Motivation

The origins of crowd sourcing can be traced back to 1907 when Sir Francis Galton elicited the wisdom of a crowd to estimate the weight of an ox. The currently used term crowdsourcing is much younger and was used for the first time by Howe (2006) in a now widely quoted article in Wired Magazine, and has in the meantime been complemented by the synonym swarm intelligence (the former is predominantly used by economists, the latter by computer scientists). The conviction underlying both, the turn of the century experiment and the contemporary use of the term, is that crowds can make better judgements or decisions than an individual can. A number of recent field and laboratory studies suggest that this may indeed be true (e.g., Adams & Ferreira, 2010; Charness, Karni, & Levin, 2010; Charness & Sutter, 2012).

A recent online community that uses the wisdom of a crowd (or the intelligence of a swarm, respectively) is the platform www.transfermarkt.de. In 2007, the website (1) registered 4.3 million individual users and over 70 million visits, making it a very attractive football platform for marketers. The self-reported key user group consists of young males with rather high income and diverse, yet football-related product interests. The average user is a football aficionado and the website emphasizes its unique user intensity and individual retention time. Since members are not paid for their time-consuming activity, they must derive utility from the joy of discussing their opinion with other football fans, thus investing in and enjoying the returns to "consumption capital" in the sense of Adler (1985). A key aspect of the website is the estimation of player market values. First, users individually evaluate and judge the market values of soccer players. In a second step, this information is used by experienced members called "experts" who then, based on the market values suggested by hundreds or even thousands of individuals, derive an "objective" value for each of these players. In most team sports leagues in Europe, player salaries are not disclosed, implying that "fair" estimates of market values enable researchers to better analyze various labor market phenomena, such as pay determination, contract and career length and transfer probabilities. This, however, requires that these market value estimates are reliable. In a first step, we therefore investigate the precision of the market value estimations provided by the user group on transfermarkt.de. We then try to answer the question of how crowd wisdom--in this case an online platform--emerges, develops and matures. Once these two questions can be answered, it should also be possible to evaluate the importance of crowd wisdom for the analysis of salary determination in professional team sports leagues.

In this paper, we use data from 10 consecutive seasons of Major League Soccer (MLS, 2006-2015) to answer our research questions. MLS individual salary information is published every year by the players union and, therefore, presents one of the few opportunities to work with reliable and first-hand wage information. (2) Moreover, the league is very young. It was founded in 1993 and the first season was played in 1996 with 10 teams. Moreover, MLS is a single-entity league, that is it is organized centrally. The commissioner (since 1999, Don Garber) has the full power, among others, to implement rules, determine which clubs are admitted to MLS, and which investors can buy themselves into a particular team. Thus, all teams are owned by the league and investors can only buy shares of a particular team. Moreover, MLS is a closed league with no promotion and relegation system. Another consequence of the central organization is that the league formally contracts all players and pays the player salaries and bonuses. To extenuate the (bargaining) power of this central organization, a players union was founded in 2003 with the purpose to "ensure [...] protection of the rights of all MLS players, while also promoting their best interests" (MLSPA, 2016). The MLS Players Association negotiates a collective bargaining agreement (CBA) every five years that determines each team's salary budget, minimum and maximum salaries, health insurance benefits, and other relevant factors. Finally, possibly to retain or even improve competitive balance among clubs, each team is limited in their player selection by two major regulations: (a) a maximum of 160 international roster spots that are divided equally among the current 20 clubs (these spots can, however, be traded between clubs) and (b) a salary cap. In the 2015 season, the cap was set at $3.490 million for the senior roster (spots 1-20). In 2007, the league softened the strict cap, implementing a new rule that is often referred to as the "Beckham Rule," because David Beckham was among the first players to benefit from it. Arguably, the rule was institutionalized just to bring him into the league. Officially it is called the Designated Player Rule, which allows the teams to bring in a certain number of "superstar" players--currently a maximum of three--and pay them outside of the CBA's maximum pay regulations and with limited effect on the salary cap.

