What are your stats? Lets compare! (Show and tell)
Level : 37 - Mystic
Total XP: 10,131,750
Start date: 30 Oct 2016
16,392 pokemon caught
15,119 pokestops
3,854 pokemon evolved
1,327 eggs hatched
1,266 km walked
Battle girl: 1,032
Ace trainer: 365
Raids: 56 (no t4, t5 or solo t3 yet)
Gym hours: 9,623
Gold badges: 13
Pokedex: 233 caught / 237 seen
Feel free to add any stats or comments and attach a screen shot. Thanks!

Answers
Key missing stat IMO: money given to Niantic.
To me the winning metric is ROI: get the max PoGo performance out of the least possible $ to Niantic.
Also missing:
km of non-human-powered travel involved
number of uses of bots, including finding rare spawns and raids
number of hours spoofing
The best players have the highest ratio between the stats you listed above (high as possible) and these 4 stats (low as possible).
Valor - 35
Total Xp: 7,093,821
Start Date : 7/11/2016
14,141 Pokemon Caught
10,909 Pokestops
1,194 Evolved
568 Eggs hatched
1,261 KM walked
Battle Girl: 4,077
Ace Trainer: 1,267
Raids: 45
Gym hours: 8,601 hours
Gold Badges: 9 (Moved a little over a month ago so had to restart in new city. Close to 9 new ones now )
Pokedex: 228/241 (Waiting for 91%+ IVs to fill lots of entries that I have plenty of candies for already. Looking at you Dragonite)
$0 spent on Pokecoins
Level : 38 - Valor
Total XP: 13,508,853
Start date: 7/14/16
28,503 pokemon caught
34,797 pokestops
4,304 pokemon evolved
1,059 eggs hatched
2252.4 km walked
Battle girl: 5,417
Ace trainer: 3,945
Raids won: 45
Gym hours: 3,247
Pokedex: 237/242
free player, no money spent on pokecoins, but reliable maximum gym rewards, both before and after the gym rework.
OK, if we’re going to whip them out and measure, here it is. Comparing with others, I notice that for my level, I tend to have more km walked, stops spun and gyms trained as opposed to battled.
Level : 35 (oh so close to 36) - Mystic
Total XP: 7,442,610
Start date: 11 July 2016
14,125 pokemon caught
23,710 pokestops
1,239 pokemon evolved
972 eggs hatched
1,852 km walked
Battle girl: 1,002
Ace trainer: 2,502
Raids: 30
Gym hours: 4,023
Gold badges: 11 in top section, 16 gold type badges
Pokedex: 237 caught / 233 seen
Level : 35 - Mystic
Start date: 25 August 2016
Total XP: 6162702
12932 pokemon caught
12066 pokestops
2,262 pokemon evolved
386 eggs hatched
1000.4 km walked (got the badge today)
Battle girl: 1257
Ace trainer: 859
Raids: 34
Gym hours: 5453
Gold badges: 4 plus 2 others will turn gold in the next 7 days
Pokedex: 232 caught / 238 seen
Gold medals: 8 in the top section, 14 in the bottom section
Cash to Niantic: 0
Playing solo or with wife, fitting it in after work hours and around life in general.