In GenIV, I created "Double Attack" and "Triple Attack" analysis. This is however, obsolete now that the type chart has changed. With the addition of Fairy as an attacking and defending type, as well as nerfs to Steel... it is time to redo my analysis.
The analysis is simple. There are not 18 types in the game... but instead 171 (theoretical) types in the game. The 171 types are Normal, Normal/Fire, Normal/Water, Normal/Ghost (etc. etc.) all the way to Dragon/Fairy. For every combination of attacks, I wrote a program to count up the total number of types that "Don't Resist" and "Are Weak against" a particular type combination. Abilities, such as Levitate or Flash Fire, were not taken into account however. So this analysis should only serve as a heuristic, a starting point for all trainers.
For example, the canonical attack combo "Electric / Ice" hits 68 types super-effective, and hits 168 types neutral or better.
Organized by "Most Super Effective":
	
	
	
		
Organized by Most Neutral:
	
	
	
		
Most of the staples of old remain the best. Ground / Ice has always had excellent offensive potential, and Fighting / Ghost has always been perfect (outside of the non-existant Normal/Ghost). Fighting / Ghost hits the top of non-resist list.
EdgeQuake makes it nearly to the top of both lists as expected, and Bolt/Beam is near the top of the "most neutrals" list.
Dragon / Fire has fallen from perfection however. Fairy / Water, Fairy / Fire, Fairy / Rock, and Fairy / Dragon all resist Dragon / Fire hard. However, outside of the UU Pokemon Azumarill and Carbink, these pokemon don't really exist. The offensive combo Dragon / Fire may be "theoretically walled" by these types... but this offensive core will probably do fine in the OU Metagame. IMO, the chart simply demonstrates one area where theory isn't going to match up with practice.
Dragon / Ghost has rose up in the charts, due to Steel's lack of resist. I don't know if any pokemon can take advantage of this... but it complements Dragon now.
The new type "Fairy" has a large number of combos that work with it. In theory, Fairy / Ground is the best, but with Skarmory being one of the most prolific pokemon, that "rogue" Steel / Flying type resists Fairy too hard. But aside from Skarmory, Fairy and Ground perfectly complement each other, Fairy hitting most types hard... with Ground backing up on Fairy's Poison / Steel resists.
Also remember, the above charts don't take Levitate into account. Bronzong will wall Fairy / Ground.
Fairy/Ghost and Fairy/Dark IMO will serve as a more important "offensive core" for Fairies. (Mega) Mawile Play Rough / Sucker Punch, (Mega) Gardevoir Moon Blast / Shadow Ball, and Togekiss Dazzling Gleam / Shadow Ball will hit hard. Remember: Jirachi, Metagross and Bronzong are now weak against both Ghost and Dark.
Again, "Attack Pairs" are most useful for defensive / support pokemon. Offensive Pokemon will likely use "Attack Triplets" as an offensive core, and I don't have a chart for that yet. Still, I think these charts will serve as a good starting point in our X / Y analysis.
				
			The analysis is simple. There are not 18 types in the game... but instead 171 (theoretical) types in the game. The 171 types are Normal, Normal/Fire, Normal/Water, Normal/Ghost (etc. etc.) all the way to Dragon/Fairy. For every combination of attacks, I wrote a program to count up the total number of types that "Don't Resist" and "Are Weak against" a particular type combination. Abilities, such as Levitate or Flash Fire, were not taken into account however. So this analysis should only serve as a heuristic, a starting point for all trainers.
For example, the canonical attack combo "Electric / Ice" hits 68 types super-effective, and hits 168 types neutral or better.
Organized by "Most Super Effective":
		Code:
	
