《移动游戏产品的架构·商业化与发行工程》1.2 ARPU、ARPPU、付费率与 eCPM 的口径

3.5 × 0.92 × 0.88 × 45 / 1000 ≈ ¥0.1275

// file: src/biz/unit-economics.ts
// tier: L1
// verify: node --test test/biz/unit-economics.test.ts

export interface PeriodInput {
  readonly mau: number;
  readonly payingUsers: number;
  readonly iapRevenue: number;
  readonly adRevenue: number;
}

export interface UnitEconomics {
  readonly totalRevenue: number;
  readonly payRate: number;
  readonly arppu: number;
  readonly arpu: number;
  readonly iapArpu: number;
  readonly adArpu: number;
}

export interface ReportedPeriod extends PeriodInput {
  readonly reportedPayRate: number;
  readonly reportedArppu: number;
  readonly reportedArpu: number;
}

export interface Reconciliation {
  readonly ok: boolean;
  readonly notes: readonly string[];
}

export interface IncentiveInput {
  readonly impressionsPerDau: number;
  readonly fillRate: number;
  readonly completeRate: number;
  readonly ecpm: number;
}

function assertCount(name: string, value: number): void {
  if (!Number.isFinite(value) || value < 0) {
    throw new RangeError(`${name} must be a finite non-negative number, got ${value}`);
  }
}

function assertRatio(name: string, value: number): void {
  if (!Number.isFinite(value) || value < 0 || value > 1) {
    throw new RangeError(`${name} must be in [0, 1], got ${value}`);
  }
}

export function unitEconomics(input: PeriodInput): UnitEconomics {
  if (!Number.isInteger(input.mau) || input.mau <= 0) {
    throw new RangeError(`mau must be a positive integer, got ${input.mau}`);
  }
  if (!Number.isInteger(input.payingUsers) || input.payingUsers < 0 || input.payingUsers > input.mau) {
    throw new RangeError(`payingUsers out of range: ${input.payingUsers}`);
  }
  assertCount("iapRevenue", input.iapRevenue);
  assertCount("adRevenue", input.adRevenue);
  const totalRevenue = input.iapRevenue + input.adRevenue;
  return {
    totalRevenue,
    payRate: input.payingUsers / input.mau,
    arppu: input.payingUsers === 0 ? 0 : input.iapRevenue / input.payingUsers,
    arpu: totalRevenue / input.mau,
    iapArpu: input.iapRevenue / input.mau,
    adArpu: input.adRevenue / input.mau,
  };
}

export function relativeDrift(actual: number, reported: number): number {
  if (!Number.isFinite(actual) || !Number.isFinite(reported)) {
    throw new RangeError("relativeDrift needs two finite numbers");
  }
  if (actual === 0) {
    return reported === 0 ? 0 : Number.POSITIVE_INFINITY;
  }
  return Math.abs(reported - actual) / Math.abs(actual);
}

export function reconcile(input: ReportedPeriod, tolerance = 0.01): Reconciliation {
  assertRatio("tolerance", tolerance);
  const measured = unitEconomics(input);
  const notes: string[] = [];
  if (relativeDrift(measured.payRate, input.reportedPayRate) > tolerance) {
    notes.push("pay_rate_drift");
  }
  if (relativeDrift(measured.arppu, input.reportedArppu) > tolerance) {
    notes.push("arppu_drift");
  }
  if (relativeDrift(measured.arpu, input.reportedArpu) > tolerance) {
    notes.push("arpu_drift");
  }
  return { ok: notes.length === 0, notes };
}

export function ecpmRevenue(impressions: number, ecpm: number): number {
  assertCount("impressions", impressions);
  assertCount("ecpm", ecpm);
  return (impressions / 1000) * ecpm;
}

export function effectiveEcpm(revenue: number, impressions: number): number {
  assertCount("revenue", revenue);
  if (!Number.isFinite(impressions) || impressions <= 0) {
    throw new RangeError(`impressions must be positive, got ${impressions}`);
  }
  return (revenue / impressions) * 1000;
}

export function incentiveValuePerDau(input: IncentiveInput): number {
  assertCount("impressionsPerDau", input.impressionsPerDau);
  assertRatio("fillRate", input.fillRate);
  assertRatio("completeRate", input.completeRate);
  assertCount("ecpm", input.ecpm);
  return input.impressionsPerDau * input.fillRate * input.completeRate * (input.ecpm / 1000);
}

export function formatUnitEconomics(economics: UnitEconomics): string {
  const pct = (value: number) => `${(value * 100).toFixed(2)}%`;
  return `pay_rate=${pct(economics.payRate)} arppu=¥${economics.arppu.toFixed(2)} arpu=¥${economics.arpu.toFixed(2)} iap_arpu=¥${economics.iapArpu.toFixed(2)} ad_arpu=¥${economics.adArpu.toFixed(2)}`;
}

pay_rate=2.80% arppu=¥67.97 arpu=¥3.08 iap_arpu=¥1.90 ad_arpu=¥1.18