zenno/spurt: calculator for last spurt speed

zenno/src/lib/race.ts

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+// 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);
+}