Reality V3

This document specifies the RealityV3 calculation rules used by Milthm.

RealityV3 uses the supplied score records and chart constants to calculate the individual Reality contributed by each record, then aggregates the highest 20 contributions. The Reality category, eligible chart scope, and score record selected for each chart must be determined before applying these rules; this document defines only the calculation from those input records to a Reality value.

Input Symbols

Symbol	Meaning
$\mathcal{R}$	Input score record sequence.
$r_i$	The $i$-th score record.
$q_i$	Score stored by $r_i$.
$d_i$	Chart constant associated with $r_i$.
$M$	Number of input score records.

Reality Symbols

This document defines the following RealityV3-specific symbols.

Symbol	Name	Meaning
$R_{\mathrm{entry}}$	Single-chart Reality function	Maps a record's score and chart constant to its individual Reality.
$v_i$	Single-chart Reality	Reality contributed by the $i$-th score record.
$v_{(j)}$	Ranked single-chart Reality	The $j$-th value after sorting all $v_i$ in descending order.
$K$	Aggregation count	Number of records actually included in the total Reality calculation.
$TR$	Total Reality	Final RealityV3 value.

Single-Chart Reality

For a score $q$ and chart constant $d$, the single-chart Reality function is:

$$R_{\mathrm{entry}}(q,d) = \begin{cases} d + 1.5, & q \ge 1{,}000{,}000, \\ d + \dfrac{q - 850{,}000}{100{,}000}, & 850{,}000 \le q < 1{,}000{,}000, \\ \max\left( d\left(0.5 + \dfrac{q - 700{,}000}{300{,}000}\right) + \dfrac{q - 850{,}000}{100{,}000}, 0 \right), & 700{,}000 \le q < 850{,}000, \\ \max\left( (d - 3)\dfrac{q - 600{,}000}{200{,}000}, 0 \right), & 600{,}000 \le q < 700{,}000, \\ 0, & q < 600{,}000. \end{cases}$$

Therefore, the single-chart Reality contributed by the $i$-th score record is:

$$v_i = R_{\mathrm{entry}}(q_i,d_i)$$

The segments are continuous at the boundaries $600{,}000$, $700{,}000$, $850{,}000$, and $1{,}000{,}000$. The maximum single-chart Reality is $d + 1.5$, reached when $q \ge 1{,}000{,}000$; scores above $1{,}000{,}000$ do not increase Reality further.

Total Reality

Sort all single-chart Reality values in descending order:

$$v_{(1)} \ge v_{(2)} \ge \cdots \ge v_{(M)}$$

The number of records included in the aggregation is:

$$K = \min(M,20)$$

The total RealityV3 value is:

$$TR = \frac{1}{20}\sum_{j=1}^{K} v_{(j)}$$

Therefore, when more than 20 records are available, only the highest 20 single-chart Reality values are used. When fewer than 20 are available, the calculation is equivalent to padding the list to 20 entries with zero-valued records. The denominator is always $20$.