WN7 formula:
(1240-1040/(MIN(TIER,6))^0.164)*FRAGS
+DAMAGE*530/(184*e^(0.24*TIER)+130)
+SPOT*125*MIN(TIER, 3)/3
+MIN(DEF,2.2)*100
+((185/(0.17+e^((WINRATE-35)*-0.134)))-500)*0.45
-[(5 - MIN(TIER,5))*125] / [1 + e^( ( TIER - (GAMESPLAYED/220)^(3/TIER) )*1.5 )]

Would like to highlight that MIN() means the number capped at that value, so MIN(TIER, 5) means avg tier capped at 5, (so player avg tier is used if it is lower than 5, otherwise 5 is used) and MIN(DEF,2.2) means defense is capped at 2.2.


WN7 SUMMARY 
written by Neverwish, Crabeatoff and Praetor77
Work on WN7 is a community effort. I consider everyone who has posted in this forum to have contributed their two cents into making WN what it is today. However, I would like to highlight the contribution of the people who have dedicated the most time and effort into making WN: 
Key contributors: Tpapp157, Neatoman, Syndicate, Maokai, Makaze2048, Guerdon, DracoArgentum, Crabeatoff, TheKilltech,  etc. etc.

The WN rating was created using statistical analysis tools like correlation studies and evolutionary algorythms to create an accurate formula, using Win Rate as a proxy to accurately determine the weight each stat would have in the formula. The idea was to create a formula which actually tried to measure player skill in the most accurate way possible, using global account stats.
The Efficiency formula was the basis for an analysis to figure out what was wrong with it and create an improved formula with those problems fixed.
WN is short for Weighed and Normalized, and implements various ways to deal with statpadding, and in the end tried to develop a metric that could only be padded by actually being good at the game.

Key points of the WN Rating are:

• Damage is scaled according to your average tier and is the most important stat in the formula. The points you get for damage are carefully tied to the avg tier played, so that players with avg tier played 6 or 9 could be accurately compared, despite having very different average damage. To do this, average damage for tiers were collected from vbaddict.net and the data was carefully fitted to a non-linear curve.
  
• Players with a considerable number of battles who have an average tier lower than 4 are heavily penalized for sealclubbing. New players with few battles under their belts are not penalized until they achieve a big number of battles but remain with a low average tier played.
  
• Cap points are not counted towards your rating, since despite HUGE efforts and statistical analysis mainly performed by Syndicate, there was no statistically sound way to include cap points into the formula. The data suggests that for the average player cap points which are actually useful in winning a game for your team are drowned out by the huge amount of useless cap points gathered at the end of already won games.
  
• Winrate is used as a proxy to measure intangible stats which are not available on the player profile like spotted damage, cap used to lure the enemy out, stopping scouts from killing your arty, tracking enemies at crucial moments, keeping your teammates alive, map awareness and other crucial decisions not recorded in the stats. This term of the forumla counts for 0-10% of final WN rating.
  
• Average Defense points is capped at 2.2 to prevent padding. Defense also proved to be highly correlated to winrate, suggesting players who have map awareness and return to base when needed to stop enemy capping win more often.
  
• One of the most important characteristics of the WN Rating is the open development format, meaning any player can post in this thread and suggest modifications, which will be tested and, if successful, implemented. By having this open development model, it effectively eliminates biases which closed formulas such as Efficiency have.
  
• After the rating was released, WoTLabs was the first website to implement it, keeping it up to date every time a new version is launched. Although many people dislike the fast evolution of the rating (having gone through several changes and versions in only 4 months), this means that the formula rapidly grows more accurate. It has spread to the point where the WN Rating is now the standard rating used on the XVM mod, although transformed into a 0-99 scale rating.

Common Misconceptions
Despite having been based on advanced algorithms, the WN Rating did not pass without heavy criticism, although most, if not all, of this criticism turned out to be misconceptions.

One common complaint was that, if it was made to correlate with win rate, then we could just use win rate. Unfortunately win rate can be easily padded by platooning with good players. The WN Rating separates those padded players by using their actual stats. A veteran player with a low WN Rating but a high win rate has been probably been heavily padded.

