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

zenno/src/lib/race.ts

@@ -1,6 +1,8 @@
 // Umamusume race mechanics adapted from KuromiAK's doc:
 // https://docs.google.com/document/d/15VzW9W2tXBBTibBRbZ8IVpW6HaMX8H0RP03kq6Az7Xg/edit?usp=sharing
 
+import { binomPMF } from "./prob";
+
 /**
  * Fundamental stats of umas.
  */
@@ -246,6 +248,17 @@ export function spotStruggleDuration(gutsStat: number, frontAptitude: AptitudeLe
 	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.
@@ -256,6 +269,18 @@ 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
@@ -292,3 +317,12 @@ export function speedGain(speedBonus: number, dur: number, accel: number | null,
 	// 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;
+}