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Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement in online games

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The problem of skill acquisition is ubiquitous and fundamental to life. Most tasks in modern society involve the cooperation with other subjects. Notwithstanding its fundamental importance, teammate selection is commonly overlooked when studying learning. We exploit the virtually infinite repository of human behavior available in Internet to study a relevant topic in anthropological science: how grouping strategies may affect learning. We analyze the impact of team play strategies in skill acquisition using a turn-based game where players can participate individually or in teams. We unveil a subtle but strong effect in skill acquisition based on the way teams are formed and maintained during time. "Faithfulness-boost effect" provides a skill boost during the first games that would only be acquired after thousands of games. The tendency to play games in teams is associated with a long-run skill improvement while playing loyally with the same teammate significantly accelerates short-run skill acquisition.
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RESEARCH ARTICLE
Faithfulness-boost effect: Loyal teammate
selection correlates with skill acquisition
improvement in online games
Gustavo Landfried
1,2
, Diego Ferna
´ndez SlezakID
1,2
*, Esteban MocskosID
1,3
*
1Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Computacio
´n,
Buenos Aires, Argentina, 2CONICET-Universidad de Buenos Aires, Instituto de Investigacio
´n en Ciencias de
la Computacio
´n (ICC), Buenos Aires, Argentina, 3CONICET, Centro de Simulacio
´n Computacional p/Aplic
Tecnolo
´gicas (CSC), Buenos Aires, Argentina
*dfslezak@dc.uba.ar (DFS); emocskos@dc.uba.ar (EM)
Abstract
The problem of skill acquisition is ubiquitous and fundamental to life. Most tasks in modern
society involve the cooperation with other subjects. Notwithstanding its fundamental impor-
tance, teammate selection is commonly overlooked when studying learning. We exploit the
virtually infinite repository of human behavior available in Internet to study a relevant topic in
anthropological science: how grouping strategies may affect learning. We analyze the
impact of team play strategies in skill acquisition using a turn-based game where players
can participate individually or in teams. We unveil a subtle but strong effect in skill acquisi-
tion based on the way teams are formed and maintained during time. “Faithfulness-boost
effect” provides a skill boost during the first games that would only be acquired after thou-
sands of games. The tendency to play games in teams is associated with a long-run skill
improvement while playing loyally with the same teammate significantly accelerates short-
run skill acquisition.
Introduction
Skill is mainly acquired from individual experience. Humans, due to its social characteristic,
also incorporate knowledge by learning from others. Social learning may affect the skill acqui-
sition process expected from experience, and involve beneficial and risky alterations to subject
abilities [1]. In this article, we exploit the virtually infinite repository of human behavior avail-
able in Internet to study a relevant topic in anthropological science: how grouping strategies
may affect skill acquisition.
The study on expert decision-making grew out of research on master chess players [24].
When making decisions under uncertainty, experts rely on heuristics that generally lead to
non-rational and suboptimal behavior [5,6]. Individual experience has long been a major
topic, studied as the main factor in performance improvement. Newell argued in 1981 that the
generalized power law describes all of the practice data [7]. In recent years, some authors dis-
cuss that power law is limited to explain population learning curves and propose other
PLOS ONE | https://doi.org/10.1371/journal.pone.0211014 March 5, 2019 1 / 26
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OPEN ACCESS
Citation: Landfried G, Ferna
´ndez Slezak D,
Mocskos E (2019) Faithfulness-boost effect: Loyal
teammate selection correlates with skill acquisition
improvement in online games. PLoS ONE 14(3):
e0211014. https://doi.org/10.1371/journal.
pone.0211014
Editor: Gustavo Stolovitzky, IBM Thomas J Watson
Research Center, UNITED STATES
Received: November 1, 2017
Accepted: January 7, 2019
Published: March 5, 2019
Copyright: ©2019 Landfried et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: Data are available
from Dryad (DOI: 10.5061/dryad.888gm50).
Funding: This work was supported by Universidad
de Buenos Aires: UBACyT 20020130200096BA
and 20020170100765BA (E.M. received
grants); CONICET (Consejo Nacional de
Investigaciones Cientı
´ficas y Tecnolo
´gicas):
PIO13320150100020CO (E.M. received grant);
STICAmSud (CC-SEM); ANPCyT (Agencia Nacional
de Promocio
´n Cientı
´fica y Tecnolo
´gica): PICT-
2015-2761 and PICT-2015-0370 (E.M. received
functions to approximate individual learning curves [8]. However, the individual learning
curves are more irregular than averaged learning curves and predicting large time scale perfor-
mance based on small time scale events probed to be hard [9,10]. Practice is an important
learning factor but is not the only one. Other essential components should be taken into
account in order to better understand the learning processes.
One of the factors that cause an alteration in expected learning curves is, for prosocial ani-
mals, the social learning ability. Social learning is defined as long-term changes in behavior
caused by stimuli derived from observation of—or interaction with—other individuals [11,
12]. Our species was involved in a unique gene-culture coevolution that caused the emergence
of our special social learning abilities: a costly cognitive machinery enabling efficient acquisi-
tion of complex traditions [13]. Humans learn things from others, improve and transmit them
to the next generation, leading to a cultural accumulation that can not be developed by a single
individual during her lifetime [14]. The ability to acquire behaviors based on the experience of
others without having to build it by trial and error leads to a cumulative culture evolution,
allowing humans populations to adapt rapidly to changes and new environments [1]. A degree
of credulity is required for this process to work, and therefore social learners can acquire inap-
propriate information even in uniform and stable environments [15,16]. Deciphering how to
take advantage of social information while handling the inconveniences that arise from their
use has become the main topic in the research on strategies of social learning [17,18].
Many models of social learning strategies and their emerging population dynamics have
been proposed. Researchers have identified several theoretical strategies [18,19], which can be
classified as: (a) those that specify the circumstances under which individuals copy others, and
(b) those that identify from whom individuals learn. Recently, many studies of social learning
have been conducted using different methods such as field observations [20], controlled labo-
ratory experiments [19,2128] and field experiments [2932]. Social learning now constitutes
a major area of study within behavioral and evolutionary biology [33].
One difficulty inherent to all the mentioned methods is their reliance on small samples.