	Atk1    Atk2    Supers    Not Resists
GROUND   ICE   109   169
FLYING   GROUND   105   168
ROCK   GROUND   104   169
FAIRY   GROUND   101   168
GROUND   FIRE   99   166
ROCK   FIGHTING   92   162
STEEL   GROUND   91   165
FIGHTING   ICE   91   159
BUG   GROUND   91   153
ROCK   ICE   90   159
FAIRY   ROCK   90   159
GROUND   POISON   88   164
GROUND   ELECTRIC   88   157
GROUND   FIGHTING   88   146
GHOST   GROUND   86   165
FLYING   FIGHTING   86   164
DARK   GROUND   84   162
ROCK   GRASS   82   157
GROUND   GRASS   82   137
GHOST   FIGHTING   81   170
ROCK   WATER   81   165
STEEL   ICE   81   141
FLYING   WATER   80   167
FAIRY   WATER   80   167
ROCK   FLYING   80   157
PSYCHIC   GROUND   79   164
ICE   WATER   79   159
DARK   FIGHTING   79   157
ROCK   PSYCHIC   79   156
GROUND   WATER   79   155
ROCK   BUG   78   147
DRAGON   GROUND   77   167
GHOST   ROCK   77   165
STEEL   ROCK   77   155
FIGHTING   FIRE   77   154
PSYCHIC   FIGHTING   76   158
FAIRY   FIGHTING   76   154
WATER   FIRE   76   148
DARK   ROCK   75   155
FIGHTING   WATER   75   153
STEEL   FLYING   75   148
STEEL   FIGHTING   74   155
FLYING   ICE   74   153
GHOST   ICE   73   163
FAIRY   ICE   73   146
FIGHTING   ELECTRIC   72   150
FAIRY   FIRE   72   146
FAIRY   STEEL   72   146
POISON   FIGHTING   72   142
ICE   FIRE   72   138
DARK   ICE   71   159
PSYCHIC   ICE   71   153
ICE   GRASS   71   146
ROCK   POISON   71   143
FLYING   GRASS   70   155
FAIRY   GHOST   69   168
FAIRY   DARK   69   168
BUG   WATER   68   159
ROCK   FIRE   68   152
BUG   FIGHTING   68   127
ICE   ELECTRIC   67   168
GHOST   WATER   67   165
GHOST   FLYING   67   165
DARK   FLYING   67   165
STEEL   WATER   67   154
FAIRY   FLYING   67   154
ELECTRIC   WATER   67   146
BUG   ICE   67   140
POISON   WATER   66   164
DRAGON   ROCK   66   156
ROCK   ELECTRIC   66   151
FAIRY   GRASS   66   138
FIGHTING   GRASS   66   131
GROUND   NORMAL   65   166
PSYCHIC   WATER   65   162
DARK   WATER   65   162
FAIRY   ELECTRIC   65   162
FLYING   ELECTRIC   65   154
GRASS   FIRE   65   138
STEEL   GHOST   64   163
STEEL   DARK   64   163
STEEL   ELECTRIC   63   151
POISON   ICE   63   148
STEEL   BUG   63   140
DRAGON   FIGHTING   62   157
STEEL   PSYCHIC   62   152
GHOST   FIRE   61   161
ELECTRIC   FIRE   61   151
BUG   FLYING   61   148
FAIRY   POISON   61   141
STEEL   FIRE   61   134
BUG   PSYCHIC   59   158
DARK   FIRE   59   156
PSYCHIC   FIRE   59   150
FAIRY   BUG   59   135
DRAGON   WATER   58   166
FAIRY   PSYCHIC   58   156
GHOST   PSYCHIC   58   153
STEEL   GRASS   58   141
DARK   PSYCHIC   57   154
PSYCHIC   FLYING   56   153
PSYCHIC   GRASS   56   147
GHOST   GRASS   55   157
DRAGON   FLYING   55   155
BUG   ELECTRIC   55   152
GHOST   ELECTRIC   54   163
GHOST   POISON   54   162
ROCK   NORMAL   54   153
FLYING   FIRE   54   141
POISON   GRASS   54   140
BUG   FIRE   54   131
BUG   GRASS   54   123
DARK   POISON   53   162
STEEL   DRAGON   53   157
DRAGON   ICE   53   154
DARK   GRASS   53   150
STEEL   POISON   53   147
GRASS   WATER   53   144
FLYING   POISON   53   140
GHOST   BUG   52   164
PSYCHIC   ELECTRIC   52   159
DARK   ELECTRIC   52   159
DRAGON   FIRE   52   153
PSYCHIC   POISON   52   148
FIGHTING   NORMAL   50   153
ICE   NORMAL   50   151
POISON   ELECTRIC   50   146
DARK   BUG   49   144
POISON   FIRE   49   134
GRASS   ELECTRIC   48   140
DRAGON   GRASS   46   151
BUG   POISON   46   125
DRAGON   GHOST   45   167
FAIRY   DRAGON   44   154
DRAGON   ELECTRIC   43   164
DRAGON   PSYCHIC   43   154
DARK   DRAGON   43   153
DRAGON   BUG   43   143
WATER   NORMAL   42   165
FAIRY   NORMAL   42   152
FLYING   NORMAL   42   141
DRAGON   POISON   40   154
STEEL   NORMAL   39   153
FIRE   NORMAL   36   139
DARK   GHOST   33   153
GHOST   NORMAL   31   166
GRASS   NORMAL   30   150
BUG   NORMAL   30   137
DARK   NORMAL   29   165
PSYCHIC   NORMAL   29   151
ELECTRIC   NORMAL   27   159
POISON   NORMAL   25   124
DRAGON   NORMAL   16   152
	Organized by Most Neutral:
		Code:
	
