---
url: https://milthm.cn/wiki/en/manual/mechanics/accuracy-v2.md
description: Formal AccV2 calculation rules for Milthm.
---

# Accuracy V2

This document specifies the AccV2 accuracy metric used by *Milthm*.

AccV2 uses the ordinary judgment sequence $\Xi = {\xi_1, \xi_2, \cdots, \xi_N}$ defined in [Judgment Definitions](https://milthm.cn/wiki/en/manual/mechanics/judgment/definitions.md). Lightning judgments are isolated from this sequence and do not enter ordinary accuracy calculation.

## Input Symbols

These symbols are defined in [Judgment Definitions](https://milthm.cn/wiki/en/manual/mechanics/judgment/definitions.md) and are used as inputs in this document.

| Symbol | Meaning |
|--------|---------|
| $\mathcal{J}$ | Ordinary judgment set. |
| $\Xi$ | Ordinary judgment sequence. |
| $\xi_i$ | The $i$-th ordinary judgment. |
| $N$ | Ordinary judgment count. |

## Accuracy Symbols

This document defines the following accuracy-specific symbols.

| Symbol | Name | Meaning |
|--------|------|---------|
| $A\_{\mathrm{judge}}$ | Stepwise accuracy function | Maps an ordinary judgment grade to its accuracy value. |
| $ACC_n$ | Accuracy | Accuracy up to the $n$-th ordinary judgment. |
| $TA$ | Overall accuracy | Final AccV2 accuracy. |

## Stepwise Accuracy

The stepwise accuracy function $A\_{\mathrm{judge}}: \mathcal{J} \to \mathbb{R}$ maps ordinary judgment grades to accuracy values.

| Grade | Accuracy |
|-------|----------|
| $s$ | $100%$ |
| $p$ | $100%$ |
| $g$ | $60%$ |
| $n$ | $30%$ |
| $b$ | $15%$ |
| $m$ | $0%$ |

## Overall Accuracy

The accuracy up to the $n$-th ordinary judgment is:

$$
ACC_n = \frac{\sum\_{i=1}^{n} A\_{\mathrm{judge}}(\xi_i)}{n}
$$

The overall AccV2 accuracy is:

$$
TA = ACC_N
$$

The maximum accuracy is $100%$, achieved if and only if every ordinary judgment is Exact or Perfect:

$$
\forall \xi \in \Xi,\ \xi \in {s, p}
$$