With the advent of datasets from virtual communities, we set to study social learning in a mas-
sive data environment. We rely on a vast corpus (*4.5 millions of games), capitalizing on a
worldwide tendency of people to play multi-player online games and on the existence of serv-
ers that accumulate public data. This novel methodology seeks statistical emergent of poten-
tially subtle effects, which may be detectable only with a remarkable number of observations
and might remain undetected in a small sample sizes typical of laboratory studies [34]. Our
study also incorporates the current capacity to analyze the value of skill acquisition with high
accuracy. These results are obtained from a very unique experimental condition in which play-
ers engage in natural relationships, free to choose their teammates and opponents, and pro-
duce reliable outcomes which can be measured directly without hinge on indirect methods
such as self-reported choice.
Online games have already been used as a model to study complex cooperative processes in
social science [35,36], neuroscience [34,37], and computational social science [3841]. Chess
has been, by its complexity and clear rules, a privileged model for the study of learning and
decision making. Massive chess data allowed the analysis of the influence of age, cohorts, gen-
der and other features on learning [9,10,4245].
Here we set to investigate the impact of team play strategies on skill acquisition in Conquer
Club, an online multiplayer turn-based game. Unlike the individual game nature of chess, at
Conquer Club (inspired by the board game RISK) a variable amount of players can take part in
each game, playing individually or in teams (Section A in S1 File). In Conquer Club there is a
strong incentive for collaboration: the results of the games are by teams. All the players of a
team win or lose together. A player who is eliminated during a game can still end up winning
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
PLOS ONE | https://doi.org/10.1371/journal.pone.0211014 March 5, 2019 2 / 26
grants); and Ministerio de Ciencia, Tecnologı
´a e
Innovacio
´n Productiva, CC-SEM (E.M. received
grant). The funders had no role in study design,
data collection and analysis, decision to publish, or
preparation of the manuscript.
Competing interests: The authors have declared
that no competing interests exist.
if her teammates defeat the rest of the teams. Therefore, it is essential that teammates can coor-
dinate their actions. In contrast to other platforms, there is no paid content, offering the same
conditions for all players. There is no skill matching mechanism based on the probability of
winning of the players. The platform has a “Join a Game” section, where all the players can see
all the open games (Section A in S1 File). A typical Conquer Club game environment has four
relevant elements: the current map with troops occupation in each region, the game status
showing current round and a summary of players information, a public game chat, and a log
of movements.
Researchers studying skill acquisition in chess rely on Elo, an estimator of skill used by
the World Chess Federations [46,47]. Elo can estimate a player’s skill, a hidden variable, by
observing only her games outcomes. The model assumes that, in each game, the players exhibit
performance, another hidden random variable related to the true skill value with some con-
stant noise. The player who exhibits the greater performance is the winner. Under these
assumptions, we can infer in each game who had the highest performance by observing the
game outcome (win/lose). Moreover, based on the previous skill estimate we can compute the
probability of an outcome, i.e. the probability that one player will have higher performance
than her opponent. The skill estimator is updated according to the direction and magnitude of
the surprise, i.e. the difference between the expected result (the prediction) and the observed
result (the outcome of a game). We rely on TrueSkill [48], an extension of the Elo ranking
system.
TrueSkill extends Elo through a Bayesian model. Firstly, TrueSkill uses a prior belief distri-
bution, instead of a scalar, to represent the skill estimates. Since the initial skill value is
unknown, the accepted procedure is to initialize all players with the same mean and a high var-
iance. This allows the system to make big changes to the skill estimate early, and small changes
after a series of consistent games have been played. As a result, TrueSkill can identify players’
skill through a few games. Secondly, TrueSkill adds a model of team performance, which
allows the system to deal with any team assignment. The team’s performance assumption is
only used to adopt the skill of individual players such that the team outcome can be best pre-
dicted based on the additive assumptions of the skills. Finally, TrueSkill uses a non-arbitrary
update function, the posterior of the Bayesian model that could be computed by performing a
marginalization over the factor graph [49] (See details at Methods section).
With our massive dataset, we can investigate the impact of team play strategies on individ-
ual skill acquisition that otherwise would not be possible to study.
Results
Law of practice
First, we study how players improve performance as they gain experience, i.e. the law of prac-
tice. We estimate the experience of each player by the number of games played. Skill is esti-
mated according to the TrueSkill method [48]. The skill difference between opponents
indicates with high precision the probability of winning (Fig A in S1 File). With two opponents
(teams or individuals), the probability of winning when the other has the same skill is 1/2 and
a difference of 4 tsp (TrueSkill points) increases the probability of winning to 2/3.
In our context, the learning curve is the skill progression as experience is acquired (i.e. the
number of games played). As mentioned, population learning curves should follow a power
law function [7],
Skill ¼Skill0Experienceað1Þ
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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where αis the learning rate characteristic of the population, and Skill
0
the population skill after
the first game.
To analyze the law of practice, we split players according to their total activity: (1) players
with at least 8 games and less than 16, (2) players with at least 16 games and less than 32, and
so on. Thus, we fit these parameters to each set of players in these subpopulation activity cate-
gories. In concordance to the law of practice, we observe a linear dependency in the log-log
learning curves in all the population segmentation (Fig 1).
Learning curves have a dependency on players who churn out, showing lower skill for sub-
populations with lower total activity. However, the learning rate (α) remains stable for
Fig 1. Law of practice. Log-log learning curve of the subpopulation of players with different total activity. Each learning curve shows the skill of
the first 2
n
games played of the subpopulation with at least 2
n
games played and less than 2
n+1
. Subplots show the parameterized values (i.e. α
and Skill
0
) of each learning curve following Eq 1.
https://doi.org/10.1371/journal.pone.0211014.g001
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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subpopulations with at least 32 games played (upper right inlet in Fig 1). The difference
between them causes little variation in long-term skill acquisition, providing less than 0.24 tsp
after 1000 games played. The initial subpopulation skill (Skill
0
) is also affected by churning out
(bottom left inlet in Fig 1). Nevertheless, all subpopulations with at least 64 games played, do
not have a significantly different initial skill (Wilcoxon rank-sum test at Table A in S1 File).
Therefore, all cohorts with at least 64 games played have almost equivalent learning curves.
