({ per: 1, span: [0, 0] });
@@ -153,15 +185,15 @@
 </script>
 
 <h1 class="text-4xl">Stamina Calculator</h1>
-<div class="mx-auto mt-8 grid max-w-5xl grid-cols-1 rounded-md text-center shadow-md ring md:grid-cols-6">
+<div class="mx-auto mt-8 grid max-w-5xl grid-cols-1 gap-2 rounded-md p-2 text-center shadow-md ring md:grid-cols-6">
 	{#each race.StatList as stat (stat)}
 		{@const statName = race.Stat[stat]}
-		<div class="m-4">
+		<div class="">
 			<label for={statName}>{statName}</label>
 			<input type="number" class="w-full" id={statName} required bind:value={rawStats[stat]} />
 		</div>
 	{/each}
-	<div class="m-4">
+	<div class="">
 		<label for="mood">Mood</label>
 		<select class="w-full" id="mood" required bind:value={mood}>
 			{#each race.MOODS as mood (mood)}
@@ -169,7 +201,7 @@
 			{/each}
 		</select>
 	</div>
-	<div class="m-4">
+	<div class="">
 		<label for="style">Style</label>
 		<select class="w-full" id="style" required bind:value={style}>
 			{#each race.RUNNING_STYLES as [name, style] (style)}
@@ -177,7 +209,7 @@
 			{/each}
 		</select>
 	</div>
-	<div class="m-4">
+	<div class="">
 		<label for="distanceApt">{race.Distance[distType]} Aptitude</label>
 		<select class="w-full" id="distanceApt" required bind:value={distanceApt}>
 			{#each race.APTITUDE_LEVELS as apt (apt)}
@@ -185,7 +217,7 @@
 			{/each}
 		</select>
 	</div>
-	<div class="m-4">
+	<div class="">
 		<label for="surfaceApt">{race.Surface[surface]} Aptitude</label>
 		<select class="w-full" id="surfaceApt" required bind:value={surfaceApt}>
 			{#each race.APTITUDE_LEVELS as apt (apt)}
@@ -193,7 +225,7 @@
 			{/each}
 		</select>
 	</div>
-	<div class="m-4">
+	<div class="">
 		<label for="styleApt"
 			>{race.RUNNING_STYLES[style != race.RunningStyle.Runaway ? style : race.RunningStyle.FrontRunner][0]}</label
 		>
@@ -203,7 +235,7 @@
 			{/each}
 		</select>
 	</div>
-	<div class="m-4 self-center">
+	<div class=" 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>
@@ -214,13 +246,41 @@
 	</div>
 	{#each race.StatList as stat (stat)}
 		{@const statName = race.Stat[stat]}
-		<div class="m-4">
+		<div class="">
 			<label for={`${statName}Bonus`}>{statName}</label>
 			<input type="number" class="w-full" id={`${statName}Bonus`} required bind:value={skillStatBonus[stat]} />
 		</div>
 	{/each}
 </div>
-<div class="mx-auto mt-8 grid max-w-5xl grid-cols-1 gap-4 rounded-md text-center shadow-md ring md:grid-cols-6">
+<div class="mx-auto my-2 grid max-w-4xl grid-cols-2 rounded-md text-center shadow-md ring md:grid-cols-7">
+	<div class="col-span-full mt-1 text-lg">Recoveries</div>
+	{#each recovCounts as s (s.r)}
+		<div class="grid grid-cols-3 p-2 md:grid-cols-1 md:flex-col">
+			<label for={`recov${s.r}`}>{rate(s.r)}</label>
+			<input id={`recov${s.r}`} type="number" min="0" bind:value={s.n} class="col-span-2" />
+		</div>
+	{/each}
+	<div class="col-span-full border-t pt-1 text-lg md:col-span-2">Self-Damage</div>
+	<div class="col-span-full border-t border-l pt-1 text-lg md:col-span-5">Debuffs (No Wit Check)</div>
+	{#each selfDebuffCounts as s (s.r)}
+		<div class="grid grid-cols-3 p-2 md:grid-cols-1 md:flex-col">
+			<label for={`selfdamage${s.r}`}>{rate(s.r)}</label>
+			<input id={`selfdamage${s.r}`} type="number" min="0" bind:value={s.n} />
+		</div>
+	{/each}
+	{#each debuffCounts as s, i (s.r)}
+		<div class={{ 'grid grid-cols-3 p-2 md:grid-cols-1 md:flex-col': true, 'border-l': i === 0 }}>
+			<label for={`debuff${s.r}`}>{rate(s.r)}</label>
+			<input id={`debuff${s.r}`} type="number" min="0" bind:value={s.n} />
+		</div>
+	{/each}
+	<div class="col-span-2 flex flex-row py-2">
+		<label for="risky" class="mr-1 ml-auto">Risky Business</label>
+		<input id="risky" type="checkbox" bind:checked={risky} class="mr-auto ml-1 h-6 w-6" />
+	</div>
+	<div class="border-l"><!-- only here for the border --></div>
+</div>
+<div class="mx-auto my-2 grid max-w-5xl grid-cols-1 gap-4 rounded-md text-center shadow-md ring md:grid-cols-6">
 	<div class="m-4 flex md:col-span-2">
 		<input
 			class="col-span-2 my-auto w-full justify-self-center-safe"
@@ -330,22 +390,16 @@
 	</table>
 </div>
 
