Player statistics are compiled out of existing games available for given player. When such games does not exist, or the calculations are not yet done the statistics are marked as "Not available". 
Opening statistic for chess players is based on ECO (Encyclopedia of Chess Openings) classification.
The Encyclopaedia of Chess Openings is a classification system for the opening moves in a game of chess. It is presented as a five volume book collection (now also a computer database) describing chess openings. The moves were taken from hundreds of thousands of games between masters, from published analysis in the Chess Informant since 1966, and then compiled by notable chess players. Instead of the traditional names for the openings, ECO has developed a unique coding system: There are five main categories, "A" to "E", each of which is divided into one hundred subcategories. Openings are typically provided in an ECO table that concisely presents the best opening lines. When we present the opening repertoire for a player we first structure it by major opening lines (For example as listed here) and then refined by the detailed ECO code [4]. For example, the line "Sicilian defence (35%): B92 B70 B34 B45 B98" means that 35% of the games that this player has played as white were Sicilian defence, and from those games the most frequent lines were B92 (Opocensky Variation: 1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6 6.Be2), then B70 (1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 g6) and so forth. 
By anaylising chess games one can extract various properties of the play styles of the opponents. We can compare how often a player has played a move that is the same as what a strong chess engine (like e.g. Stockfish) would play, as well as find out how his/her move compares in strenght to the evaluation of the computer move. Such analysis is often not trivial to interpret, as it can be seen here. For example, a positional player would tend to play more optimal moves in comparison to a tactical player. While a tactical player plays less optimal, he/she would put opponents in complicated positions which he/she practically can play better (in which his/her opponent do more mistakes). Nevertheless, even with such complications one can still achieve proper clustering and meaningful conclusions. On the other hand, play style tendencies like:
The following chapters provide description of the main properties which we have included in our game analysis. 
By calculating the average material quantity (For example, by using Standard or Fischer's valuations [7]) we can observe player's inclination to simplify positions (tendency to exchange pieces). This was analysed for several world champions in [1], however we believe that the authors in this work assumed in their measurements that the material after the game has ended is zero. Thus the conclusions in the paper (That, e.g. "Kramnik obviously dealt with less material on board") are possibly incorrect, or at least ambiguous. Calculating the material after the game has ended as zero leads to lower average numbers, for which one explanation could be tendency to simplify positions, but also just that the player has played shorter games (by faster accepting draws, resigning, or making his opponent to resign earlier). Thus, in our calculations and game statistics we do not count the material after the game has ended to be zero, but we calculate the average material per move by counting only the games (for given move) in which this move was reached. Figure 1. Exchange tendencies for Top 50 ELO players Figure 2. Material per move (as calculated in [1]) Figure 3. Exchange tendencies by ELO range Figure 4. Average material on move 20 for top 50 Super GMs. As example, from Figure 4. above one can see that the material value in the games of Giri vs. Topalov at move 20 is 3 points (pawns) higher for Giri. This seems consistent with the knowledge that Topalov is more of a tactical player, who prefers more complex positions, of course insufficient to be concluded alone from the tendency to exchange pieces. When we present "Exchange tendancy" for given player in our reports we present the numeric value difference to the average of all players, as well as the material graph in comparison to players like Kramnik, Carlsen, Giri on one hand and Topalov, Kamsky and Movsesian on the other. 
This metric aims to represent the tendencies of players to draw games: Would a player go for a fast draw in calm and balanced positions, or would one play until all the material is gone and the draw is "obvious"?
To answer this for a given player we calculate the median of the sequence of game lengths which finished with draw. For example, if a player has 11 games
which finished with a draw, and the length of this games was 20, 25, 30, 35, 37, 39, 40, 55, 61, 80, 120 moves, the median is 39 moves (the (n/2+1)th move in the sorted list of n
game lengths). The results of this analysis for top 50 super GMs as well as per ELO cluster are shown on Figure 5 and 6, the number for each player is then calculated and shown in comparison to those.
Figure 5. Average median draw move by ELO range Figure 6. Average median draw move for top 50 Super GMs. 
Chapters and analysis over the following properties are work in progress: Blunder Rates and types of blunders, Postional vs. Tactical play, Optimal Play, Resign tendencies, Specific endgames play.

1. Computer Analysis of World Chess Champions [link] 
2. Using HeuristicSearch Based Engines for Estimating Human Skill at Chess [link] 
3. Stockfish Chess Engine [link] 
4. Bill Wall's chess pages [link] 
5. ECO classificaiton [link] 
6. Wikipedia, ECO [link] 
7. Wikipedia, Chess Piece Relative Value [link] 
8. PGN Specification [pdf] 