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Project Ladder Achievements Project 2 - Gen 5 Pokebilities - WEEK 2

For probabilistic context, Just checked the code and there's like 7.75 Gem users (Acro users / Hitmonlee, subtracting sets without them) out of 356 possible species (not counting alternate forms), that would be a 2.18% Gem rate. If my math is right, that means every team has a 12.37% to contain at least one gem user, or about 1/8 (which cannot possibly be right unless I got really unlucky too).


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Sources:
https://github.com/smogon/pokemon-showdown/blob/master/data/random-battles/gen5/sets.json
https://github.com/smogon/pokemon-showdown/blob/master/data/random-battles/gen5/teams.ts (lines 609-610)

In case you were wondering, I like probability.
 

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Shynii21 said:
For probabilistic context, Just checked the code and there's like 7.75 Gem users (Acro users / Hitmonlee, subtracting sets without them) out of 356 possible species (not counting alternate forms), that would be a 2.18% Gem rate. If my math is right, that means every team has a 12.37% to contain at least one gem user, or about 1/8 (which cannot possibly be right unless I got really unlucky too).
Click to expand...
These five on the right total up to 1.75 gem mons, and the acro mons might not have guaranteed gem? All 6 of them would surprise me
Like who is it? ledian, vespiqueen, emolga, can't think of the rest honestly
 
Inazuma-Fulgur said:
These five on the right total up to 1.75 gem mons, and the acro mons might not have guaranteed gem? All 6 of them would surprise me
Like who is it? ledian, vespiqueen, emolga, can't think of the rest honestly
Click to expand...
I checked the code and it said that if the Mon runs Acro, then the item is always F Gem, which makes sense as it otherwise would have to run no item or another item, thus missing the full boost. The mons with guaranteed Acro and by extension Gem are Ledian, Drifblim, Archeops, Emolga, Jumpluff and Vespiquen.

Some mons like Charizard and Tornadus have multiple sets, some of them with no Acro, so we cannot count them the same as Drifblim or Archeops, which always run it.

The other condition is being Unburden Hitmonlee with Fake Out for Normal Gem or Fighting Gem otherwise. The other set is choiced Reckless.
 
As for the total number of species, I just took the whole amount from the JSON and individually looked for the ones with -'s (such as Wormadam-Trash and Arceus-Fire) to delete the alt forms (since Ho-Oh and P-Z just happen to have dashes without being alt forms). Iirc, every species has an equal chance of being genned, so those with multiple forms will have a proportional, lower chance for each form and so we cannot weight them the same.

Anyway, math.
 
True, but I ain't doing that. However, I did find a small mistake in my calcs.

I took every single chance of getting a Mon with no Gem as 97.82%, which should actually increase over time as your team fills up since you cannot repeat species. So it would start at 7.75/356, then 7.75/355, 7.75/354, and so on until 7.75/351 for the last mon. We should not decrease the numerator at all since we are calculating the chance that we get no Gem mons, so the amount of Gem mons in the pool remains constant. Then, we just take the product of them all and a more accurate result would be 12.45% (it's bigger, so yay?).

1760559737750.png


And I'm still not accounting for the way the team gen works with typings or the chance to gen the right species with non-Gem sets, but at that point we could just do a couple thousand simulations and call it a day.
 
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