	Atk1    Atk2    Supers    Not Resists
GHOST   FIGHTING   81   170
GROUND   ICE   109   169
ROCK   GROUND   104   169
FLYING   GROUND   105   168
FAIRY   GROUND   101   168
FAIRY   GHOST   69   168
FAIRY   DARK   69   168
ICE   ELECTRIC   67   168
FLYING   WATER   80   167
FAIRY   WATER   80   167
DRAGON   GROUND   77   167
DRAGON   GHOST   45   167
GROUND   FIRE   99   166
GROUND   NORMAL   65   166
DRAGON   WATER   58   166
GHOST   NORMAL   31   166
STEEL   GROUND   91   165
GHOST   GROUND   86   165
ROCK   WATER   81   165
GHOST   ROCK   77   165
GHOST   WATER   67   165
GHOST   FLYING   67   165
DARK   FLYING   67   165
WATER   NORMAL   42   165
DARK   NORMAL   29   165
GROUND   POISON   88   164
FLYING   FIGHTING   86   164
PSYCHIC   GROUND   79   164
POISON   WATER   66   164
GHOST   BUG   52   164
DRAGON   ELECTRIC   43   164
GHOST   ICE   73   163
STEEL   GHOST   64   163
STEEL   DARK   64   163
GHOST   ELECTRIC   54   163
ROCK   FIGHTING   92   162
DARK   GROUND   84   162
PSYCHIC   WATER   65   162
DARK   WATER   65   162
FAIRY   ELECTRIC   65   162
GHOST   POISON   54   162
DARK   POISON   53   162
GHOST   FIRE   61   161
FIGHTING   ICE   91   159
ROCK   ICE   90   159
FAIRY   ROCK   90   159
ICE   WATER   79   159
DARK   ICE   71   159
BUG   WATER   68   159
PSYCHIC   ELECTRIC   52   159
DARK   ELECTRIC   52   159
ELECTRIC   NORMAL   27   159
PSYCHIC   FIGHTING   76   158
BUG   PSYCHIC   59   158
GROUND   ELECTRIC   88   157
ROCK   GRASS   82   157
ROCK   FLYING   80   157
DARK   FIGHTING   79   157
DRAGON   FIGHTING   62   157
GHOST   GRASS   55   157
STEEL   DRAGON   53   157
ROCK   PSYCHIC   79   156
DRAGON   ROCK   66   156
DARK   FIRE   59   156
FAIRY   PSYCHIC   58   156
GROUND   WATER   79   155
STEEL   ROCK   77   155
DARK   ROCK   75   155
STEEL   FIGHTING   74   155
FLYING   GRASS   70   155
DRAGON   FLYING   55   155
FIGHTING   FIRE   77   154
FAIRY   FIGHTING   76   154
STEEL   WATER   67   154
FAIRY   FLYING   67   154
FLYING   ELECTRIC   65   154
DARK   PSYCHIC   57   154
DRAGON   ICE   53   154
FAIRY   DRAGON   44   154
DRAGON   PSYCHIC   43   154
DRAGON   POISON   40   154
BUG   GROUND   91   153
FIGHTING   WATER   75   153
FLYING   ICE   74   153
PSYCHIC   ICE   71   153
GHOST   PSYCHIC   58   153
PSYCHIC   FLYING   56   153
ROCK   NORMAL   54   153
DRAGON   FIRE   52   153
FIGHTING   NORMAL   50   153
DARK   DRAGON   43   153
STEEL   NORMAL   39   153
DARK   GHOST   33   153
ROCK   FIRE   68   152
STEEL   PSYCHIC   62   152
BUG   ELECTRIC   55   152
FAIRY   NORMAL   42   152
DRAGON   NORMAL   16   152
ROCK   ELECTRIC   66   151
STEEL   ELECTRIC   63   151
ELECTRIC   FIRE   61   151
ICE   NORMAL   50   151
DRAGON   GRASS   46   151
PSYCHIC   NORMAL   29   151
FIGHTING   ELECTRIC   72   150
PSYCHIC   FIRE   59   150
DARK   GRASS   53   150
GRASS   NORMAL   30   150
WATER   FIRE   76   148
STEEL   FLYING   75   148
POISON   ICE   63   148
BUG   FLYING   61   148
PSYCHIC   POISON   52   148
ROCK   BUG   78   147
PSYCHIC   GRASS   56   147
STEEL   POISON   53   147