They are what we call the “learning curve expected by experience”. This baseline learning can
be altered by many factors. For example, the commitment to finish the games is undoubtedly a
relevant factor in the process of skill acquisition. Indeed, players who always finish their games
have a higher learning curve than the rest of the population, around 0.5 tsp (Fig C in S1 File).
Social learning
Social learning is essential to pro-social animals. We hypothesize that the learning curve
expected by experience could be altered by different grouping behaviors. To study it, we ana-
lyze players’ behavior in team selection.
In the game platform, users can choose between playing individually or in teams. We define
players’ team-oriented behavior (TOB) as the number of team games played divided by the
total number of games played:
Team oriented behavior ¼Team games played
Games played ð2Þ
To evaluate the influence of TOB on learning curves we split the population into strong,
medium and weak TOB (i.e. 0.8 <TOB 1, 0.4 <TOB 0.6, and 0 <TOB 0.2, respec-
tively). Hereinafter, we excluded players with less than four team games played.
In the long-run, between 200 and 500 games of experience, the learning curves are ordered
according to their TOB level, exhibiting higher skill level for populations with higher TOB (Fig
2). The strong team-oriented players evince after 250 games played, a significantly higher final
skill compared to medium and weak TOB (Wilcoxon rank-sum test, p<1×10
4
). In this
interval strong and medium TOB population are distanced by about 1 tsp. A more team-ori-
ented behavior has, in the long-run, higher skill value even compared with players without
team games (i.e TOB = 0, Fig D in S1 File).
Faithfulness-boost effect
Players can choose between playing with the same teammate or selecting different players in
each game. We hypothesize that a loyal behavior may affect learning (increase or decrease the
rate of skill acquisition) when playing in teams. If we look at how many recurrent players each
player has, we find that most recurrent players are teammates instead of opponents. Thus, we
focus our analysis only on the loyalty of teammates as loyalty in opponents is not present in
our database. We define players’ loyalty as the proportion of times played with the most recur-
rent teammate divided by the number of team games played:
Loyalty ¼Maximum of games played with a partner
Team games played ð3Þ
To evaluate the influence of loyalty over learning, we examine players’ skill evolution in
strong TOB based on their loyalty value. We define a player as loyal when loyalty >0.5, and a
player as casual when loyalty 0.2.
If we compare the learning curves of loyal and casual players, we obtain a substantial sepa-
ration between them at the first games of experience. Loyal players show an increment in the
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
PLOS ONE | https://doi.org/10.1371/journal.pone.0211014 March 5, 2019 5 / 26
median skill of approximately 4 tsp over casual players (Fig 3). The skill distribution at each
point of the learning curve is significantly different until 386 games played (Wilcoxon rank-
sum test p<0.01). An analogous behavior between loyal and casual subclasses is found for
medium and weak TOB, less intense as they are less team-oriented (Fig E in S1 File).
To study the interaction between TOB and loyalty on skill acquisition, we fix the number of
games played to 100. By isolating this interaction (without the interference of experience) we
find that an increase in loyalty always implies an increase in skill, more prominent for higher
TOB values (Fig 4). Conversely, increasing TOB values shows a decrease in skill for low levels
Fig 2. Social learning. 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.
https://doi.org/10.1371/journal.pone.0211014.g002
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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of loyalty, and only implies an increase in skill for high levels of loyalty. The skill difference
from the minimum to maximum is greater than 4.5 tsp.
The interaction between loyalty and TOB can be summarized by Loyalty TOB =faithful-
ness defined as,
Faithfulness ¼Maximum of games played with a partner
Games Played ð4Þ
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.
https://doi.org/10.1371/journal.pone.0211014.g003
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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which is simply the proportion of times played with the most repeating teammate over all the
games played.
To measure the influence over skill acquisition of loyalty, TOB and faithfulness, we build a
linear model solved by least squares. The correlation between variable loyalty and TOB is low
(0.11), and the Variance Inflation Factor is nil (1.01), suggesting no evidence of collinearity.
skillib1loyaltyiþb2TOBiþb3faithfulnessið5Þ
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.
https://doi.org/10.1371/journal.pone.0211014.g004
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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At 100 games played, loyalty has a significant positive slope, TOB has a significant nega-
tive one, while faithfulness has a significant steep positive slope (Table 1). Faithfulness is
strong enough to reverse the negative TOB contribution over skill to a positive one when
loyalty >0.27. The faithfulness-boost effect is around 3.7 tsp, which generates a skill differ-
ence between players with the same experience extremely relevant in terms of probability of
winning.
We repeat this procedure for players with the same experience, starting from 100 to 1300
games, by 100 games played (Fig F in S1 File). The faithfulness-boost effect remains significant
until 400 games played, always above 3 tsp. Starting at 500 played games, faithfulness ceases to
be significant but TOB slope reverses its contribution to a significantly positive one. Loyalty
has a significant positive effect at any level of experience (100 games played). Although the
interaction effect of the linear model (faithfulness) is no longer significant from 500 games of
experience onwards, the point of maximum skill is always achieved by maximizing both loyalty
and team-oriented behavior. The magnitude of this contribution is always relevant in terms of
winning probability, with more than 2 tsp.
In order to integrate all the partial observations made up to here, we perform one overall
model fitted to all data including experience, loyalty, TOB as the predictors, and individual
player as a random effect (Table 2). We choose a linear mixed model because the relationship
between the experience and skill is linear on a log-log scale (Eq 1). The dependent variable,
players’ skill, was transformed to a logarithmic scale,
log10ðskillÞ ¼ log10ðexperienceÞ þ loyalty þTOB þindividual player þε
Table 1. Influence over skill acquisition of loyalty, TOB and faithfulness (linear model). We report the estimated slope value, their standard deviation and their signifi-
cance difference with respect to a zero slope. All players have 100 games of experience.
Estimate Std. Error t value Pr(>|t|)
Intercept 28.5707 0.0405 705.59 p<2e
16
Loyalty 0.7594 0.0972 7.82 p<2e
14
Team-oriented -1.0042 0.1088 -9.23 p<2e
16
Faithfulness 3.7077 0.2611 14.20 p<2e
16
https://doi.org/10.1371/journal.pone.0211014.t001
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 = 10
1.415
, exp = 10
1.415+ 0.016
10
1.415
). Method: REML converged.
Number of groups: 65335. Max Group size: 491. Mean group size: 99.5.
