Size and weight variation: Difference between revisions

'''Size and weight variation''' is a game mechanic where multiple {{OBP|Pokémon|species}} of the same species can vary in size or weight.

As a special case, if ''y'' < 10, then the Magikarp's length is equal to <math display="inline">190 + y</math>. Otherwise, the value ''y'' is used to find the corresponding values of ''x₀'', ''y₀'', and ''m'' in the following table, which defines a piecewise linear approximation of the inverse of a {{wp|normal cumulative distribution function}} with mean 800 and standard deviation 179. Due to an off-by-one error, the values of ''x₀'' are calculated as 2 plus the zero-based index of the column (giving a mean of 800), rather than 3 plus the zero-based index of the column (giving a mean of 900). The column selected was intended to be the first column where ''y'' is less than the ''y₀'' value of that same column. Due to a programming error, only the high bytes of ''y'' and ''y₀'' are compared; this causes values to be looked up incorrectly from the table (including rendering the first and last columns inaccessible).

In [[Generation III|Generations III]] and {{gen|IV}}, there are occasionally [[Non-player character|NPCs]] who want to see large Pokémon. If shown a Pokémon that exceeds the previous record, the NPC will give the player a prize if it exceeds the previous record. A Pokémon is considered to have beat the previous record if its calculated size in millimeters (in all Generation III games and non-English Generation IV games) or its calculated size in tenths of an inch (in English-language Generation IV games) is greater than the previous record.

The size of these Pokémon is calculated from its [[individual values]] (IVs) and its [[personality value]]. Sizes follow a {{wp|normal distribution}}, with a {{wp|mean}} of the species' [[Pokédex]] height and {{wp|standard deviation}} of 0.179 times the species Pokédex height (approximately).

! Games

! Location

! Pokémon

! colspan="2" | Initial record

! Prize

| 15.7 in

| 40.0 cm <!-- y = 0x8100 -->

| 19.6 in

| 50.0 cm <!-- y = 0x8000 -->

| colspan="2" | None

| colspan="2" | None

| colspan="2" | None

| 106.5 cm <!-- y = 56150 -->

Only the lowest two bytes of the personality value are used in the calculation: ''p''₁ (highlighted in <span style="background:#9999FF">blue</span> below) is the least significant byte, while ''p''₂ (highlighted in <span style="background:#FF9999">red</span>) is the second least significant byte.

For the next step, the value ''y'' is used to find the corresponding values of ''x₀'', ''m'', and ''y₀'' in the following table, which defines a piecewise linear approximation of the inverse of a {{wp|normal cumulative distribution function}} with mean 1000 and standard deviation 179. The column selected is the first column where ''y'' is less than the ''y₀'' value of the next column.

The values of ''x₀'', ''m'', and ''y₀'' are then used to convert the uniformly distributed value ''y'' to the normally distributed value ''x''.

The final part of the calculation scales ''h'' (the species' [[List of Pokémon by height|height]] in tenths of a meter) by the ''x'' value to produce the Pokémon's size in millimeters. The size is bounded between 0.29 and 1.725 times the standard metric height for the species (as listed in the Pokédex), rounded down.

<math display="block">\textit{Size} = \left\lfloor\frac{h \cdot x}{10}\right\rfloor</math>

If the game converts this number to inches, the final result will be rounded down to the nearest tenth of an inch.

Once again, a Fisherman on [[Route 222]] can be shown {{p|Remoraid}}, and will judge their height. The game uses the same calculation from Generation III and IV, only substituting the Pokémon's [[Personality value]] for its [[Encryption constant]].