Item Probability Changes

[Amy54Desu]

This issue is suggesting a complete change to the Item Probability Formula.
Below is my linked spreadsheet where y'all can toy around with my proposed idea.

Description

We take the player average and compare it to your stars. Item odds are then calculated depending on how high or low you are compared to the average. This should fix things such as first place getting static odds on powerUPs, Mega Mushrooms spawning for 2nd place even if they're 1 or 2 stars behind and bigger lobbies generally having pretty annoying item spawns for first.

New formula is

playerAvg = (sum of all player stars) / (number of alive players);
avgDiff = myStars - avg;
bonus = (avgDiff > 0 ? item.aboveBonus : item.belowBonus) * log(Mathf.abs(avgDiff)+1) * (1 - ((starsToWin - playerAvg) / starsToWin));
weight = max(0, item.initSpawnChance + bonus);

If not clear, if you're above the average then you get the aboveBonus which should be different than the belowBonus for those below the average.

Comparison

Here's an example of the old system with first place having 10/15 stars. Notice how if you're just 1 star behind you have a low but fair chance of spawning a Mega Mushroom. Assuming this is a 9 player lobby and rounding the .9678 chance UP to .97, there is roughly a 24% chance that ANY player will spawn a Mega Mushroom UPon completing one coin cycle, and that's assuming that all of them are 1 star behind first.

These catchUP powerUPs will spawn for players that actually need to catch UP. We also can prevent first place from getting more OP items.

Spreadsheet

Link to my spreadsheet, made extra snayp-y!

https://docs.google.com/spreadsheets/d/1w0OOfNtDHt_1yZue5x9BfCYq6PbXRmh_Jt2UmW3Fadc/edit?gid=0#gid=0