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doc/fans: new article for career fan gain formula
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2026-10-17 14:25:57 -04:00
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zenno/src/routes/doc/fans/+page.svelte
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<script lang="ts">
import { asset, 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 fanBonus = $state(0);
let finishOrder = $state(1);
let margin = $state(0);
let skills = $state(0);
let glowsticks = $state(false);
const marginFans = $derived(fans.marginFans(baseFans, finishOrder, margin / 1.18));
const skillFans = $derived(fans.skillFans(baseFans, skills));
const glowstickBonus = $derived(glowsticks ? 50 : 0);
const gainedFans = $derived(fans.gained(baseFans, marginFans, skillFans, fanBonus, glowstickBonus));
const marginType = $derived(finishOrder === 1 ? 'Win Margin' : 'Margin vs. Winner');
const orderPct = [
[1, 100],
[2, 40],
[3, 25],
[4, 15],
[5, 10],
[6, 9],
[7, 8],
[8, 7],
[9, 6],
[10, 5],
[11, 4],
[12, 3],
[13, 2],
[14, 2],
[15, 1],
[16, 1],
[17, 1],
[18, 1],
] as const;
const marginBonus = [
['≤3/4 L', 0, 9],
['3/4 L – 2.5 L', 2, 6],
['2.5 L – 4 L', 4, 4],
['4 L – 6 L', 6, 2],
['>6L', 9, 0],
] as const;
const skillBonus = [
['0', 0],
['1-3', 2],
['4-6', 3],
['7-9', 5],
['10+', 8],
] as const;
</script>
<Article>
{#snippet head()}
<Sec h={1} id="top" class="text-center pointer-coarse:mb-8">Career Fan Gain Is Solved</Sec>
<p>
Thanks to work by Moxa and Werseter on the Hakuraku Discord, a precise formula for fans gained from career races has been
found.
</p>
<p>
There is no random component to fan gain, except insofar as the race itself is random. It is now known to be entirely
determined by five factors:
</p>
<ul class="mb-4 list-disc pl-4">
<li>Base fans, according to the race and finish placement.</li>
<li>Fan bonus from support cards.</li>
<li>Margin of the win, or margin behind the winner if the player's trainee did not win.</li>
<li>Number of skills the trainee activated during the race.</li>
<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 results so far have important implications both for fan runs and for low fan bonus decks for which debut can fall short
of fan requirements for early 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. Due to some <a href="#margin">internal details</a>, the margin
displayed in game may differ by up to a length from the margin used to calculate fans. (This calculator takes displayed
margin, so its report can differ from actual gains in edge cases.)
</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>
<input id="calc-base-fans" class="max-w-32" type="number" min="0" max="30000" step="100" bind:value={baseFans} />
</div>
<div>
<label for="calc-fan-bonus">Fan Bonus</label>
<input id="calc-fan-bonus" class="max-w-32" type="number" min="0" max="150" step="5" bind:value={fanBonus} />
</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} />
</div>
<div>
<label for="calc-margin">{marginType} (L)</label>
<input id="calc-margin" class="max-w-32" type="number" min="0" step="0.25" bind:value={margin} />
</div>
<div>
<label for="calc-skills">Activated Skills</label>
<input id="calc-skills" class="max-w-32" type="number" min="0" step="1" bind:value={skills} />
</div>
<div class="my-auto">
<input id="calc-glowsticks" class="min-h-6 min-w-6 align-middle" type="checkbox" bind:checked={glowsticks} />
<label for="calc-glowsticks">Glowsticks</label>
</div>
</form>
<div class="grid grid-cols-1 md:grid-cols-12">
<CalcInfo title="Fans from Margin" class="md:col-span-4 md:col-start-3">{marginFans}</CalcInfo>
<CalcInfo title="Fans from Skills" class="md:col-span-4">{skillFans}</CalcInfo>
<CalcInfo title="Fans Gained" class="md:col-span-4 md:col-start-5">{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.
