feat: add return rate and retention metrics to global stats

- Overall return rate: % of all-time players who played more than once
- New player return rate: 7-day rolling avg of daily first-timer return rates, with velocity vs prior 7 days
- 7-day and 30-day retention over time: per-cohort-day retention series

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/routes/global/+page.server.ts

@@ -15,6 +15,12 @@ function prevDay(d: string): string {
 	return dt.toISOString().slice(0, 10);
 }
 
+function addDays(d: string, n: number): string {
+	const dt = new Date(d + 'T00:00:00Z');
+	dt.setUTCDate(dt.getUTCDate() + n);
+	return dt.toISOString().slice(0, 10);
+}
+
 export const load: PageServerLoad = async () => {
 	const todayEst = estDateStr(0);
 	const yesterdayEst = estDateStr(1);
@@ -120,12 +126,17 @@ export const load: PageServerLoad = async () => {
 		.where(gte(dailyCompletions.date, ninetyDaysAgo))
 		.orderBy(asc(dailyCompletions.date));
 
-	// Group dates by user (ascending)
+	// Group dates by user (ascending) and users by date
 	const userDatesMap = new Map<string, string[]>();
+	const dateUsersMap = new Map<string, Set<string>>();
 	for (const row of recentCompletions) {
 		const arr = userDatesMap.get(row.anonymousId);
 		if (arr) arr.push(row.date);
 		else userDatesMap.set(row.anonymousId, [row.date]);
+
+		let s = dateUsersMap.get(row.date);
+		if (!s) { s = new Set(); dateUsersMap.set(row.date, s); }
+		s.add(row.anonymousId);
 	}
 
 	// ── Streak distribution ───────────────────────────────────────────────────
@@ -177,7 +188,8 @@ export const load: PageServerLoad = async () => {
 	const firstDates = await db
 		.select({
 			anonymousId: dailyCompletions.anonymousId,
-			firstDate: min(dailyCompletions.date)
+			firstDate: min(dailyCompletions.date),
+			totalCompletions: count()
 		})
 		.from(dailyCompletions)
 		.groupBy(dailyCompletions.anonymousId);
@@ -190,6 +202,109 @@ export const load: PageServerLoad = async () => {
 	// Net growth = truly new arrivals minus departures
 	const netGrowth7d = newUsers7d - churned7d;
 
+	// ── Return rate ───────────────────────────────────────────────────────────
+	// "Return rate": % of all-time unique players who have ever played more than once.
+	const playersWithReturn = firstDates.filter((r) => r.totalCompletions >= 2).length;
+	const overallReturnRate =
+		firstDates.length > 0
+			? Math.round((playersWithReturn / firstDates.length) * 1000) / 10
+			: null;
+
+	// Daily new-player return rate: for each day D, what % of first-time players
+	// on D ever came back (i.e. totalCompletions >= 2)?
+	const dailyNewPlayerReturn = new Map<string, { cohort: number; returned: number }>();
+	for (const r of firstDates) {
+		if (!r.firstDate) continue;
+		const existing = dailyNewPlayerReturn.get(r.firstDate) ?? { cohort: 0, returned: 0 };
+		existing.cohort++;
+		if (r.totalCompletions >= 2) existing.returned++;
+		dailyNewPlayerReturn.set(r.firstDate, existing);
+	}
+
+	// Build chronological array of daily rates (oldest first, days 60→1 ago)
+	// Days with fewer than 3 new players get rate=null to exclude from rolling avg
+	const dailyReturnRates: { date: string; cohort: number; rate: number | null }[] = [];
+	for (let i = 60; i >= 1; i--) {
+		const dateD = estDateStr(i);
+		const d = dailyNewPlayerReturn.get(dateD);
+		dailyReturnRates.push({
+			date: dateD,
+			cohort: d?.cohort ?? 0,
+			rate: d && d.cohort >= 3 ? Math.round((d.returned / d.cohort) * 1000) / 10 : null
+		});
+	}
+
+	// 7-day trailing rolling average of the daily rates
+	// Index 0 = 60 days ago, index 59 = yesterday
+	const newPlayerReturnSeries = dailyReturnRates.map((r, idx) => {
+		const window = dailyReturnRates
+			.slice(Math.max(0, idx - 6), idx + 1)
+			.filter((d) => d.rate !== null);
+		const avg =
+			window.length > 0
+				? Math.round((window.reduce((sum, d) => sum + (d.rate ?? 0), 0) / window.length) * 10) /
+					10
+				: null;
+		return { date: r.date, cohort: r.cohort, rate: r.rate, rollingAvg: avg };
+	});
+
+	// Velocity: avg of last 7 complete days (idx 53–59) vs prior 7 (idx 46–52)
+	const recentWindow = newPlayerReturnSeries.slice(53).filter((d) => d.rate !== null);
+	const priorWindow = newPlayerReturnSeries.slice(46, 53).filter((d) => d.rate !== null);
+	const current7dReturnAvg =
+		recentWindow.length > 0
+			? Math.round(
+					(recentWindow.reduce((a, d) => a + (d.rate ?? 0), 0) / recentWindow.length) * 10
+				) / 10
+			: null;
+	const prior7dReturnAvg =
+		priorWindow.length > 0
+			? Math.round(
+					(priorWindow.reduce((a, d) => a + (d.rate ?? 0), 0) / priorWindow.length) * 10
+				) / 10
+			: null;
+	const returnRateChange =
+		current7dReturnAvg !== null && prior7dReturnAvg !== null
+			? Math.round((current7dReturnAvg - prior7dReturnAvg) * 10) / 10
+			: null;
+
+	// ── Retention over time ───────────────────────────────────────────────────
+	// For each cohort day D, retention = % of that day's players who played
+	// again within the next N days. Only compute for days where D+N is in the past.
+
+	function retentionSeries(
+		windowDays: number,
+		seriesLength: number
+	): { date: string; rate: number; cohortSize: number }[] {
+		// Earliest computable cohort day: today - (windowDays + 1)
+		// We use index windowDays+1 through windowDays+seriesLength
+		const series: { date: string; rate: number; cohortSize: number }[] = [];
+		for (let i = windowDays + 1; i <= windowDays + seriesLength; i++) {
+			const dateD = estDateStr(i);
+			const cohort = dateUsersMap.get(dateD);
+			if (!cohort || cohort.size < 3) continue; // skip tiny cohorts
+			let retained = 0;
+			for (const userId of cohort) {
+				for (let j = 1; j <= windowDays; j++) {
+					if (dateUsersMap.get(addDays(dateD, j))?.has(userId)) {
+						retained++;
+						break;
+					}
+				}
+			}
+			series.push({
+				date: dateD,
+				rate: Math.round((retained / cohort.size) * 1000) / 10,
+				cohortSize: cohort.size
+			});
+		}
+		series.reverse(); // chronological (oldest first)
+		return series;
+	}
+
+	const retention7dSeries = retentionSeries(7, 30);
+	const retention30dSeries = retentionSeries(30, 30);
+
 	return {
 		todayEst,
 		stats: {
@@ -212,6 +327,15 @@ export const load: PageServerLoad = async () => {
 			netGrowth7d
 		},
 		last14Days,
-		streakChart
+		streakChart,
+		retention7dSeries,
+		retention30dSeries,
+		overallReturnRate,
+		newPlayerReturnSeries: newPlayerReturnSeries.slice(-30),
+		newPlayerReturnVelocity: {
+			current7dAvg: current7dReturnAvg,
+			prior7dAvg: prior7dReturnAvg,
+			change: returnRateChange
+		}
 	};
 };