Fig 1.
Log-log learning curve of the subpopulation of players with different total activity. Each learning curve shows the skill of the first 2n games played of the subpopulation with at least 2n games played and less than 2n+1. Subplots show the parameterized values (i.e. α and Skill0) of each learning curve following Eq 1.
Fig 2.
The learning curve for strong, medium and weak team-oriented behavior. The band represents 95% Wilcoxon rank-sum confident interval, and the middle line represents the pseudomedian. As a reference, we show the learning curve of the whole population. Results are analogous to those obtained with mean and 95% t-test confident interval.
Fig 3.
Loyalty influence over strong TOB learning curve.
Learning curves of the loyal and casual subclasses of strong TOB. The band represents 95% Wilcoxon rank-sum confident interval, and the middle line represents the pseudomedian. As a reference, we show the learning curve of the whole population and the strong TOB. Results are analogous to those obtained with mean and 95% t-test confident interval. The vertical line at 100 of games played indicates the analysis performed in Fig 4.
Fig 4.
Skill interaction between loyalty and TOB for all players.
The role of experience was isolated by taken the skill of players at the same point of experience. All players have 100 of games played. The average skill of each bin is reported by the gray-scale. Contour lines are shown. Empty bins have less than five players.
Table 1.
Influence over skill acquisition of loyalty, TOB and faithfulness (linear model).
We report the estimated slope value, their standard deviation and their significance difference with respect to a zero slope. All players have 100 games of experience.
Table 2.
Linear mixed model for one overall model fitted to all data between 10 and 500 games played of individual experience.
At column normalized estimates (Norm.Est.) we transform the estimators, in logarithmic scale, to their normalized value, (e.g. Intercept = 101.415, exp = 101.415+ 0.016 − 101.415). Method: REML converged. Number of groups: 65335. Max Group size: 491. Mean group size: 99.5.
Fig 5.
a) The current game board showed as a graph with continents (regions of the same shape), players (regions of the same grayscale), and a number of troops in each region. The capital characters represent the names of the closest region. b) General game status: current round, the active player, and remaining time to play; and a summary of total troops and controlled regions for each player. c) Example of chat session during a game. d) Log of game used to extract game information with a scrapper.
Fig 6.
Joint probability of the performance of two players i, j under the assumption of si > sj and independence.
All lines parallel to the diagonal pi = pj represent “difference of performances” isobars dij = pi − pj.
Fig 7.
The probability of the outcome of a game under the assumptions of the Elo rating system with si > sj.
The area under the curve in the positive interval (dij > 0) is the winning probability for the player i, and the area under the curve in the negative interval is the winning probability of player j.
Fig 8.
Performance distributions, N(pi; si, β2) weighted by the probability of the skill belief distribution .
The area under the solid line must be integrated to compute a certain probability pi.
Fig 9.
Joint probability of the performance of two teammates i, j.
Lines parallel to the diagonal te = c represent team performance isobars.
Fig 10.
Bayes network of TrueSkill method.
Fig 11.
Bayes factor network of TrueSkill method.
Fig 12.
TrueSkill update procedure for the winning case, where δ is the expected difference between teams.
Fig 13.
TrueSkill update procedure for losing case, where δ is the expected difference between teams.