zenno/doc/fans: new data coverage and fix off-by-ones

zenno/src/routes/doc/fans/+page.svelte

@@ -1,17 +1,18 @@
 <script lang="ts">
-	import { asset, resolve } from '$app/paths';
+	import { resolve } from '$app/paths';
 	import CalcInfo from '../../race/CalcInfo.svelte';
 	import Article from '../Article.svelte';
 	import Sec from '../Sec.svelte';
 	import * as fans from './fans';
 
-	let baseFans = $state(700);
+	let winFans = $state(700);
 	let fanBonus = $state(0);
 	let finishOrder = $state(1);
 	let margin = $state(0);
 	let skills = $state(0);
 	let glowsticks = $state(false);
 
+	const baseFans = $derived(fans.baseFans(winFans, finishOrder));
 	const marginFans = $derived(fans.marginFans(baseFans, finishOrder, margin));
 	const skillFans = $derived(fans.skillFans(baseFans, skills));
 	const glowstickBonus = $derived(glowsticks ? 50 : 0);
@@ -76,18 +77,21 @@
 			<li>In Trackblazer/MANT, use of glowsticks.</li>
 		</ul>
 		<p>
-			The identified formula perfectly fits hundreds of recorded career race gains, including losses. Some questions remain, but
+			The identified formula perfectly fits hundreds of recorded career races, including losses. These results have important
-			the results so far have important implications both for fan runs and for low fan bonus decks for which debut can fall short
+			implications both for fan runs and for low fan bonus decks for which debut can fall short of fan requirements for early
-			of fan requirements for early career goals.
+			career goals.
 		</p>
 	{/snippet}
 
 	<Sec h={2} id="calc-fans">Calculate Fans</Sec>
-	<p>This tool will calculate your exact fan gain from a race.</p>
+	<p>
+		This tool will calculate your exact fan gain from a race. Use the fan value displayed in the race selection menu for the Race
+		Fans field.
+	</p>
 	<form class="mx-auto mb-4 grid grid-cols-1 gap-2 rounded-md p-4 text-center shadow-md ring md:max-w-2xl md:grid-cols-3">
 		<div>
-			<label for="calc-base-fans">Base Fans</label>
+			<label for="calc-base-fans">Race Fans</label>
-			<input id="calc-base-fans" class="max-w-32" type="number" min="0" max="30000" step="100" bind:value={baseFans} />
+			<input id="calc-base-fans" class="max-w-32" type="number" min="0" max="30000" step="100" bind:value={winFans} />
 		</div>
 		<div>
 			<label for="calc-fan-bonus">Fan Bonus</label>
@@ -95,7 +99,11 @@
 		</div>
 		<div>
 			<label for="calc-finish-order">Finish Order</label>
-			<input id="calc-finish-order" class="max-w-32" type="number" min="1" max="18" step="1" bind:value={finishOrder} />
+			<select id="calc-finish-order" class="max-w-32" bind:value={finishOrder}>
+				{#each orderPct as [v] (v)}
+					<option value={v}>{v}</option>
+				{/each}
+			</select>
 		</div>
 		<div>
 			<label for="calc-margin">{marginType} (L)</label>
@@ -110,17 +118,18 @@
 			<label for="calc-glowsticks">Glowsticks</label>
 		</div>
 	</form>
-	<div class="grid grid-cols-1 md:grid-cols-12">
+	<div class="mx-auto grid max-w-2xl grid-cols-1 md:grid-cols-3">
-		<CalcInfo title="Fans from Margin" class="md:col-span-4 md:col-start-3">{marginFans}</CalcInfo>
+		<CalcInfo title="Base Fans">{baseFans}</CalcInfo>
-		<CalcInfo title="Fans from Skills" class="md:col-span-4">{skillFans}</CalcInfo>
+		<CalcInfo title="Fans from Margin">{marginFans}</CalcInfo>
-		<CalcInfo title="Fans Gained" class="md:col-span-4 md:col-start-5">{gainedFans}</CalcInfo>
+		<CalcInfo title="Fans from Skills">{skillFans}</CalcInfo>
+		<CalcInfo title="Fans Gained" class="md:col-start-2">{gainedFans}</CalcInfo>
 	</div>
 
 	<Sec h={2} id="base-fans">Base Fans</Sec>
 	<p>
 		Base fans is a parameter per race and finish placement, defined in <a href={resolve('/doc/mdb')}>master data</a>. The number
 		shown in the career race selection menu is the base fans for first place. While it is defined separately for each race and
-		finish order, every race currently follows the same curve for all placements.
+		finish order, every race currently follows the same curve for all placements, up to rounding.
 	</p>
 	<table class="mx-auto mb-4 border text-center">
 		<thead>
@@ -140,14 +149,10 @@
 	</table>
 
