Wrote about TR and little bit about APP and VS/APM

Meaning-and-the-essence-of-stats.md

@@ -8,28 +8,55 @@ In TETR.IO, there is a variety of stats. But what are they all mean? Let's figur
 ## Multiplayer stats
 ### Calculated by game
 #### [TR] Tetra Rating
-1500 GLICKO with 350 RD = 12500 TR - every unranked with 0 games played
+
+Main metric, that supposed to show the true skill of player. It's based on [GLIXARE](https://www.smogon.com/forums/threads/gxe-glixare-a-much-better-way-of-estimating-a-players-overall-rating-than-shoddys-cre.51169/), which is based on GLICKO-2 win probability equation. So, TR actually shows your chance of winning against average player, which is considered to have 1500 GLICKO with 350 RD (= 12500 TR - every unranked with 0 games played). TR calculated with this formula:
+
+`TR = 25000 / (1 + 10^(((1500 - GLICKO) * pi / sqrt(3 * ln(10)^2 * RD^2 + 2500 * (64 * pi^2 + 147 * ln(10)^2)))))`
+
+The only differences from GLIXARE formula is that 25000 was 10000 in GLIXARE formula and whole equation was rounded and divided on 100.
+
 #### [GLICKO] GLICKO-2 rating
+
 Whole GLICKO-2 rating system is a method of assessing a player's strength in competitive games. It described with a bunch of difficult formulas ([look here for them](https://en.wikipedia.org/wiki/Glicko_rating_system#Glicko-2_algorithm)), but basically, after each TL match you gain/lose somewhere around rating difference, adjusted with RD. If you win a player with glicko being a lot bigger, than yours, you gain a lot of glicko. If you lose to a player with glicko being a lot bigger, than yours, you lose only a small amount of glicko. Vise versa with a player with glicko, being a lot smaller, than yours.
 
 GLICKO-2 system also has a system constant, responsible for "change in volatility over time". So, yeah, each player has hidden variable, called "volatility", which is high if you successfully compete against higher rated players (or vise versa), and low if you play "on your rating". The value of constant, hoverer, unknown.
+
 #### [RD] Rating deviation
+
 That number tells, how the rating system uncertain about player rating. It goes down every played match on some amount, that calculated very weirdly and goes up by 1 each day after week of inactivity (if RD less, than 350). RD also has a soft floor of 60 RD, but it's possible to get lower RD by playing big amount of games. If your RD higher, than 100, your rank gets hidden. 
+
 #### [WR] Win Rate
+
 Very very old and inaccurate way to determine players skill. It's just a ratio of wins to played games.
+
 #### [APM] Attack per Minute
+
 That one is easy to understand. It's just a ratio of attack (sent + cancelled lines) to time (minutes). The only problem is — it's still may be not accurate, since you can send 20 attack in 5 seconds with opener and then have no skill to play midgame, having in total, let's say, 120 APM, or just play good midgame without opener and be really strong opponent with same 120 APM.
+
 #### [PPS] Pieces per Second
+
 That's also easy. It's a measurement of speed. It's just a ratio of placed pieces to time (seconds). The faster you place pieces, the bigger it is.
+
 #### [VS] Versus Score
+
 That metric was invented by osk and promoted in game, as "general indicator of skill". It calculated with this formula: 
 
 `VS = [ ( attack + garbage lines cleared ) / pieces ] * PPS * 100`, where constant of 100 here is just for scale. 
 
 That metric encourages player for using garbage lines.
+
 ### Calculated by using fancy math
+
+Only the metrics listed above are available for calculations.
+
 #### [APP] Attack per Piece
+
+That's a ratio of attack to number of placed pieces. Basically, an efficiency metric.
+
 #### [VS/APM] Versus Score per Attack per Minute
+
+That's a ratio of versus score to attack per minute.
+
 #### [DS/S] Downstack per Second
 #### [DS/P] Downstack per Piece
 #### [APP + DS/P] Summary of Attack per Piece and Downstack per Piece