Pokémon Go

Line 236:

Given that every species has exactly one or two (distinct) types, there are 306 (18 * 17) total type pairs possible plus the base 18, for a total of 18<sup>2</sup> = 324 possible species typings (not all of them are actually populated in the game). Against a given typing, an Attack could theoretically have an exponent as low as -4 and as high as 2. No Attack type is very ineffective against two different types, though, so the actual minimum is -3.

As an ~~example~~, ~~Normal is~~ -2 against one type, and -1 against two types. It is thus:

Define BN2 as the number of types against which an Attack is very ineffective, BN1 for ineffective, and BP1 for effective (-2, -1, and 1 from the table above). B0 = 18 - BN2 - BN1 - BP1.

* -3 against Ghost-Steel and Ghost-Rock

* -2 against Ghost, Steel-Rock, and Ghost-{anything but Steel or Rock}

* 2: effective against both types (2 cannot be accomplished against a singly-typed species): BP1*(BP1-1)

* -1 against Steel, Rock, Steel-{anything but Rock or Ghost}, and Rock-{anything but Steel or Ghost}

* 1: effective against the single type, or effective against one of two types while neutral against the other: BP1*(B0+1)

* 0 against all other combinations

* 0: neutrality against all types, or effectiveness against one combined with ineffectiveness against the other: BP1*BN1 + B0<sup>2</sup>

* -1: ineffective against the one type, or ineffective against one type and neutral against the other, or very ineffective against one type and effective against the other: BN1*(B0+1) + BN2*BP1

* -2: very ineffective against the single type, or very ineffective against one type and neutral against the other, or ineffective against both types: BN2(B0+1) + BN1*(BN1 - 1)

* -3: very ineffective against one type, and ineffective against the other: BN2*BN1

** Since BN2 is always 0 or 1, this reduces to BN1 or 0

The sum over these five values will always be 171.

As an example, Normal is BN2 against one type, BN1 against two types, and BP1 against zero. It is thus:

* -3 against Ghost-Steel and Ghost-Rock (2)

* -2 against Ghost, Steel-Rock, and Ghost-{anything but Steel or Rock} (18)

* -1 against Steel, Rock, Steel-{anything but Rock or Ghost}, and Rock-{anything but Steel or Ghost} (32)

* 0 against all other combinations (273)

A 2 requires being very effective against both types (2 cannot be accomplished against a singly-typed species). A 1 requires being very effective against the single type, or very effective against one of two types while neutral against the other. A 0 requires neutrality against all types, or effectiveness against one combined with ineffectiveness against the other.

{| class="wikitable"

! Attack type !! ~~Base -2~~ !! ~~Base -1~~ !! ~~Base 1~~ !! -3 !! -2 !! -1 !! 0 !! 1 !! 2

! Attack type !! BN2 !! BN1 !! B0 !! BP1 !! -3 !! -2 !! -1 !! 0 !! 1 !! 2

|-

| Normal || 1 || 2 || 0 || 2 || 17 || 32 || ~~273~~ || 0 || 0

| Normal || 1 || 2 || 15 || 0 || 2 || || || || 0 || 0

|-

| Fighting || 1 || 6 || 5 || 6 || 31 || 47 || || || 20

| Fighting || 1 || 6 || 6 || 5 || 6 || || || || ||

|-

| Flying || 0 || 2 || 3 || 0 ||

| Flying || 0 || 2 || 13 || 3 || 0 || 1 || ||

|-

| Poison || 1 || 4 || 2 || 4 ||

| Poison || 1 || 4 || 11 || 2 || 4 || ||

|-

| Ground || 1 || 2 || 5 || 2 ||

| Ground || 1 || 2 || 10 || 5 || 2 ||

|-

| Rock || 0 || 3 || 4 || 0 ||

| Rock || 0 || 3 || 11 || 4 || 0 ||

|-

| Bug || 0 || 7 || 3 || 0 ||

| Bug || 0 || 7 || 8 || 3 || 0 ||

|-

| Ghost || 1 || 1 || 2 || 1 ||

| Ghost || 1 || 1 || 14 || 2 || 1 ||

|-

| Steel || 0 || 4 || 3 || 0 ||

| Steel || 0 || 4 || 11 || 3 || 0 ||

|-

| Fire || 0 || 4 || 4 || 0 ||

| Fire || 0 || 4 || 10 || 4 || 0 ||

|-

| Water || 0 || 3 || 3 || 0 ||

| Water || 0 || 3 || 12 || 3 || 0 ||

|-

| Grass || 0 || 7 || 3 || 0 ||

| Grass || 0 || 7 || 8 || 3 || 0 ||

|-

| Electric || 1 || 3 || 2 || 3 ||

| Electric || 1 || 3 || 12 || 2 || 3 ||

|-

| Psychic || 1 || 2 || 2 || 2 ||

| Psychic || 1 || 2 || 13 || 2 || 2 ||

|-

| Ice || 0 || 4 || 4 || 0 ||

| Ice || 0 || 4 || 10 || 4 || 0 ||

|-

| Dragon || 1 || 1 || 1 || 1 ||

| Dragon || 1 || 1 || 15 || 1 || 1 ||

|-

| Dark || 0 || 3 || 2 || 0 ||

| Dark || 0 || 3 || 13 || 2 || 0 ||

|-

| Fairy || 0 || 3 || 3 || 0 ||

| Fairy || 0 || 3 || 12 || 3 || 0 ||

|-

|}

Pokémon Go: Difference between revisions

Dank (talk | contribs)

