While I wouldn't say I'm obsessed with my statistics in World of Warships, I definitely keep and eye on them and try to improve over time.
I've pointed you at the Warhshipstats.com website before, and it remains a constant site to visit because it keeps track of historical data so I can watch as my win percentage rate goes up and down. The statistics page on World of Warships' main site is also very useful because it has some more detailed stats and layout that makes it easier to compare ships of the same class, or the best results for certain ships.
I peaked in my win percentage at 52.27% on Sept 9 and stayed close to 52% until mid October. My average damage peaked in early October at just over 40K per game. Then in mid October both stats took a nosedive to around 51% for win rate where it has stabilized, and my average damage has fallen to over 38K per game. I say 'nosedive' but really both are pretty minor in the grand scheme of things.
I suspect I know the reasons for both drops. For one, my win rate and damage are still correcting from the sheer power of the pre-nerfed Imperial Japanese Navy aircraft carriers who were dominating for me up until half way through my tier VII Hiyru. With 200 battles they have my best win rate of 55% and average damage 54K per game. Even in my tier VIII Shokaku which I never had pre-nerf I'm still doing 53% win rate and 60K avg damage per game.
But I've been playing my carrier less as I started up the Russian Destroyer and German Cruiser lines. In lower tier battles (I through to III) it doesn't often matter how well you do, sometimes people still learning the game on the other side of the map can lose it for you, so win rate suffers a bit. I've finally gotten to tier IV in both lines and I noticed an improvement in win rate as a result.
Average damage is a weird stat to cover overall as well. If you do nothing but carriers and battleships, as I did for a long time, average damage will be a lot higher than a captain focusing on cruiser or destroyer lines. Plus if start doing more low tier matches, average damage is lower as those ships just plan do less damage. Since I've started both working more on destroyers AND in low tiers, my average damage has dropped a lot and will continue to do so as I maintain a balanced approach.
All of this is to say I'm overall pretty happy with my statistics right now. I'm not the best player but I feel confident I'm middle of the road, solid and dependable most of the time.
My best ships based on ships I've used for more than 5 battles:
Win rate: IJN Tenryu cruiser (III), 87.5% over 8 battles
Average Experience: IJN Ryujo carrier (VI), 1796 over 46 battles (pre-nerf)
Average Damage: IJN Ryujo carrier (VI), 66,054 over 46 battles (pre-nerf)
Kill Death Ratio: IJN Ryujo carrier (VI), 5.69 over 46 battles (pre-nerf)
Ship Kill Rate: IJN Ryujo carrier (VI), 1.61 over 46 battles (pre-nerf)
Hmmm... ok, ignoring the pre-nerf carriers for those last four?
Average Experience: IJN Shokaku carrier (VI), 1771 over 15 battles
Average Damage: IJN Shokaku carrier (VI), 60,475 over 15 battles
Kill Death Ratio: IJN Shokaku carrier (VI), 5.00 over 15 battles
Ship Kill Rate: USN Omaha cruiser (IV), 1.40 over 25battles
I guess I'm just my best when I'm in my carrier!