Estimate Norm.Est. t value [0.005 0.995]
Intercept 1.415 26.00 5966.264 1.414 1.415
exp 0.016 0.98 225.628 0.016 0.017
loyal -0.007 -0.42 -28.846 -0.008 -0.006
tob -0.044 -2.51 -91.773 -0.045 -0.043
(faithful) loyal:tob 0.090 5.99 91.801 0.088 0.093
exp:tob 0.016 0.98 70.829 0.015 0.016
exp:loyal 0.004 0.24 29.678 0.003 0.004
exp:loyal:tob -0.026 -1.51 -56.129 -0.027 -0.025
Group Var 0.002
https://doi.org/10.1371/journal.pone.0211014.t002
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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The dataset used contains the values of all the players for each game between 10 and
500 games played of individual experience. The collinearity between variables is nil in terms
of Variance Inflation Factor computed from a linear model solved by least squares (i.e. all
VIF less than 1.5). Therefore, we can fit the linear model without incurring in artificial
results.
This overall model confirms the observations already introduced. Experience is the main
predictor in terms of their level of significance, has the most significant slope. Initially, loyalty
only has a positive effect in contexts of team-oriented behavior (loyal:tob). Be loyal without a
team-oriented behavior has a very marginal effect (loyal). Without a stable teammate, playing
team games results in a bad plan (tob). However, as more experience is gained, while the
boost-effect provided by faithfulness interaction loses strength (exp:loyal:tob), the loyalty (exp:
loyal) and team-oriented behavior effect (exp:tob) reverses their contribution to a positive one.
Due to this dynamic, the point of maximum skill is always reached with both maximum team-
oriented behavior and loyalty (i.e. maximum faithfulness).
Discussion
Traditionally, learning is modeled as a function of experience. In this article, we focus on how
the learning curve expected from practice could be altered by different grouping strategies. We
exploit the virtually infinite repository of human behavior available on the Internet to study a
relevant topic in anthropological science: how grouping strategies may affect skill acquisition.
Our method is based on massive data which enabled conducting a longitudinal study with
very high precision to detect subtle changes.
We analyze learning in the context of competing players, such as chess or RISK. In this
types of games, learning is measured in terms of the probability that a player beats others.
Unlike tasks in which it can be determined the absolute amount of errors that an individual
makes when solving it, in competitive games the probability of winning is a relative property
that depends on the learning level of opponents. Learning curves arising from tasks in which
the skill is measured in relative terms are more volatile than those measured in absolute terms.
Thus, individual learning curves of competing players are sometimes hard to fit [9,10].
Regardless, the individual learning curves are more irregular than averaged learning curves
and the variation among them must be explained. We hypothesized that social learning would
expose a second-order effect in skill acquisition. According to social learning theories, players
have two options for learning: i) discover for themselves the keys to better play; or ii) imitate
the strategy of others available in her network. We rely on Conquer Club, an online game
that—in contrast to chess—may also be played in teams. In Conquer Club both opponents and
teammates are observable and, in consequence, they could be seen as models to imitate. How-
ever, we focus our analysis only on the loyalty of teammates as loyalty in opponents is not pres-
ent in our database.
For instance, a simple social learning strategy consists of copying the majority of other
available models, which is known as frequency-based strategy. Another social learning strategy
is copying the most successful available model, named as the payoff-based strategy. As far as we
know, no social learning strategy has been proposed which takes into account different group-
ing strategies. We found that grouping strategies affect significantly how the skill is acquired.
As in other species, it has been studied in ancient anthropology that homo-sapiens success
relies on group formation [13,50]. We explored if this behavior affects skill acquisition using a
controlled environment, i.e. Conquer Club. The decision on playing individually or in teams
(i.e. the team-oriented behavior) is associated with a long-run skill improvement. We found
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
PLOS ONE | https://doi.org/10.1371/journal.pone.0211014 March 5, 2019 10 / 26
that tendency of playing in groups (the number of played team games divided by the total
number of played games) improves significantly the skill level achieved.
Mathematical models show that relations between groups by individual migrants can be a
risk factor for social learning when environments in which groups live differs [51]. We studied
a reductionist version of migration among groups by analyzing how players repeat teammates,
that leads to a intra-group stability (i.e. loyalty). Following environment change risk theory, we
claim that there are no environmental modifications in Conquer Club and therefore inter-
group mobility is not a source for the spread of maladaptive ideas. On the contrary, migration
would imply the access to different groups and thus learn from different players an increase in
skills by learning from a larger variety of teammates. In this sense, we tested the hypothesis
that migration is beneficial for improving skill acquisition. However, we found the opposite.
First, we check the law of practice in our dataset. We found the empirical shape of what we
call the “learning curve expected by experience”. Taking it as a baseline, we quantify to what
extent different grouping behaviors alter the skill acquisition expected by experience. We
found that a team-oriented behavior (the proportion of the played team games and the total
played games) is related to a significant improvement of skill level achieved in the long-run. A
tendency of an intra-group stability (loyalty, i.e. the number of times played with the recurrent
teammate divided by the team games played) is associated with a rapid skill improvement in
the short run. The combination of these two features contains a positive effect that may be
exploited by learners. This faithfulness-boost effect provides a skill boost that would be
acquired, through experience, only after thousands of games of practice.
We claim that the current skill of the potential partner may be ignored. There are no side
effects derived from the skill heterogeneity between teammates. The winning probability of a
team is independent of the difference between teammates (Fig G in S1 File). It is also impor-
tant to point out that being part of a team with a low probability of winning does not mean los-
ing the skill. Partnering with a lower-skill teammate will effectively entail a decrease in the
probability of winning but not necessarily imply a decrease in skill. If collaboration is strong,
both players will benefit from skill acquisition.
The evidence leaves important open questions that may have practical implications for
planning training strategies. Our hypothesis suggests that sociability is the underlying learning
factor of different grouping tactics. However, more work is needed to be able to formulate reli-
able explanations and recommendations. Experimental research is necessary to determine
with certainty the causes of those observed effects. We believe that the positive effect of part-
nership emerges from social commitment. The socio-cognitive derivatives of loyalty such as
trust, constancy, and fluid communication outweighs the costs of coordination and the reduc-
tion in the range of relationships that can be established.