Due to its unique characteristics, MLS has recently attracted the interest of an increasing number of sports economists (see Coates et al., 2016; Jewell, 2017; Kuethe & Motamed, 2010; Sonntag & Sommers, 2014; Twomey & Monks, 2011). We contribute to this literature by investigating the impact of crowd wisdom on the emergence and the accuracy of player valuations on transfermarkt.de, as well as the overall relevance of crowd wisdom for the economic analysis of professional team sports leagues.

Related literature

Crowd Wisdom and Group Decision-Making

In his famous crowd wisdom experiment mentioned above, Sir Francis Galton asked 787 visitors of a cattle show in Plymouth to estimate the weight of an ox. His result showed that "the vox populi is correct to within 1 percent of the real value, and that the individual estimates are abnormally distributed in such a way that it is an equal chance whether one of these, selected at random, falls within or without the limits of -3.7 percent and +2.4 percent of their middlemost value. This result is, I think, more creditable to the trustworthiness of a democratic judgement than might have been expected" (Galton, 1907, p. 451).

Recently, a number of field as well as laboratory studies have convincingly demonstrated that groups make better decisions than individuals. In a widely cited study, Adams and Ferreira (2010) compare guesses on ice break-ups in Alaska made by individual bettors with guesses from groups of bettors. They find that group decisions are more accurate, "either because groups have to reach a compromise when their members disagree or because individuals with more extreme opinions are less likely to be part of a group" (Adams & Ferreira, 2010, p. 882). While Charness and Sutter (2012) find that groups produce more rational output than individuals, Charness et al. (2010) document that groups in a lab experiment violate the conjunction fallacy less often than individuals. Finally, Sutter (2005, p. 41) shows--again in a lab experiment--that "teams with four members outperform teams with two members and single persons" in an experimental beauty-contest game.

Moreover, a rapidly growing strand of literature emphasizes the value of collective judgements or collective decision-making for assessing the probability of future events. Mollick and Nanda (2016) compare funding decisions for proposed theater projects made by distinguished experts and a crowdfunding website and find significant agreement between the two. Atanasov et al. (2017) compare the performance of prediction markets, where traders are motivated by profits to buy and sell shares of contracts about future events with the performance of prediction polls, where participants offer probabilistic forecasts (either independently or as members of a team) and update their beliefs as often as they wish. Their main finding is that "crowds of several hundred individuals can produce highly accurate predictions on a wide range of political and economic topics" (Atanasov et al., 2017, p. 15). Finally, using data from a large investment-related social media website, Chen, De, Hu, and Hwang (2014) find that the opinions revealed on this website very well predict future stock returns as well as earnings surprises.

A number of recent studies are closely related to the research questions addressed in this paper. Using data from transfermarkt.de, Herm, Callsen-Bracker, and Kreis (2014) find that in a sample of 67 player transfers occurring during the winter break 2011-12 in the German Bundesliga, the market values explain almost entirely ([R.sub.2] = 0.90) the variance in the actually paid transfer fees. Peeters (2018) finds in a sample of more than 1,000 qualifying matches and World Cup/Euro Cup matches over the period 2008 to 2014 that forecasts of match results based on crowd evaluations are far more accurate than standard predictors, such as the FIFA ranking or the ELO rating of the two opposing teams. Using wage bill estimations provided by a panel of experienced sport journalists and a team quality measure (expressed in school grades) provided by equally experienced "experts" (former national players and famous head coaches), Frick and Wicker (2016) find that in a model predicting the league table at the end of the season, both variables (relative grade and relative wage bill) are statistically significant, suggesting that the two types of predictions are complements rather than substitutes. Consequently, soccer experts and sports economists seem to rely on completely different sources of information when making their predictions. Finally, Herzog and Hertwig (2011) use respondent recognition knowledge of names as a proxy for their familiarity with football to predict the outcome of World Cup and Euro Cup matches and find that "ignorant crowds" perform as well as official rankings and only slightly worse that betting odds.

