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FRLG+ Bulbasaur+ Hidden Power Manip

ironlung18
Feb 22nd, 2022 (edited)
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  1. Pokémon FRLG+ Bulbasaur+ Route - Hidden Power Routing
  2.  
  3. So it turns out that Hidden Power helps a lot with the Bulbasaur+ route in FRLG+ Any% Speedruns. FRLG+ is a FRLG ROM Hack created by Deokishisu, see here for more information: https://www.pokecommunity.com/showthread.php?t=454382
  4.  
  5. Hidden Power is a neat move (I say this unironically, the mechanics of it are quite interesting). To make a long story short, it is impossible to manip specifically for the Hidden Power type (Psychic) and base power (or BP, optimally 60+) using the Gen 3 manip tool. However, based on the mechanics of how Hidden Power is calculated, you can enter specific IV constraints which maximize your chances of getting a runnable Bulbasaur that also yields a high BP Psychic Hidden Power. I've done this and am happy to share my findings in this pastebin!
  6.  
  7. ---
  8.  
  9. SOME BASICS
  10.  
  11. From Gen 3 to Gen 5, Hidden Power BP can range from 30 to 70 and can take on one of sixteen types (all of the currently released types except Normal). Hidden Power's type and BP are both based on the Pokémon's IVs. There are formulas which are used to determine this. A lot of information (including the formulas) I took from this great source on Bulbapedia: https://bulbapedia.bulbagarden.net/wiki/Hidden_Power_(move)/Calculation
  12.  
  13. Anyone familiar with FRLG might know that the TM for Hidden Power is not available in any static location - it is only available by chance using a Pokemon with the Ability Pickup. This is obviously not viable as a speedrun strat in FRLG, as Save and Quit manips are not viable RTA (TAS only). In this hack, Hidden Power is a Celadon Dept Store TM, so it is 100% consistent to acquire it (just costs a pretty penny at $10000).
  14.  
  15. ---
  16.  
  17. SOME MATH AND PROBABILITY (Naturally, since it's Pokémon!)
  18.  
  19. The output of the type formula dictates the Hidden Power type. Psychic corresponds to the output value 12, which means that the sum of the "type bits" (a + 2b + 4c + 8d + 16e + 32f, where a through f depend on HP, Atk, Def, Speed, Sp Atk, and Sp Def respectively) must equal either 51, 52, 53 or 54. As it turns out, for that sum to equal one of those 4 values, the following is ALWAYS the case:
  20.  
  21. - Speed IV MUST be an even number
  22. - Special Attack IV MUST be an odd number
  23. - Special Defense IV MUST be an odd number
  24.  
  25. On top of this, for 3 of the 4 values (52, 53, and 54), Defense IV must be odd. HP and Attack can either be even or odd, depending on whether those as well as Defense are even or odd.
  26.  
  27. For BP, there is another formula, which assigns a 0 or 1 to each stat depending on its remainder when the corresponding IV is divided by 4. In order for us to get a BP of 60 or higher, the sum of the "damage bits" (u + 2v + 4w + 8x + 16y + 32z, where u through z depend on HP, Atk, Def, Speed, Sp Atk, and Sp Def respectively) must equal at least 48. It's pretty obvious that x (Speed), y (Sp. Atk), and z (Sp. Def) should all equal 1 if you want a high BP, and, not surprisingly, those 3 have a HUGE influence on the BP (i.e. HP, Atk and Def make a significantly smaller dent on the BP). When you combine this with the fact that Speed must be even, and the Special stats should be odd (see above), you optimally want the following "magic" IVs for these three stats:
  28.  
  29. Speed: 18, 22, 26 or 30 (2, 6, 10, and 14 also work but are too low for the route)
  30. Special Attack: 19, 23, 27 or 31 (3, 7, 11, and 15 also work but are too low for the route)
  31. Special Defense: same as Special Attack, but the lower values are fine.
  32.  
  33. Now, obviously we run into a problem with the starter program, which searches for starters based on a minimum IV, not from a list of desirable IVs (if the latter were true, that would be amazing!). Therefore, we need to choose appropriate minimums which give us the highest possible chance of getting one of the "magic" IV values.
  34.  
  35. As an example, for Special Attack, if we set a minimum of 19, we have a 4 in 13 chance of getting 19, 23, 27 or 31 IV. If we narrow that threshold, the chance goes up, but the likelihood of even finding a runnable starter given the frame range (typically for speedruns of the Charmander or Squirtle routes, we use a frame range of roughly 300-500 frames) becomes more difficult. In that case, you'd need to widen the frame range, which may mean waiting a long time for a runnable Bulbasaur. The odds of getting a "magic" value for Special Attack is the following for each of those values as the minimum:
  36.  