 	<Sec h={2} id="margin">Fans from Margin</Sec>
-	<p>
+	<p>When the trainee places in the top five, she receives a bonus percentage of base fans according to the finish margin.</p>
-		When the trainee places in the top three (top five?), she receives a bonus percentage of base fans according to the finish
-		margin.
-	</p>
 	<p>
 		The bonus depends on whether the trainee won the race. If so, it is calculated by her margin versus second place. Otherwise,
-		her total margin behind the winner is used. If she did not place in the top three (top five?), then she gains no fans from
+		her total margin behind the winner is used. If she did not place in the top five, then she gains no fans from margin.
-		margin.
 	</p>
 	<table class="mx-auto mb-4 border text-center">
 		<thead>
@@ -190,34 +195,44 @@
 	<Sec h={2} id="rounding">Calculation Order and Rounding</Sec>
 	<p>The calculation is perfomed as if in the following order.</p>
 	<ol class="mb-4 list-decimal pl-4">
-		<li>Calculate fans from win margin and round down.</li>
+		<li>Look up base fans for the race and placement. This value is always an integer.</li>
-		<li>Calculate fans from skill activation count and round down.</li>
+		<li>Calculate fans from win margin as a proportion of base fans and round down.</li>
+		<li>Calculate fans from skill activation count as a proportion of base fans and round down.</li>
 		<li>Calculate the sum of base fans, win margin fans, and skill activation fans.</li>
-		<li>Apply fan bonus to the sum and round to the nearest integer with halfway cases away from zero.</li>
+		<li>Apply fan bonus to the sum in single-precision floating point, without otherwise rounding.</li>
+		<li>
+			Round to five significant figures with halfway cases rounded up, then round down. Examples are useful here.
+			<ul class="list-[revert] pl-8">
+				<li>
+					700 base plus 14 from margin with 88% fan bonus = <span class="inline-block">714&times;1.88</span> = 1342.32, rounded to five
+					significant figures becomes 1342.3, rounded down to 1342.
+				</li>
+				<li>
+					10500 base plus 210 from margin with 105% fan bonus =
+					<span class="inline-block">10710&times;2.05</span>
+					= 21955.5, rounded to five significant figures becomes 21956, rounded down to 21956.
+				</li>
+				<li>
+					100 base fans plus 2 fans from skills with 88% fan bonus = <span class="inline-block">102&times;1.88</span> = 191.76, rounded
+					to five significant figures becomes 191.76, rounded down to 191.
+				</li>
+			</ul>
+		</li>
 		<li>(Trackblazer/MANT) If glowsticks were used for the race, apply their multiplier and round down.</li>
 	</ol>
 
-	<Sec h={2} id="data">Data and Limitations</Sec>
+	<Sec h={2} id="data">Data</Sec>
 	<p>
-		The data for this research comes from 193 races and fan results dumped using <a
+		The data for this research comes from 325 races and fan results dumped using <a
 			href="https://werseter.github.io/umadump/"
 			target="_blank"
 			rel="noopener noreferrer">Umadump</a
-		>. The races come from sixteen careers run between 19 Aug and 11 Oct 2026. These careers include five different values of race
+		>. The races come from careers run between 19 Aug and 18 Oct 2026. These careers include fan bonus values of 50, 55, 65, 70,
-		bonus ranging from 55 to 105. The identified formula predicts the actual fan gain perfectly for all of the races. You can
+		80, 88, and 105. The identified formula predicts the actual fan gain perfectly for all of the races. You can
 		<a
 			href="https://docs.google.com/spreadsheets/d/1_jtOv6qk9dP4jJTagJqG53Pvj48IVd6gl2zKpyT6Kvs/edit?gid=463816108#gid=463816108"
 			target="_blank"
 			rel="noopener noreferrer">view the data</a
 		>.
 	</p>
-	<p>
-		There are some gaps in the data. No collected race had a finish placement of 4th or 5th, nor lower than 6th, so the exact
-		details of the win margin fan bonus remain open. Similarly, no race featured a trainee who activated more than ten skills, so
-		it is unknown whether there are further tiers of skill activation count fan bonus.
-	</p>
-	<p>
-		Once these edge cases are covered, this article will be updated. If you'd like to contribute, please contact me
-		(@zephyrtronium) via Discord on the Hakuraku, uma.moe, GameTora, or EoG servers.
-	</p>
 </Article>

zenno/src/routes/doc/fans/fans.ts

@@ -1,3 +1,15 @@
+const placementPms = [1000, 400, 250, 150, 100, 90, 80, 70, 60, 50, 40, 30, 25, 20, 15, 10, 10, 10] as const;
+
+/**
+ * Calculate base fans for a given placement in a race.
+ * @param winBase Base fans for a win, as displayed in the race menu
+ * @param finishOrder Placement of the trainee, with winner being 1
+ * @returns Base fans for the race and placement together
+ */
+export function baseFans(winBase: number, finishOrder: number): number {
+	return Math.round(winBase * placementPms[finishOrder - 1] / 1000);
+}
+
 const margins = [
 	[0.75, 0.0, 0.09],
 	[2.5, 0.02, 0.06],
@@ -9,15 +21,15 @@ const margins = [
 /**
  * Calculate fans gained from a career race due to the margin of the finish.
  * @param baseFans Base fans from the race and finish order
- * @param finishOrder Placement of the trainee
+ * @param finishOrder Placement of the trainee, with winner being 1
  * @param margin Margin in lengths between the trainee and second if a win, or the winner and trainee if a loss
  * @returns Fans gained due to finish margin
  */
 export function marginFans(baseFans: number, finishOrder: number, margin: number): number {
-	if (finishOrder > 3) {
+	if (finishOrder > 5) {
 		return 0;
 	}
-	const [, wb, lb] = margins.find(([m]) => margin < m)!;
+	const [, wb, lb] = margins.find(([m]) => margin <= m)!;
 	const b = finishOrder === 1 ? wb : lb;
 	return Math.floor(baseFans * b);
 }
@@ -52,7 +64,10 @@ export function skillFans(baseFans: number, skillsActivated: number): number {
  */
 export function gained(baseFans: number, marginFans: number, skillFans: number, fanBonus: number, itemBonus?: number): number {
 	const f = baseFans + marginFans + skillFans;
-	const d = Math.round(f * (1 + fanBonus / 100));
+	const s = Math.fround(f * Math.fround(1 + fanBonus / 100));
+	const p = Math.exp((4 - Math.floor(Math.log10(s))) * Math.LN10);
+	// Add half a significant figure to account for precision.
+	const d = Math.floor(Math.round(s * p + 5e-6) / p + 5e-6);
 	const b = itemBonus ?? 0;
 	return Math.floor(d * (1 + b / 100));
 }