The grouping strategies identified cannot be classified either into those social learning strat-
egies that specify under which circumstances copy others, nor those that describe from whom
individuals learn. However, by definition, they are social learning strategies due to the evi-
dence of long-term changes in behavior caused by stimuli derived from observation and inter-
action with other individuals.
Materials and methods
All games were downloaded from Conquer Club, a free service that offers to play RISK like
games. The website allows any person, and not just registered participants, to explore the
matches and browse their related data. Registered users are identified by their nicknames and,
to be accepted as users, they have to agree with having their games stored in a publicly accessi-
ble server. Moreover, during the downloading process, each player is identified by an internal
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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id number, anonymizing the data. In consequence, there is no need for individual consent due
to this double layer of anonymity and the open nature of the website. We contacted Conquer
Club’ owners to get authorization for performing this process, thus complying with this site’
terms of use.
The application consists of a Python script that connects to the Conquer Club server. The
data between 2006/01/03 and 2009/07/12 is stored in a PostgreSQL database. There are
near 4.4 million games played by almost 270 thousand different users.
To compute the skill, we use the TrueSkill 0.4.4 package for Python. All players
start with a skill mean μ= 25 and a skill standard deviation of σ= 8.33. The draw probability
value was set to 0 since there is no chance of drawing in Conquer Club.
The game
Gameplay. At the beginning of a game, the regions of the selected map are randomly dis-
tributed among the players and populated with troops. Each turn consists of i) deploy new
troops, ii) assault neighboring opponent’s regions, and iii) reinforce the regions. The game
environment has four relevant elements: the current board, a panel with the game status, a
public chat and a log of movements (Fig 5).
Fig 5. Scheme of Conquer Club game. 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.
https://doi.org/10.1371/journal.pone.0211014.g005
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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In this example, a double team game is played between two teams. The nodes of the graph
represent the regions, the color indicates the player’s owner, the numbers represent the num-
ber of troops, and the shapes indicate to which zone it belongs. Alongside there is a panel with
the round number, the active player, and the time remaining time to play the current round,
and a summary of total troops and total controlled regions for each player. The color beside
the nickname identifies each players’ regions in the map. A public chat service is available
within each game. The Log records all movements of players, especially useful when players
interact with the game sporadically.
At the beginning of every turn, the players earn new troops. The troop amount results from
the number of occupied regions and the bonus of the controlled zone and eventually by the
exchange of spoils (Section A in S1 File). We can see in the first line of the log in Fig 5d that
player creceived troops for holding Continent 4. These troops may be deployed at her occu-
pied regions. For example, player cdeploy all their troops at region M.
Once the deploy is finished the assault stage begins. A player can assault any opponent’s
region as long as both are adjacent and the assaulting region has a minimum of two troops.
The game engine rolls a die for each assaulting troop, except for one troop that needs to stay at
the region, up to a maximum of three troops. Then, the system rolls a die for each defending
troop, up to a maximum of two troops. The obtained values of each side are ordered increas-
ingly and then compared one by one. If the assaulting dice is higher, then the defending region
loses a troop. If the defending dice is higher or equal, then the assaulting region loses a troop.
If the attacker destroys all the defending troops, some of the remaining troops have to be
moved to occupy the newly conquered region. In our example, player cassaults region Nfrom
region Mand conquers it from player a. Then, this player uses the recently moved troops to
conquer another region.
When the player finishes the assaults, some troops can be used to reinforce the defending
position. The player may move some (but not all) the troops from one of the owned regions to
any other occupied and connected region. The reinforcements game configuration option
determines how many of these reinforcement plays are allowed. In our example, player crein-
forces region Pby moving two troops from region M. Finally, player cfinishes the turn and
player bstarts with her round.
Matchmaking. The platform has a “Join a Game” section, where all the players can see all
the open games. When a player creates a game, she chooses: a) gameplay options, b) game
type, free-for-all or team game, c) the number of participants, and d) the join method, public,
public with reserved slots, and private. Public games are those to which anyone can join. The
public games with reserved slots have slots assigned to particular players, and the rest are open
to general players. Private games can be accessed by any player who has access to the game’s
password.
In this platform, there is no skill matching mechanism based on the probability of winning of
the players. There are an internal ranking and a point system that players can use as a reference
to estimate the skill of others. The point system is updated as D¼min Loser’s score
Winner’s score 20 ;100
 .
However, they are not precise indicators of players’ skill and the probability of winning between
opponents. The internal ranking is the conjunction between the number of games played and
the points reached.
When a player selects a game, she can see the names of those who are already joined. An
icon and a star appear next to the names. The icons represent the players’ ranking. The stars
summarize the opinion about the player that some of her previous opponents reported. At the
end of a game, players can report, on a scale of 1 to 5, the behavior of the rest of the players
regarding Fair Play, Gameplay, and Attitude.
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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Skill estimator
TrueSkill was inspired by Elo method, developed by Arpad Elo in 1959 and adopted in 1970 by
the World Chess Federation (FIDE).
Elo. The main idea of the Elo system is to model the probability of an outcome game
based on players’ skill s
i
,s
j
. The model assumes that, in each game, the players exhibit a perfor-
mance, a hidden random variable normally distributed, p
i
*N(s
i
,β
2
), centered at their
unknown true skill value with some constant noise. It is assumed that the player who exhibits
the greater performance is the winner. Under these assumptions, we can infer in each game
who had the highest performance by observing the game outcome (win/lose). Then, the proba-
bility that player iwins is P(p
i
>p
j
|s
i
,s
j
) = P(p
i
p
j
>0 | s
i
,s
j
).
The “difference of performances” isobars d
ij
=p
i
p
j
are all lines parallel to the diagonal
p
i
=p
j
at Fig 6. Then, the probability of a certain difference of performances d
ij
is computed as,
Pðdijjsi;sjÞ ¼ ZZ Iðdij ¼pipjÞNðpi;si;b2ÞNðpj;sj;b2Þdpidpjð6Þ
It can be shown, based on Gaussians’ properties, that the difference of performance d
ij
is
also normally distributed, centered at the skill difference point with double variance (Fig 7).
Pðdijjsi;sjÞ ¼ Nðdij ;sisj;2b2Þ ð7Þ
This reduces the problem of computing the probability of the game outcome to a single-
dimension problem related to the performance difference.