  37. 19+ : 4 in 13 (30.8%)
  38. 23+ : 3 in 9 (33.3%)
  39. 27+ : 2 in 5 (40%)
  40. 31 : 1 in 1 (100%)
  41.  
  42. Since high Special Attack also helps with damage ranges in the route, I opted to aim for 27+ IV. This yields a decent chance of getting a "magic" IV value that produces a high BP (40%) but also is 60% to be an odd number which is required for Psychic typing. It also strikes a nice balance with still getting a decent list of Bulbasaurs to pick from, as opposed to if we chose 31 IV.
  43.  
  44. The same applies for Speed and Special Defense. Special Defense is easy: set a minimum of 3 IV, and you exclude 0, 1 and 2 which cannot produce a high base power, and in the case of 0 and 2, can't produce Psychic type. You could set the Special Defense minimum higher, but the odds of finding a runnable starter falls off a cliff and Special Defense doesn't matter too much for the route. The odds of getting a Sp Def IV with a "magic" value is 27.6%, which isn't that much worse than if I restricted to, say, 23+ (33.3%).
  45.  
  46. Speed follows a similar approach. I opted for 18+ as my IV restriction here, which means there is a 4 in 14 (28.57%) chance of hitting one of the "magic" values, as well as a 50% chance of the IV being an even number. The more allowable IVs, the more likely to find a runnable Bulbasaur. Since Speed literally does not matter as long as it's 16 or higher, taking the lowest IV minimum that captures as many "magic" IVs as possible is the obvious play.
  47.  
  48. Since, in most cases, Defense is odd, I do the same thing as for Sp. Def and set a minimum of 3+ since it slightly improves the chances of being an odd number by excluding 0 and 2, and 1 IV doesn't add to the base power. I've been thinking of taking out really low Defense IVs on Lonely nature since Defense matters a lot in this route (Rival's bird sends his greetings!), so this could be restricted further.
  49.  
  50. Attack can be even or odd, so it's hit or miss regarding Hidden Power type, but we have a bit more flexibility to squeeze out a couple extra BP. The base minimum is 14+ IV (24+ if you want to avoid ranges) but looking at the "magic" IVs in that range (14, 15, 18, 19, 22, 23, 26, 27, 30 and 31), these requirements can be modified a bit. The odds of getting a "magic" IV given the respective constraints is as follows:
  51.  
  52. 14+ : 55.56%
  53. 18+ : 57.14%
  54. 22+ : 60%
  55. 26+ : 66.67%
  56. 30+ : 100%
  57.  
  58. Therefore, it is most logical to take the lowest possible Attack IV (more allowable IVs = more runnable Bulbasaurs) minimum to give the best chance to generate a high damage bit. It's a bit deceptive, as you'd think going for 30+ would be better (both 30 and 31 are "magic"), but that's only 2 of a possible 32 IVs the Bulbasaur can take on! As it turns out, going for the 24+ to avoid ranges may not be the greatest idea as 24 and 25 IV are not "magic" IV values. Going with 22+ or 26+ is probably better.
  59.  
  60. HP has little to no effect on BP no matter what, so that is left alone.
  61.  
  62. ---
  63.  
  64. THE VERDICT
  65.  
  66. Taking all of this into consideration, here are my stat requirements for the FRLG+ Bulbasaur+ Hidden Power route:
  67.  
  68. HP: 0+
  69. Atk: x / x / 14+ (26+ if you want to avoid a few ranges)
  70. Def: 3+ / 3+ / x
  71. Sp. Atk: x / 27+ / x
  72. Sp. Def: 3+ / 3+ / x
  73. Speed: x / 18+ / x
  74.  
  75. Just taking the Sp. Atk, Sp. Def, and Speed into account, I calculated that any given Bulbasaur will have a 3.15% chance of getting a Psychic Hidden Power with at least 65 power. If we drop the BP requirement to 60+, which only requires Special Attack and Special Defense to both be odd, those odds shoot up to 11.03%!
  76.  
  77. Anyone who is familiar with Gen III manips might think the Defense and Sp. Defense requirements are a bit odd (for example 0 IV neutral Def, which is excluded, is much better than 1 IV minus, which is included). Makes more sense when you consider the above! ;)
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