A second research stream deals with the optimal composition of different types of crowds. Lamberson and Page (2012), for example, show that group size plays a critical role in determining the optimal group. In small groups, accurate forecasters should dominate, while in large groups consistent forecasters should form the majority. Budescu and Chen (2015) suggest as a strategy to improve the quality of crowd decision-making the successive elimination of poorly performing individuals from that crowd. However, a lab experiment conducted by Lorenz, Rauhut, Schweitzer, and Helbing (2011) demonstrates that already mild social influence can undermine the wisdom of the crowd effect. Providing information about the estimates of others narrows the initial diversity of opinions in three ways: Due to the "social influence effect," the diversity of opinions is diminished without improvement of the collective error. Due to the "range reduction effect," "the crowd becomes less reliable in providing expertise to external observers," and, finally, due to the "confidence effect," individual belief in their estimate increases despite lack of improved accuracy (Lorenz et al, 2011, p. 9020).

The Emergence of Online Communities

Online (or virtual) communities are "social aggregations that emerge from the Net when enough people carry on [...] public discussions [...], with sufficient human feeling, to form webs of personal relationships in cyberspace" (Rheingold, 1993, p. 6).

A well-known and fast-growing example of such a community is transfermarkt. de--a portal whose registered users discuss and express their opinions about, inter alia, the market values of players in designated forums. It was founded in Germany in 2000 and is by now available in eight languages; the English version for example was added in 2009. To become a user, one first has to register for participation in one or more of the various forums, abying to the "11 commandments" (3) and second to follow the structures of the respective sub-forum. The portal offers different levels of participation, the most exclusive ones being the discussion of market values, participation in the rumor mill and participation in surveys dedicated to particular topics. A user is admitted to the exclusive areas only after s/he has published a minimum of 100 qualitative posts, which leads to promotion to the status of an "expert." Individual users can also apply, after having reached a certain level of blog activity, for leadership positions such as data scout or godfather.

Transfermarkt.de is selective in the sense that player values are not simply calculated as the mean (or the median) of the individual suggestions. Instead, a particularly empowered community member--a "judge"--chooses to aggregate the information provided by the community on a case-by-case basis, implying that s/he is entitled to reduce the impact of values s/he considers "outliers" or even completely delete these. Thus, the judge performs the complex task of filtering, weighting, and aggregating information by taking into account the source of information (a person with a limited number of suggestions vs. an experienced community member with hundreds of suggestions) as well as the reason(s) provided as justification(s) for particular estimates (only one or two player characteristics vs. a lengthy description of that player's abilities). In this sense, transfermarkt.de is not an entirely "democratic" community. Figure 1 illustrates the process of decision-making on that platform (for further details, see Herm et al, 2014).

The question, thus, is whether transfermarkt.de users can be considered a wise crowd. Simmons, Nelson, Galak, and Frederick (2011, p. 5) propose four conditions that need to be met before a crowd can be considered wise. The individual members are knowledgeable, motivated to be accurate, independent, and diverse. The conditions proposed by Surowiecki (2005) in his best-selling book, The Wisdom of Crowds, look quite similar (diversity, independence, decentralization, and aggregation; see Figure 2).

Figure 2. How wise is the crowd on www.transfermarkt.de?
Source: Herm et al. 2014, p. 486.

Criteria (Surowiecki, 2005]      Transfermarkt.de

* Diversity in opinion        [check] Individual backgrounds of
("each person should hove        members, huge diversity in
some private information,        posts evident
even if it's just an eccentric
interpretation of the
known facts ")
* Independence                [check] Own opinions incentivized
("people's opinions are not      with point system; but
determined by the                streams do develop
opinions of those
around them")
* Decentralization            [check] Fans discuss across
("people are able to specialize  teams and
and draw on                      across nationalities
local knowledge")
* Aggregation                 [check] Achieved members
("some mechanism exists          function
for turning private              as judges
judgements into a
collective decision")

Football aficionados who have registered as users of the platform are indeed highly diverse and decentralized in the sense that they are located all over the world, discussing across teams and across national borders. The mechanism to aggregate the individual opinions and estimations is performed by particularly experienced members (the judges). With respect to independence, one might be tempted to argue that people are influenced in their opinions by the evaluations provided by others in the respective forums. To counter this convergence, transfermarkt.de incentivizes own opinions within its points system.

