Calculate weight variate and showcase score range from height/weight for use in map filter/display #215
Description
Calculate weight variate (weight/average weight - height/average height) for use in map filter and display.
Since 4/11/2023, height variate has been rerolled for each trainer within each height range (XXS to XXL). Weight is determined by multiplying average weight by the sum of height variate and weight variate, with weight variate constant for each spawn for all trainers level 30+. During evolution, height is re-rolled but weight variate is unchanged.
Weight variate has a normal distribution with mean of 0 and standard deviation of 0.125 and is constrained to the range of -0.5 to +0.5.
Having weight variate information would be helpful as it determines the potential showcase score range for a given spawn. Also for events with many XXL spawns, the ability to filter notifications and map spawns above a selected weight variate threshold would be beneficial. The weight variate range corresponds to a showcase score range of 60 to 73 points, depending on the species XX-Class (or max height, 1.55, 1.75, or 2.0, with exception of Pumpkaboo and Gorgeist). This has a greater effect on showcase score than IV sum, which has a 50 point range.
Showcase score for a given spawn with including IV:
800/xc * hv + 150/(xc + 0.5) * (hv + wv) + 50/45 * (IV sum) + if(XXL,7300/41)
with xc=XX-Class, hv=height variate, wv=weight variate
For example an XXL 1.55 XX-Class spawn with weight variate of +0.25 (97th percentile) and 80% IV (36 IV sum) would have a showcase score range of 1120.29 to 1149.76, depending on height variate rolled for each trainer. An XXL 1.55 XX-Class spawn with weight variate of -0.25 and 80% IV would have a showcase score range of 1083.71 to 1113.17.
References:
https://twitter.com/bmenrigh_pogo/status/1618456354712350720
https://twitter.com/bmenrigh_pogo/status/1680851346768150528
https://twitter.com/bmenrigh_pogo/status/1718927008736927980
https://www.reddit.com/r/TheSilphRoad/comments/12jy9xe/weight_and_height_for_pokemon_caught_in_the_wild/
https://www.reddit.com/r/TheSilphRoad/comments/1aqd5lh/how_the_great_buddy_showcases_work/
https://docs.google.com/spreadsheets/d/1ZZwlZ2DOYeO0ouUgu-jXn3qmIf8jE4WTa3BhmtVupHc/