Another common criticism is that we should stop caring about statistics and just play the game, since statistics eventually lead to mockery. Unfortunately World of Tanks is a competitive game, and as in all competitive games, there must be a measuring stick in order to know if you are improving and how much you are improving, otherwise we might as well go play Farmville. Shooting tanks for the heck of it gets boring after a while. The idea behind WN is to use it as a tool to make sure you keep improving, and also as a wealth of information when used in XVM to help you make critical decisions based on the skill of your teammates and enemies.

Other players criticize the formula for not taking things like spotting damage into account. This can hardly be pinned on the WN Rating, since Wargaming has not released this information publicly. The WN Rating can only work with what it has available. To account for those invisible stats that help win games, Win Rate has been added to the formula.

Lastly, many players criticized using winrate in the formula, since the very same winrate was used as a proxy to weigh the other stats in the evolutionary formula. However, as posted above, the idea was not to reward winrate, but to use it as a proxy for intangible stats. Also, the reward for these "intangibles" are carefully tailored by Neatoman into an S-curve with diminishing returns for winrates above 60%, where correlation to stats drop significantly, suggesting winrates above this value are purely due to platooning and companies. Also supporting this data is the fact that Zakaladas (quite possibly NA server´s best player) almost always plays solo and averages 64% wins.

Limitations and problems

Formulas can only be created from stats that are made available via the official WoT website. Efficiency depends on those same stats. Everything WoT-news computes is off those same stats. More information on YOUR history is available from the cached dossier file, but unless everyone starts mass uploading those (which will never happen), then the official website stats are THE source for data.
What isn't in WoT website stats?

• Normalized Experience (XP) - theoretically WG could keep track of experience based on whether a user had a premium account or not, and then either remove the premium bonus OR give all standard account users the bonus (for stats purposes) to normalize XP across users.

• Damage Upon Detection - Damage done to targets you are spotting yourself, by tanks who are not spotting them themselves. The latter is the bread and butter of light tanks (LTs) and of front line fighters. The other bonuses are relatively small compared to the latter. But it is the most noticeably missing in all rating calculations, and it particularly screws over LTs.

• Per tank anything - the website cannot tell you damage per tank, spots per tank, etc. This information lives in your dossier and somewhere on the WG servers. If you use a dossier parsing tool (there are several web based and one local), you can obtain this information on your per tank performances. There is something called an API which gives you this kind of information, but currently the NA server API does not work correctly, like for example it says I have 15.4 spots per game on my IS-4.

Implications of these limitations

Light tanks
Due to the lack of DUD (damage upon spotting) on the WG website, light tanks are unfairly measured by WN7. They normally get lower WN7 scores than heavy, med or TDs of the same tier. That being said, WN7 is actually the metric that gives one of NA server´s best scouts (Redparadize) the highest rating...
PR: 1842
Eff2.0: 1742
WN7: 1943

SPGs
SPGs also cause issues, as their tiers are not lined up with the rest of tanks! They do much more damage than their tier value would indicate for a HT, MT or TD. This is a known limitation of the formulas. Extensive programming (parsing the website stats for SPG counts and adjusting their tier) COULD fix this, but the problem will go away when the SPGs tiers are stretched to match (per the latest ASAP with SerB). For now...we deal with it. Who care about SPG players stats anyways, amirite?!?!?

Some statistical limitations
When measuring a population, its not going to be possible to put every single person on the scale and have the scale make sense. Again, returning to a notable outlier, Tazilon and his 20k+ VK2801 games. This massive number of games means his average tier played is 5.35, which is lower than is "generally expected" for someone with 28k total games. It takes longer to move through higher tier tanks, and so you end up with more weight at 6+. Because WN7 is designed to measure the population relative to each other, some assumptions have to be made about the habits of the general population. Most players don't play 20k games in any single class or tier below 8, let alone 20k in a single tier 5. If someone plays 10k games in the MS-1....outlier! Takeaway: population ratings cannot account for every outlier.


Back to the formula
A detailed explanation of each portion of the WN7 formula by Crabeatoff and Praetor77.
Includes the answer to questions like "Why is cap not included in the formula?", "How much does winrate contribute to the equation" and "How does the low tier penalty work?":