How is order determined in the recommended Pokémon list when fighting at a gym?

As far as I've seen, it orders them by CP, skipping any that are not at full health. This can be kind of ridiculous when you have a 1000cp Pokemon with 89/90 health, and it suggests a 700cp Pokemon with 68/68 health over it, but this game is not perfect, it just does the best it can.

I'd also guess that the game takes type effectiveness into account, I've seen this happen in training a gym. The game suggested a weaker vaporeon over a stronger flareon, because the first opponent in the gym was a fire-type pokemon. I have no idea if the suggestions are just based on the first opponent or every opponent in the gym though.

I observed that there are some criteria it looks for:

• High cp pokemon have a higher chance to show up
• High remaining hp pokemon have a higher chance to show up, it may suggest pokemon with lower hp as long as its remaining hp is higher than your others
• Tries to counter the pokemon types in the gym
• Does not take DPS, move strength or speed in consideration at all

I'm sure there is a formula, which mixes these variables with different weights. I'm also searching for it.

Bah, humbug. @Ellesedil has provided a counterexample to my speculation. I'll still leave this here in case it's of any use to anybody.

I strongly suspect it's ordered simply by Pokemon level. I'm not sure what it does in case of ties, since I don't have enough data on it, but this is a start. This fits both my suggested Pokemon in Gym battles, and yours.

You provided that you have Vaporeon (143 hp, 1293 cp), Golem (93 hp, 1050 cp), Arcanine (96 hp, 1133 cp). From this, it's possible to calculate that your Vaporeon is level 33-36, your Golem is level 29-36, and your Arcanine is level 25-28.

^{(Incidentally, your Vaporeon is 44-53% perfect, your Golem is 22-98% perfect, and your Arcanine is 40-69% perfect. I can also tell from this that your trainer level was 17 or 18 when you submitted that comment!)}

Level range can be determined from the stardust cost to level up. Here's one such chart:

Level | Stardust Cost | Candy Cost
------+---------------+-----------
1     | 200           | 1
2     | 200           | 1
3     | 200           | 1
4     | 200           | 1
5     | 400           | 1
6     | 400           | 1
7     | 400           | 1
8     | 400           | 1
9     | 600           | 1
10    | 600           | 1
11    | 600           | 1
12    | 600           | 1
13    | 800           | 1
14    | 800           | 1
15    | 800           | 1
16    | 800           | 1
17    | 1000          | 1
18    | 1000          | 1
19    | 1000          | 1
20    | 1000          | 1
21    | 1300          | 2
22    | 1300          | 2
23    | 1300          | 2
24    | 1300          | 2
25    | 1600          | 2
26    | 1600          | 2
27    | 1600          | 2
28    | 1600          | 2
29    | 1900          | 2
30    | 1900          | 2
31    | 1900          | 2
32    | 1900          | 2
33    | 2200          | 2
34    | 2200          | 2
35    | 2200          | 2
36    | 2200          | 2
37    | 2500          | 2
38    | 2500          | 2
39    | 2500          | 2
40    | 2500          | 2
41    | 3000          | 3
42    | 3000          | 3
43    | 3000          | 3
44    | 3000          | 3
45    | 3500          | 3
46    | 3500          | 3
47    | 3500          | 3
48    | 3500          | 3
49    | 4000          | 3
50    | 4000          | 3
51    | 4000          | 4
52    | 4000          | 4
53    | 4500          | 4
54    | 4500          | 4
55    | 4500          | 4
56    | 4500          | 4
57    | 5000          | 4
58    | 5000          | 4
59    | 5000          | 4
60    | 5000          | 4
61    | 6000          | 6
62    | 6000          | 6
63    | 6000          | 6
64    | 6000          | 6
65    | 7000          | 8
66    | 7000          | 8
67    | 7000          | 8
68    | 7000          | 8
69    | 8000          | 10
70    | 8000          | 10
71    | 8000          | 10
72    | 8000          | 10
73    | 9000          | 12
74    | 9000          | 12
75    | 9000          | 12
76    | 9000          | 12
77    | 10000         | 15
78    | 10000         | 15
79    | 10000         | 15
80    | 10000         | 15

Additionally, based on your trainer level, you can only power up Pokemon to a certain level. Here's that chart:

Trainer | Max Pokemon
Level   | Level
--------+------------
1       | 4
2       | 6
3       | 8
4       | 10
5       | 12
6       | 14
7       | 16
8       | 18
9       | 20
10      | 22
11      | 24
12      | 26
13      | 28
14      | 30
15      | 32
16      | 34
17      | 36
18      | 38
19      | 40
20      | 42
21      | 44
22      | 46
23      | 48
24      | 50
25      | 52
26      | 54
27      | 56
28      | 58
29      | 60
30      | 62
-- below here is speculation --
31      | 64
32      | 66
33      | 68
34      | 70
35      | 72
36      | 74
37      | 76
38      | 78
39      | 80
40      | 82