@@ Line 236: / Line 236: @@
 Given that every species has exactly one or two (distinct) types, there are 306 (18 * 17) total type pairs possible plus the base 18, for a total of 18<sup>2</sup> = 324 possible species typings (not all of them are actually populated in the game). Against a given typing, an Attack could theoretically have an exponent as low as -4 and as high as 2. No Attack type is very ineffective against two different types, though, so the actual minimum is -3.
-As an example, Normal is -2 against one type, and -1 against two types. It is thus:
+Define BN2 as the number of types against which an Attack is very ineffective, BN1 for ineffective, and BP1 for effective (-2, -1, and 1 from the table above). B0 = 18 - BN2 - BN1 - BP1.
-* -3 against Ghost-Steel and Ghost-Rock
-* -2 against Ghost, Steel-Rock, and Ghost-{anything but Steel or Rock}
+* 2: effective against both types (2 cannot be accomplished against a singly-typed species): BP1*(BP1-1)
-* -1 against Steel, Rock, Steel-{anything but Rock or Ghost}, and Rock-{anything but Steel or Ghost}
+* 1: effective against the single type, or effective against one of two types while neutral against the other: BP1*(B0+1)
-* 0 against all other combinations
+* 0: neutrality against all types, or effectiveness against one combined with ineffectiveness against the other: BP1*BN1 + B0<sup>2</sup>
+* -1: ineffective against the one type, or ineffective against one type and neutral against the other, or very ineffective against one type and effective against the other: BN1*(B0+1) + BN2*BP1
+* -2: very ineffective against the single type, or very ineffective against one type and neutral against the other, or ineffective against both types: BN2(B0+1) + BN1*(BN1 - 1)
+* -3: very ineffective against one type, and ineffective against the other: BN2*BN1
+** Since BN2 is always 0 or 1, this reduces to BN1 or 0
+The sum over these five values will always be 171.
+As an example, Normal is BN2 against one type, BN1 against two types, and BP1 against zero. It is thus:
+* -3 against Ghost-Steel and Ghost-Rock (2)
+* -2 against Ghost, Steel-Rock, and Ghost-{anything but Steel or Rock} (18)
+* -1 against Steel, Rock, Steel-{anything but Rock or Ghost}, and Rock-{anything but Steel or Ghost} (32)
+* 0 against all other combinations (273)
-A 2 requires being very effective against both types (2 cannot be accomplished against a singly-typed species). A 1 requires being very effective against the single type, or very effective against one of two types while neutral against the other. A 0 requires neutrality against all types, or effectiveness against one combined with ineffectiveness against the other.
 {| class="wikitable"
-! Attack type !! Base -2 !! Base -1 !! Base 1 !! -3 !! -2 !! -1 !! 0 !! 1 !! 2
+! Attack type !! BN2 !! BN1 !! B0 !! BP1 !! -3 !! -2 !! -1 !! 0 !! 1 !! 2
 |-
-| Normal || 1 || 2 || 0 || 2 || 17 || 32 || 273 || 0 || 0
+| Normal || 1 || 2 || 15 || 0 || 2 ||  ||  ||  || 0 || 0
 |-
-| Fighting || 1 || 6 || 5 || 6 || 31 || 47 || || || 20
+| Fighting || 1 || 6 || 6 || 5 || 6 ||  ||  || || ||
 |-
-| Flying || 0 || 2 || 3 || 0 ||
+| Flying || 0 || 2 || 13 || 3 || 0 || 1 ||  ||
 |-
-| Poison || 1 || 4 || 2 || 4 ||
+| Poison || 1 || 4 || 11 || 2 || 4 ||  ||
 |-
-| Ground || 1 || 2 || 5 || 2 ||
+| Ground || 1 || 2 || 10 || 5 || 2 ||
 |-
-| Rock || 0 || 3 || 4 || 0 ||
+| Rock || 0 || 3 || 11 || 4 || 0 ||
 |-
-| Bug || 0 || 7 || 3 || 0 ||
+| Bug || 0 || 7 || 8 || 3 || 0 ||
 |-
-| Ghost || 1 || 1 || 2 || 1 ||
+| Ghost || 1 || 1 || 14 || 2 || 1 ||
 |-
-| Steel || 0 || 4 || 3 || 0 ||
+| Steel || 0 || 4 || 11 || 3 || 0 ||
 |-
-| Fire || 0 || 4 || 4 || 0 ||
+| Fire || 0 || 4 || 10 || 4 || 0 ||
 |-
-| Water || 0 || 3 || 3 || 0 ||
+| Water || 0 || 3 || 12 || 3 || 0 ||
 |-
-| Grass || 0 || 7 || 3 || 0 ||
+| Grass || 0 || 7 || 8 || 3 || 0 ||
 |-
-| Electric || 1 || 3 || 2 || 3 ||
+| Electric || 1 || 3 || 12 || 2 || 3 ||
 |-
-| Psychic || 1 || 2 || 2 || 2 ||
+| Psychic || 1 || 2 || 13 || 2 || 2 ||
 |-
-| Ice || 0 || 4 || 4 || 0 ||
+| Ice || 0 || 4 || 10 || 4 || 0 ||
 |-
-| Dragon || 1 || 1 || 1 || 1 ||
+| Dragon || 1 || 1 || 15 || 1 || 1 ||
 |-
-| Dark || 0 || 3 || 2 || 0 ||
+| Dark || 0 || 3 || 13 || 2 || 0 ||
 |-
-| Fairy || 0 || 3 || 3 || 0 ||
+| Fairy || 0 || 3 || 12 || 3 || 0 ||
 |-
 |}