GROUND   FIGHTING   88   146
FAIRY   ICE   73   146
FAIRY   FIRE   72   146
FAIRY   STEEL   72   146
ICE   GRASS   71   146
ELECTRIC   WATER   67   146
POISON   ELECTRIC   50   146
GRASS   WATER   53   144
DARK   BUG   49   144
ROCK   POISON   71   143
DRAGON   BUG   43   143
POISON   FIGHTING   72   142
STEEL   ICE   81   141
FAIRY   POISON   61   141
STEEL   GRASS   58   141
FLYING   FIRE   54   141
FLYING   NORMAL   42   141
BUG   ICE   67   140
STEEL   BUG   63   140
POISON   GRASS   54   140
FLYING   POISON   53   140
GRASS   ELECTRIC   48   140
FIRE   NORMAL   36   139
ICE   FIRE   72   138
FAIRY   GRASS   66   138
GRASS   FIRE   65   138
GROUND   GRASS   82   137
BUG   NORMAL   30   137
FAIRY   BUG   59   135
STEEL   FIRE   61   134
POISON   FIRE   49   134
FIGHTING   GRASS   66   131
BUG   FIRE   54   131
BUG   FIGHTING   68   127
BUG   POISON   46   125
POISON   NORMAL   25   124
BUG   GRASS   54   123
	Most of the staples of old remain the best. Ground / Ice has always had excellent offensive potential, and Fighting / Ghost has always been perfect (outside of the non-existant Normal/Ghost). Fighting / Ghost hits the top of non-resist list.
EdgeQuake makes it nearly to the top of both lists as expected, and Bolt/Beam is near the top of the "most neutrals" list.
Dragon / Fire has fallen from perfection however. Fairy / Water, Fairy / Fire, Fairy / Rock, and Fairy / Dragon all resist Dragon / Fire hard. However, outside of the UU Pokemon Azumarill and Carbink, these pokemon don't really exist. The offensive combo Dragon / Fire may be "theoretically walled" by these types... but this offensive core will probably do fine in the OU Metagame. IMO, the chart simply demonstrates one area where theory isn't going to match up with practice.
Dragon / Ghost has rose up in the charts, due to Steel's lack of resist. I don't know if any pokemon can take advantage of this... but it complements Dragon now.
The new type "Fairy" has a large number of combos that work with it. In theory, Fairy / Ground is the best, but with Skarmory being one of the most prolific pokemon, that "rogue" Steel / Flying type resists Fairy too hard. But aside from Skarmory, Fairy and Ground perfectly complement each other, Fairy hitting most types hard... with Ground backing up on Fairy's Poison / Steel resists.
Also remember, the above charts don't take Levitate into account. Bronzong will wall Fairy / Ground.
Fairy/Ghost and Fairy/Dark IMO will serve as a more important "offensive core" for Fairies. (Mega) Mawile Play Rough / Sucker Punch, (Mega) Gardevoir Moon Blast / Shadow Ball, and Togekiss Dazzling Gleam / Shadow Ball will hit hard. Remember: Jirachi, Metagross and Bronzong are now weak against both Ghost and Dark.
Again, "Attack Pairs" are most useful for defensive / support pokemon. Offensive Pokemon will likely use "Attack Triplets" as an offensive core, and I don't have a chart for that yet. Still, I think these charts will serve as a good starting point in our X / Y analysis.
			
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