-<div class="mx-auto mt-8 flex max-w-3xl">
-	<div class="m-2 flex-1 rounded-md border text-center shadow-sm transition-shadow hover:shadow-md">
-		<span class="block text-lg">Max HP</span>
-		<span class="block text-2xl">{Math.floor(maxHP)}</span>
-	</div>
-	<div class="m-2 flex-1 rounded-md border text-center shadow-sm transition-shadow hover:shadow-md">
-		<span class="block text-lg">Spurt Threshold</span>
-		<span class="block text-2xl">{Math.ceil(needHP)} ({needHPPer.toFixed(1)}%)</span>
-	</div>
-	<div class="m-2 flex-1 rounded-md border text-center shadow-sm transition-shadow hover:shadow-md">
-		<span class="block text-lg">Late Race Start</span>
-		{#if spurtStartHP != null}
-			<span class="block text-2xl">{Math.ceil(spurtStartHP[1])} &ndash; {Math.ceil(spurtStartHP[0])}</span>
-		{/if}
-	</div>
-</div>
+<InfoPanels
+	{maxHP}
+	{needHP}
+	{spurtStartHP}
+	{effStam}
+	showStats={distribution.size > 1}
+	mode={statistics.mode}
+	modePer={statistics.modePer}
+	mean={statistics.mean}
+/>
 <!--
 <table class="mt-8 w-full border text-center">
 	<thead>
@@ -393,3 +447,8 @@
 	</tbody>
 </table>
 -->
+{#if skills.length != 0 || risky}
+	<div class="mx-auto h-96 max-w-5xl">
+		<HPChart {distribution} {maxHP} />
+	</div>
+{/if}

zenno/src/routes/race/stam/HPChart.svelte

@@ -0,0 +1,52 @@
+<script lang="ts">
+	import * as Plot from '@observablehq/plot';
+	import type { Attachment } from 'svelte/attachments';
+
+	interface Props {
+		distribution: Map<number, number>;
+		maxHP: number;
+	}
+
+	let { distribution, maxHP }: Props = $props();
+	const vals = $derived([...distribution.entries()].map(([r, p]) => ({ r: (r * maxHP) / 1e4, p: p * 100 })));
+
+	let width = $state(1);
+	let height = $state(1);
+	const makeChart: Attachment = (el) => {
+		$effect(() => {
+			el?.firstChild?.remove();
+			el?.append(
+				Plot.plot({
+					width,
+					height,
+					x: {
+						label: 'HP Mod',
+						line: true,
+					},
+					y: {
+						label: 'Probability (%)',
+						domain: [0, 100],
+						line: true,
+					},
+					marks: [
+						Plot.ruleX([0], { strokeOpacity: 0.5 }),
+						Plot.link(vals, { x: 'r', y1: 0, y2: 'p', markerEnd: 'circle-stroke', strokeWidth: 3 }),
+						Plot.tip(vals, Plot.pointerX({ x: 'r', y: 'p', className: 'plot-tip' })),
+					],
+				}),
+			);
+		});
+	};
+</script>
+
+<div bind:clientWidth={width} bind:clientHeight={height} class="h-full w-full">
+	<div role="img" {@attach makeChart}>
+		<span>the chart seems to have didn't</span>
+	</div>
+</div>
+
+<style>
+	:global(.plot-tip) {
+		--plot-background: light-dark(var(--color-mist-200), var(--color-mist-800));
+	}
+</style>

zenno/src/routes/race/stam/InfoPanels.svelte

@@ -0,0 +1,41 @@
+<script lang="ts">
+	import CalcInfo from '../CalcInfo.svelte';
+
+	interface Props {
+		maxHP: number;
+		needHP: number;
+		effStam: number;
+		spurtStartHP?: number[];
+		showStats: boolean;
+		mode: number;
+		modePer: number;
+		mean: number;
+	}
+
+	let { maxHP, needHP, effStam, spurtStartHP = [0, 0], showStats, mode, modePer, mean }: Props = $props();
+
+	const needHPPer = $derived((100 * needHP) / maxHP);
+	const white = $derived(Math.trunc(maxHP * 0.015));
+	const gold = $derived(Math.trunc(maxHP * 0.055));
+	const goldDebuff = $derived(Math.trunc(maxHP * -0.03));
+</script>
+
+<div class="mx-auto flex w-full flex-col place-items-center md:flex-row md:justify-center">
+	<CalcInfo title="Max HP" class="max-w-72 flex-1">{Math.floor(maxHP)}</CalcInfo>
+	<CalcInfo title="Spurt Threshold" class="max-w-72 flex-1">{Math.ceil(needHP)} ({needHPPer.toFixed(1)}%)</CalcInfo>
+	<CalcInfo title="Spurt Start HP" class="hidden max-w-72 flex-1">
+		{Math.ceil(spurtStartHP[1])} &ndash; {Math.ceil(spurtStartHP[0])}
+	</CalcInfo>
+</div>
+<div class="mx-auto flex w-full flex-col place-items-center md:flex-row md:justify-center">
+	<CalcInfo title="White Recovery" class="max-w-72 flex-1">+{white} HP</CalcInfo>
+	<CalcInfo title="Gold Recovery" class="max-w-72 flex-1">+{gold} HP</CalcInfo>
+	<CalcInfo title="Gold Debuff" class="max-w-72 flex-1">{goldDebuff} HP</CalcInfo>
+</div>
+{#if showStats}
+	<div class="mx-auto flex w-full flex-col place-items-center md:flex-row md:justify-center">
+		<CalcInfo title="Mode HP from Skills" class="max-w-72 flex-1">{Math.round(mode)} (P={modePer.toFixed(1)}%)</CalcInfo>
+		<CalcInfo title="Mean HP from Skills" class="max-w-72 flex-1">{Math.round(mean)}</CalcInfo>
+		<CalcInfo title="Effective Stamina" class="max-w-72 flex-1">{Math.ceil(effStam)}</CalcInfo>
+	</div>
+{/if}