Let the result of a game rij ¼Iðdij >0Þ. The probability of winning, r
ij
= 1, can be computed
as:
Pðrij ¼1jsi;sjÞ ¼ Pðdij >0jsi;sjÞ ¼ 1F0 ðsisjÞ
ffiffi
2
pb
 Fsisj
ffiffi
2
pb
  ð8Þ
where Fis the cumulative distribution function of the standard normal distribution, N(0, 1).
The highlighted equality () is derived by symmetry of the Normal density function. Then, the
probability of the result can be written as:
Pðrijjsi;sjÞ ¼ ðrij ÞPðrij ¼1jsi;sjÞ þ ð1rijÞPðrij ¼0jsi;sjÞ ð9Þ
Now we can calculate the probability of the result given the skill estimates (s
i
,s
j
). Then, we
have a reference to update them. Observing very unlikely results would indicate that the skills
estimated so far are not entirely correct and should be updated to a greater extent than if the
observed results were as expected.
D¼yij
|{z}
Direction
ðOutcomeÞ
ð1Pðrijjsi;sjÞÞ
|fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}
Magnitud
ðOutcome SurpriseÞ
ð10Þ
where the direction y
ij
= 2r
ij
1.
Finally the update in the Elo system is given by
snew
i¼sold
iþKDð11Þ
where K, an arbitrary parameter, is the maximum number of points that are disputed in each
game.
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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Even, there is a criterion to define it, this is one disadvantage of the Elo rating system. A sec-
ond problem is that the estimated skill must be considered provisional until the player reaches
a number, also arbitrary, of games. A third problem is that with Elo we cannot estimate the
skill of players when playing in teams. The Bayesian model TrueSkill solves all these problems.
TrueSkill. The TrueSkill method [48] was introduced in 2006 by Ralf Herbrich and has
two patents [52,53]. TrueSkill shares the dependency model of the Elo rating system between
skill, performance, and probability of winning. It extends it through a Bayesian model that
incorporates a belief distribution of skills (prior), a model of team performance and a non-
arbitrary update function (the posterior distribution).
Fig 6. Joint probability of the performance of two players i,junder the assumption of s
i
>s
j
and independence. All lines parallel to the
diagonal p
i
=p
j
represent “difference of performances” isobars d
ij
=p
i
p
j
.
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Skill. One of the novelties of TrueSkill is the notion of the uncertainty of the skill estima-
tion. The skill estimate s
i
, previously represented by a scalar, is now represented as a prior dis-
tribution of beliefs with normal density function.
siNðmi;s2
iÞ ð12Þ
where μand σinitially acquire arbitrary values.
This is not an issue. What matters about the average is not its absolute value but the differ-
ence with other players. On the other hand, the standard deviation should be large enough to
Fig 7. The probability of the outcome of a game under the assumptions of the Elo rating system with s
i
>s
j
.The area under the curve in the
positive interval (d
ij
>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.
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represent the uncertainty that we actually have with respect to the average. In general, μ= 25
and s¼25
3are used as initial values.
Performance. As in the Elo system, it is assumed that the final outcome of the game
depends on the p
i
performance of the players,
piNðsi;b2Þ ð13Þ
Now the probability of a given performance p
i
is defined as,
Pðpijmi;siÞ ¼ ZNðpi;si;b2ÞNðsi;mi;s2
iÞdsið14Þ
Then, we can compute the probability of a given performance, p
i
, by integrating the area
under the solid line in Fig 8. We rewrite the integral 14 using the symmetry property, N(x;μ,
σ
2
) = N(μ;x,σ
2
).
Pðpijmi;siÞ ¼ ZNðsi;pi;b2ÞNðsi;mi;s2
iÞdsið15Þ
It can be shown (S2 File) that the product of Gaussians is also normally distributed,
Pðpijmi;siÞ ¼ ZNðpi;mi;b2þs2
iÞ
|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}
Scalar independent of si
Nðsi;m;s2
Þdsi¼Nðpi;mi;b2þs2
iÞ ð16Þ
Teams. The second novelty of TrueSkill enables to update the players’ skill when they play
team games. TrueSkill model states that one team beats another when their team’s perfor-
mance is greater than the opponent team’s performance. With Athe partition of players (the
team assignment), the performance of a team is defined as the sum of the performances of its
members,
te¼X
j2Ae
pjð17Þ
Then, the probability of a given team’s performance is defined as
PðtejAeÞ ¼ ZZIðte¼X
j2Ae
pjÞY
i2Ae
Nðpi;mi;b2þs2Þ
!d~
pð18Þ
The team’s performance assumption is only used to adopt the skill of individual players
such that the team outcome can be best predicted based on the additive assumptions of the
skills. The empirical probability distribution of individual and team games are exactly the
same based on a Kolmogorov-Smirnov test, showing that the skill estimated by simple addition
preserves the probability of winning based on this measure of team skill (Fig A in S1 File).
Mathematically, a team’s performance with two players we can see graphically in Fig 9. To
compute the probability of a given team’s performance cwe must integrate the area under the
corresponding isobar, t
e
=c(See Fig 9).
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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It can be shown in a team with 2 members (S2 File),
PðtejAe¼ fi;j ¼ ZNðpi;m;s2
ÞNðte;miþmj;2b2þs2
iþs2
jÞ
zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{
Scalar independent of pi
dpi
¼Nðte;miþmj;2b2þs2
iþs2
jÞ
ð19Þ
Fig 8. Performance distributions, N(p
i
;s
i
,β
2
) weighted by the probability of the skill belief distribution Nðsi;μi;σ2
iÞ.The area under the
solid line must be integrated to compute a certain probability p
i
.
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Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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It can be shown by induction (S2 File) that in a team with nmembers the probability of a
given team’s performance is:
PðtejAeÞ ¼ N t ;X
i2Ae
mi;X
i2Ae
b2þs2
i
! ð20Þ
Fig 9. Joint probability of the performance of two teammates i,j.Lines parallel to the diagonal t
e
=crepresent team performance isobars.
