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. Lightning judgments are isolated from this sequence and do not enter ordinary accuracy calculation.

Input Symbols

These symbols are defined in Judgment Definitions 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:

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