zephyr/horse
1
0
Fork 0
Code Issues 17 Pull Requests Actions Packages Projects Releases Wiki Activity

zenno/doc/fans: new data coverage and fix off-by-ones
ci/woodpecker/push/horsebot Pipeline was successful
Details
ci/woodpecker/push/zenno Pipeline failed
Details

Browse Source
This commit is contained in:
zephyr
2026-10-18 19:31:05 -04:00
parent 75558f35ba
commit 16a5433594
2 changed files with 70 additions and 40 deletions
Download Patch File Download Diff File Expand all files Collapse all files
zenno/src/routes/doc/fans/+page.svelte
+51 -36
View File
@@ -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 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.
The identified formula perfectly fits hundreds of recorded career races, including losses. These results 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.</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>
<input id="calc-base-fans" class="max-w-32" type="number" min="0" max="30000" step="100" bind:value={baseFans} />
<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={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">
<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 class="mx-auto grid max-w-2xl grid-cols-1 md:grid-cols-3">
<CalcInfo title="Base Fans">{baseFans}</CalcInfo>
<CalcInfo title="Fans from Margin">{marginFans}</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>
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>When the trainee places in the 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
margin.
her total margin behind the winner is used. If she did not place in the top five, then she gains no fans from 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>Calculate fans from skill activation count 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 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
bonus ranging from 55 to 105. The identified formula predicts the actual fan gain perfectly for all of the races. You can
>. The races come from careers run between 19 Aug and 18 Oct 2026. These careers include fan bonus values of 50, 55, 65, 70,
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
+19 -4
View File
@@ -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));
}