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Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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Difference. The difference teams’ performances are what determines the outcome of the
game.
dab ¼tatbð21Þ
In the same way, as in the Fig 6, the difference of performance isobars are the lines parallel
to the diagonal of zero difference. To compute the probability of a given difference of perfor-
mance d
ab
is:
PðdabjAa;AbÞ ¼ ZZ Iðdab ¼tatbÞ  Nðta;X
i2Aa
mi;X
i2Aa
b2þs2
iÞ
Nðtb;X
i2Ab
mi;X
i2Ab
b2þs2
iÞdtadtb
ð22Þ
It can be shown (S2 File) that them probability of a given difference of performance d
ab
is:
PðdabjAa;AbÞ ¼ Ndab ;X
i2Aa
miX
i2Ab
mi
|fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}
Expected difference ðdÞ
;X
i2Aa[Ab
b2þs2
i
|fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl}
Total variance ðWÞ
¼Nðdab ;d;WÞð23Þ
Result. A win of a team aover another team bis modeled as:
rab ¼dab >0ð24Þ
Then, the probability of victory of a team over another is computed as:
Pðrab ¼TruejAa;AbÞ ¼ Pðdab >0jAa;AbÞ ¼ Fd
ffiffiffiffiffi
2W
p
  ð25Þ
The observed outcome of a game it is modeled with an ordered vector of teams, o, such that
to1<<tojAj.
Posterior. In summary, the TrueSkill model can be represented by a graphical network
(Fig 10).
From Bayes rule, we obtain the posterior distribution,
Pðsjo;AÞ ¼ Pðojs;AÞPðsÞ
PðojAÞð26Þ
The exact posterior could be computed by performing the sum-product algorithm [49]
over the factor graph (Fig 11).
Fig 10. Bayes network of TrueSkill method.
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Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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Fig 11. Bayes factor network of TrueSkill method.
https://doi.org/10.1371/journal.pone.0211014.g011
Fig 12. TrueSkill update procedure for the winning case, where δis the expected difference between teams.
https://doi.org/10.1371/journal.pone.0211014.g012
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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With two teams, the exact posterior update function is (See all the details S2 File),
Pðsijo;AÞ /
Nðsi;mi;s2
iÞFð0 ; dðsiÞ;Ws2
iÞWinning case
Nðsi;mi;s2
iÞð1Fð0 ; dðsiÞ;Ws2
iÞÞ Losing case
(ð27Þ
where δ(s
i
) = δμ
i
+s
i
, the expected difference between teams replacing the estimated skill (μ)
by their true skill s
i
(Figs 12 and 13).
Finally, TrueSkill takes as the posterior of the model the Gaussian that minimizes the KL
divergence with the exact posterior.
Fig 13. TrueSkill update procedure for losing case, where δis the expected difference between teams.
https://doi.org/10.1371/journal.pone.0211014.g013
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
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Statistical information
We performed a Wilcoxon rank-sum test at Figs 1,2,3, and at Tables A and B in S1 File. A
Wilcoxon confident interval was performed at Figs 2and 3. We performed a multiple linear
regression at Table 1, and at Fig F in S1 File. We performed a general linear mixed model at
Table 2. We performed a two sided Kolmogorov-Smirnov tests at Figs B and G in S1 File.
Tests were performed using R version 3.0.2 stats package, and Python version 3.6
statsmodels package.
Supporting information
S1 File. Details about the gameplay: Rules, maps, limits and mechanics. Fig A: The proba-
bility of winning as a function of the skill difference between: (a) Case of two individual oppo-
nents and two team opponents. (c) Case of three opponents. Fig B: Histogram of skill. Fig C:
Learning curve of committed population. Fig D: Learning curve of population of players with-
out team games played. Fig E: Learning curve of loyal and casual subclasses for medium (a)
and weak (b) team-oriented behavior. Fig F: Influence of loyalty, TOB, and the faithfulness
interaction over skill acquisition. Fig G: Team probability of winning at function of skill differ-
ence between teams and between teammates. Table A: Significance difference between distri-
butions of skill after the first game played at Fig 1. Table B: Significance difference between
strong, medium and weak team-oriented population.
(PDF)
S2 File. TrueSkill, Technical Report. Analytical computation of the posterior distribution.
This file includes details about update rules and the derivation of used expressions.
(PDF)
Acknowledgments
This work is supported by Universidad de Buenos Aires (UBACyT 20020170100765BA),
CONICET (PIO13320150100020CO), STICAmSud (CC-SEM), and ANPCyT (PICT-2015-
2761 and PICT-2015-0370).
Author Contributions
Conceptualization: Diego Ferna
´ndez Slezak, Esteban Mocskos.
Data curation: Gustavo Landfried.
Formal analysis: Gustavo Landfried, Esteban Mocskos.
Funding acquisition: Esteban Mocskos.
Investigation: Gustavo Landfried, Esteban Mocskos.
Methodology: Diego Ferna
´ndez Slezak, Esteban Mocskos.
Project administration: Esteban Mocskos.
Resources: Esteban Mocskos.
Software: Gustavo Landfried.
Supervision: Diego Ferna
´ndez Slezak, Esteban Mocskos.
Validation: Diego Ferna
´ndez Slezak, Esteban Mocskos.
Visualization: Gustavo Landfried.
Faithfulness-boost effect: Loyal teammate selection correlates with skill acquisition improvement
PLOS ONE | https://doi.org/10.1371/journal.pone.0211014 March 5, 2019 23 / 26
Writing – original draft: Diego Ferna
´ndez Slezak, Esteban Mocskos.
Writing – review & editing: Diego Ferna
´ndez Slezak, Esteban Mocskos.
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... At this point, an objection may be raised: why study video game popularity? To respond to this objection, it should be noted that the socioeconomic role of digital games has been growing, which is reflected in the increased scientific interest from diverse research areas such as education/training [6][7][8][9][10][11], computer/network science [12][13][14][15][16], psychology [17][18][19], and human health/neurology [20][21][22][23]. Of particular interest for the present work, it is worth mentioning that studies are investigating the popularity of video game categories [24,25] and which factors are responsible for keeping players invested in this hobby, the main ones being online play with friends (social factor), intrinsic fun of the game (immersive factor), and achievements (individual factor) [26][27][28][29]. ...
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... The Whole-History Rating model focuses on the dynamics of strength parameters over time, accounting for improvements in athletes' ability values as they gain experience and regressions with age [21,22]. The TrueSkill model is adopted in both solo and team competitions and uses the Gaussian distribution as an a priori assumption of strength and performance [23,24]. With the introduction of the TrueSkill model, the concept of athlete ability value assessment was introduced to predict the scoring of both sides of the encounter through the learning of player ability values. ...
