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And what Pokemon would you have to catch to get it?

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For Gen II, the points equation is the sum of:

4 times the max HP of the Pokémon
The sum of the Pokémon's other stats
1/8 of the current HP of the Pokémon, rounded down
1 point if the Pokémon is holding an item, 0 otherwise
Up to 29 points based on the Pokémon's individual values:
16 points if the Defense IV is odd, 0 otherwise
8 points if the Attack IV is odd, 0 otherwise
4 points if the Special IV is odd, 0 otherwise
1 point if the Speed IV is odd, 0 otherwise

Or when written out:
(HPmax * 4) + Atk + Def + SpA + SpD + Spe + (HPcurrent / 8) + item + (DefIV % 2)*16 + (AtkIV % 2)*8 + (SpcIV % 2)*4 + (SpeIV % 2)

I was originally confused by the equation having only one Special stat, when Gen II introduced to SpA/SpD split, but SadisticMystic has informed me that the two stats still rely off of one Special IV.

In Gen II, the highest score achievable would be 387, by a Scyther. Scyther would give the highest score because its BST one of the highest available during the contest, with its only competition being Pinsir who ties, and because it has the highest HP in the contest, at 70 base HP vs Pinsir's 65. Scyther would need to be a Lv14 (the highest available for Scyther), with perfect IVs across the board, holding an item (Scyther has a 100% chance to hold a Bitter Berry in these games, so that's not a problem), and caught with at least 40 HP remaining (out of 47 maximum). When plugged into the equation, it becomes:
(47 * 4) + 40 + 31 + 24 + 31 + 38 + (40 / 8) + 1 + 16 + 8 + 4 + 1 = 387


For Gen IV, the points are calculated by a sum of the following:

The level of the Pokémon relative to the maximum that can be found in the contest, as a percentage
The Pokémon's IVs relative to the maximum (186), as a percentage
The Pokémon's HP relative to its maximum, as a percentage
A rarity factor, either 60 (Caterpie, Metapod, Weedle, Kakuna, Wurmple, Silcoon, Cascoon, or Kricketot), 80 (all Pokémon not mentioned), or 100 (Scyther or Pinsir)

This would make the highest score possible 400, from either a Pinsir or Scyther. No matter which one you go with, it would either need to be at Lv14, if you have not obtained the NatDex, or Lv28, if you have. It would also need to have perfect IVs across the board, and be at full HP when caught.


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Hope this helps!

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Saying "Special IV" is meaningful, even in GSC: while the previous "Special" stat itself was split into two components, there was still only a single IV and proto-EV bank that was applied toward both stats.
Really? Okay, that makes sense.