</p>
<table class="mx-auto mb-4 border text-center">
<thead>
<tr>
<th scope="col" class="px-2">Placement</th>
<th scope="col" class="px-2">Fan Ratio</th>
</tr>
</thead>
<tbody>
{#each orderPct as [o, p] (o)}
<tr class="even:bg-mist-300 dark:even:bg-mist-900">
<td>{o}</td>
<td>{p}%</td>
</tr>
{/each}
</tbody>
</table>
<Sec h={2} id="margin">Fans from Margin</Sec>
<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>
For the purpose of this calculation, "margin" is defined as the distance covered moving at 15 m/s since the time the first
horse crossed the goal line. I.e., we observe the exact margin used to calculate fans from race replay data. The <i
>displayed</i
>
margin in the game is
<a
href="https://docs.google.com/document/d/15VzW9W2tXBBTibBRbZ8IVpW6HaMX8H0RP03kq6Az7Xg/edit?tab=t.0#heading=h.p0458fiye6y9"
target="_blank"
rel="noopener noreferrer">scaled by a factor of 1.18</a
>
to derive the margin label (e.g. &half;L instead of 0.7L). Because of this scaling and rounding, using the margin displayed in game
to calculate fans may underestimate the gain, particularly for displayed margins of 2&half;L, 5L, or 6L.
</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
margin.
</p>
<table class="mx-auto mb-4 border text-center">
<thead>
<tr>
<th scope="col" class="px-2">Actual<br />Margin Within</th>
<th scope="col" class="px-2">Bonus for Winner</th>
<th scope="col" class="px-2">Bonus for Podium</th>
</tr>
</thead>
<tbody>
{#each marginBonus as [m, w, l] (m)}
<tr class="even:bg-mist-300 dark:even:bg-mist-900">
<td>{m}</td>
<td>{w}%</td>
<td>{l}%</td>
</tr>
{/each}
</tbody>
</table>
<Sec h={2} id="skills">Fans from Skill Activations</Sec>
<p>The trainee receives a bonus percentage of base fans according to the number of skills she activated during the race.</p>
<table class="mx-auto mb-4 border text-center">
<thead>
<tr>
<th scope="col" class="px-2">Activated Skills</th>
<th scope="col" class="px-2">Bonus</th>
</tr>
</thead>
<tbody>
{#each skillBonus as [n, b] (n)}
<tr class="even:bg-mist-300 dark:even:bg-mist-900">
<td>{n}</td>
<td>{b}%</td>
</tr>
{/each}
</tbody>
</table>
<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>Calculate fans from skill activation count 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>(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>
<p>
The data for this research comes from 193 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
bonus ranging from 55 to 105. The identified formula predicts the actual fan gain perfectly for all of the races. You can
<a href={asset('/career_fan_gain_summary_193.csv')} download>download a summary</a>.
</p>
<p>
There are some gaps in the data. Moxa's original data that was used to establish that the margin bonus uses actual rather than
displayed margin was lost, so that conclusion is based on past discussion rather than available 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
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const margins = [
[0.75, 0.0, 0.09],
[2.5, 0.02, 0.06],
[4, 0.04, 0.04],
[6, 0.06, 0.02],
[Infinity, 0.09, 0.0],
] as const;
/**
* 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 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) {
return 0;
}
const [, wb, lb] = margins.find(([m]) => margin < m)!;
const b = finishOrder === 1 ? wb : lb;
return Math.floor(baseFans * b);
}
const skills = [
[0, 0.0],
[3, 0.02],
[6, 0.03],
[9, 0.05],
[Infinity, 0.08],
] as const;
/**
* Calculate the fans gained from a career race due to skills activated.
* @param baseFans Base fans from the race and finish order
* @param skillsActivated Number of skills the trainee activated during the race
* @returns Fans gained due to skill activations
*/
export function skillFans(baseFans: number, skillsActivated: number): number {
const [, b] = skills.find(([n]) => skillsActivated <= n)!;
return Math.floor(baseFans * b);
}
/**
* Calculate fan gain from a career race.
* @param baseFans Base fans from the race and finish order
* @param marginFans Fans gained due to finish margin
* @param skillFans Fans gained due to skill activations
* @param fanBonus Total fan bonus from support cards
* @param itemBonus Fan bonus from items (MANT glowsticks)
* @returns Total fans gained
*/
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 b = itemBonus ?? 0;
return Math.floor(d * (1 + b / 100));
}