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In the modern society, competitive sports have an essential place in the world. Sports can reflect not only the comprehensive strength of a country to some extent but also the cohesion of a nation. Therefore, as China’s overall strength and international influence continue to rise, sports are being given more and more importance. At the same time, research and exploration on the prediction of match results have also become a hot topic. In the large sport tournaments, there are many factors that influence the outcome of a match. In actual matches, the outcome is not only determined by the strength of the participants, but also by a number of unexpected factors. The randomness brought about by these unexpected factors makes it difficult to predict the outcome of a sporting event. In recent years, many researchers have sought to enhance the understanding of complex objects with the help of prediction of sporting outcomes. One of the more traditional methods of prediction is the probabilistic statistical method. However, the traditional prediction methods have low accuracy and do not provide satisfactory stability in the prediction results. In fact, since most sporting matches are played against each other, the ability values of the players often play a key role in the match. They can determine the winner of a match, but unexpected factors such as player play, playing time, and injury situations can also have an impact on the strength of a playing team, so these factors should not be ignored. This study establishes a reasonable causal relationship between the offensive and defensive situations in the game and the players’ ability values and builds a complex Bayesian network model. A match prediction model is then built using the latent variables present during the match so that the various ability values of the match teams can be assessed.
... Exploring the space of possible social styles of play may be an exception to this pattern of a null effect on learning rate, as demonstrated by two studies that used different operationalizations of in-game social behavior. In one study (Landfried et al., 2019), more consistent teammate selection (low exploration) was associated with faster learning, and in the other , higher assist rate (a measure of cooperative play within a selected team, and so higher exploration in social space) was associated with slower learning. ...
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... low self-efficacy agents) was half and agents in teams with 'All influencers', social learning could be seen high throughout the project, while minimum when all agents have low selfefficacy when they start working ( Figure 5-6). Social learning curves are similar to the ones obtained in other domains of study such as online gaming (Landfried et al., 2019) ...
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Collaborative teams are getting more and more popular. There is a current need to understand how the complex and dynamic system formed by collaborative teams behave when system parameters are changed to see their impact on project outcomes. Research in the past has focused on studying the single elements of the collaborative design like design task, design team structure, design tools and design process (idea generation and idea selection). Understanding the complete system of the design team collaboration is challenging to the researchers as it increases complexity. Therefore, the purpose of this research is to increase the understanding of a collaborative system composed of teams, tasks and its collaboration environment through an agent-based model called MILANO (Model of Influence, Learning, and Norms in Organizations). This computational model is implemented using the Python programming language. MILANO is developed to mimic design team collaboration of the real world, hence it serves as a platform to study and simulate different scenarios of team dynamics that are challenging to control in a laboratory setting. The model is composed of agents that are analogous to humans in design teams who work on a design task by collaboratively generating and selecting solutions. Similar to the real world, the selected solutions are proposed to the controller agent (equivalent to a leader or manager to a problem-solving team), who provides feedback to the team. The research is broadly composed of three parts that fulfil the main purpose of the study. The first one is related to the common scenario where certain individuals who have high social influence (referred to as influencers) than others in the team, affect individual thinking during idea generation and selection. This is further investigated by varying the nature of the design task and the size of the team. The second part is related to the team compositions of experience and novices and their impact on the design outcome when changing the nature of the task. The last bit of the work is related to studying the impact of the collaboration environment (i.e., virtual vs face-to-face team collaboration) on the design outcome for various test cases (like teams with an experienced agent, half of the team with high self-efficacy, all agents with same self-efficacy and all agents with same self-efficacy working on a complex design task). Though most of the model formation is based on the past literature and theories, it also has some assumptions and has parts that needed logical validation. These assumptions were validated through empirical studies conducted in the real world. The empirical results also provide insights into the relationship between model parameters and verified the logic behind its foundation. Although agent-based modelling is an effective approach for simulating collaborative design teams, the validation of the entire model is difficult, especially if there are plenty of parameters to control in a real-world setting. Therefore, continuously validating and verifying the model rationale by means of empirical studies, adds to the strength of the model and its results. The extracted simulation results of the design task outcome were measured in terms of quality, exploration and other team performance parameters like the contribution of team agents. Broadly speaking, the model simulation results showed how varying the parameters of the collaboration design affects the outcomes of a design project. For example, different influencer- team composition has a significant difference in the generated solution quality of their team members. Moreover, having an experienced agent in a team of all novices can increase the quality of the solutions while reducing the variety. Likewise, having half of the team members as more influential, could results in a better outcome when the team collaboration is virtual. From the results, it is clear that a type of team that is effective in one situation might not perform well in other situations. Besides, studying the social, cognitive and environmental factors that were unaccounted for in the past literature, this research introduces a novel way to stimulate learning in agents and metrics for measuring design outcomes related to artificial design agents’ performance. Some of the research findings conform to the literature, hence suggesting that MILANO could be used to study collaboration in design teams and could provide meaningful insights into team formation and management. These findings could be useful in determining appropriate team and task management strategies to obtain near-optimal project outcomes in organizations during the early design phase. In academia, the model that artificially simulates human collaboration could be used as a faster approach to gain insights into different design team collaboration scenarios
... The amount of social learning in the teams where the ratio of influencers to non-influencers (i.e., low self-efficacy agents) was half and agents in teams with all influencers, social learning could be seen high throughout the project, while minimum when all agents have low self-efficacy when they start working (Fig. 18). Social learning curves are similar to the ones obtained in other domains of study such as online gaming (Landfried et al., 2019) or during diffusion of innovation (O'Brien and Bentley, 2011). ...
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... A factor that influences stronger gains in skill acquisition is social play. Users who loyally play with the same teammates improve faster and reach a higher level of perfor- mance than players who endeavour on skill acquisition quest alone (Landfried, Fernández Slezak, & Mocskos, 2019). This is in contrast to players who support, follow and assist their teammates, as they are characterized by much shallower learning curves, even though they have higher initial performance . ...
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... In addition, because the conventional separation only took minutes to complete, skill acquisition, if any, was negligible because the testers already were proficient from their much longer training sessions (lasting several hours, or even days). The rate of improvement in skill drastically decreases once testers become skilled according to well documented skill acquisition curves (Landfried et al. 2019). ...
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