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I did a slightly more indepth analysis once upon a time. I didn't count Champions for reasons. It doesn't have a nice graphic like OP but here's some lovely text:
Rock/Water/Electric/Grass/Poison/Psychic/Fire/Ground
Ice/Fighting/Ghost/Dragon
Flying/Bug/Normal/Ghost/Fighting/Steel/Ice/Dragon
Psychic/Poison/Fighting/Dark
Rock/Fighting/Electric/Fire/Normal/Flying/Psychic/(Water/Water)
Dark/Ghost/Ice/Dragon
Rock/Grass/Fighting/Water/Ghost/Steel/Ice/Electric
Bug/Ground/Fire/Psychic
(Fire/Grass/Water/Normal)/(Normal/Poison)/Bug/Electric/Ground/Flying/(Ice/Dragon)/(Dragon/Water)
Ghost/Dark/Psychic/Fighting
Bug/Rock/Fighting/Grass/Electric/Fairy/Psychic/Ice
Steel/Fire/Dragon/Water
Bug
4 - 3/1 (2, E1, 3, 1)
Dark
3 - 0/3 (E4, E1, E2)
Dragon
6 - 3/3 (E4, 8, E4, 8, 7, E3)
Electric
5 - 5/0 (3, 3, 8, 4, 5)
Fairy
1 - 1/0 (6)
Fighting
6 - 4/2 (E2, 5, 2, 3, E4, 3)
Fire
5 - 3/2 (7, 4, E3, 1, E2)
Flying
3 - 3/0 (1, 6, 6)
Ghost
5 - 2/3 (E3, 4, E2, 5, E1)
Grass
4 - 4/0 (4, 2, 1, 4)
Ground
3 - 2/1 (8, E2, 5)
Ice
6 - 4/2 (E1, 7, E3, 7, 7, 8)
Normal
4 - 4/0 (3, 5, 2, 1)
Poison
3 - 2/1 (5, E2, 2)
Psychic
6 - 3/3 (6, E1, 7, E4, E3, 7)
Rock
4 - 4/0 (1, 1, 1, 2)
Steel
3 - 2/1 (6, 6, E1)
Water
6 - 5/1 (2, 8, 8, 4, 1, E4)
Dark, Dragon, Fairy, Ground, Ice, Psychic, and Steel have never been an early gym.
Bug, Dark, Grass, and Rock have never been a late gym.
Electric has been a gym the most, followed by Grass, Ice, Normal, Rock, and Water.
Electric, Fairy, Flying, Grass, Normal and Rock have never been in the Elite Four.
Dark, Dragon, Fighting, Ghost, and Psychic have been in the Elite Four the most.
Dragon, Fighting, Ice and Psychic have been used the most.
Fairy has been used the least, followed by Dark, Flying, Ground, Poison and Steel.