Based on the discussion so far, we can specify our first research question. How precise are the user estimates of player market values at transfermarkt.de?

Explaining the Emergence of Online Communities: The Bass Model

In a now seminal paper, Bass (1969) developed a diffusion model to explain the adoption of new products and technologies using innovation, imitation, and market size as potential determinants (Bass, 1969, 2004). Until today, the Bass model is one of the most widely used models in management science to describe, explain, and predict adoption, as well as innovation patterns in many industries.

Applying this model to an analysis of www.wikipedia.org, Spinellis and Louridas (2008, p. 72) found that the "mean number of first references to entries [...] rises exponentially until the referenced entry becomes an article." They call the "point in time when the referenced entry becomes an article" the inflection point, because "from then on the number of references to a defined article rises only linearly (on average)." This is comparable to the findings produced with an updated version of the Bass diffusion model presented by Mahajan et al. (1990).

The latter updated diffusion model has also been used to analyze the impact of open source software on the future profitability of firms (Jiang & Sarkar, 2009), to better "understand how information diffusion influences tourists' consumption patterns" (Hsiao, Jaw, & Huan, 2009, p. 691) and, finally, to predict the size of an internet-based online community as well as the time it takes to maximize its membership (Firth, Lawrence, Clouse, & Koohang, 2006).

Building on these analyses, we expect to explain the emergence of crowd wisdom on transfermarkt.de with the basic assumptions underlying the Bass model. In our context, MLS is the "new product" in the Bass terminology. Thus, referring to this particular model will help us to answer the second research question of this paper: How does crowd wisdom emerge and develop over time? If the emergence of crowd wisdom in online communities follows a similar curve like the one described in the Bass model, then this model is well suited as an explanatory tool not only in the present context, but also in other online communities.

Data

The data we use here covers 10 consecutive seasons of MLS from 2006-2015. We use 2006 as our start date, as it was the last season before the implementation of the rule that changed the entire salary system--the Designated Player Rule. Due to this event, more and more foreign, and particularly more European players came to the United States to play soccer, increasing the attention of European soccer fans in MLS. The first exclusive MLS discussion stream on transfermarkt.de started in July 2007, coinciding with the arrival of David Beckham at LA Galaxy. Two of our three dependent variables (annual base and guaranteed salaries, the latter including bonuses and benefits that are independent of performance) come from the MLS Players Association website. On average, guaranteed salaries are about 10 percent higher than base salaries. However, this value varies between 0 and 240 percent because the former includes potential additional bonuses that are spread over the length of the contract and are added to the base salary. The third dependent variable (player market values) as well as a wide range of player characteristics (age, nationality, preferred foot, and many more) were retrieved from transfermarkt.de. The complete data set includes 4,004 player-season observations, of which around 1,500 cannot be used in the econometric analysis due to missing values on either the dependent or one of the independent variables. Table 1 displays the descriptive statistics for the 2,542 player-season observations we use in our estimations, the results of which will be presented and discussed below.

Results

It appears from Figure 5 that in the first season of our observation period (2006) market value information was available for only 15 percent of the players for whom salary information was provided by the MLS Players Association. This value increased only slightly (up to 33 percent) in 2010. However, in 2011 a steep increase occurred. In that year, the percentage of players for whom a market value was available on transfermarkt.de reached a record high of 75 percent.

This rapid increase is explained by a number of simultaneous events. First, in the 2010 World Cup tournament, the U.S. team won their group for the first time since 1930, leaving the team from England in second place and qualifying for the knockout phase of the tournament. Although the U.S. team was eliminated by Ghana in the round of 16, this was considered a huge and unexpected success for the U.S. team. Second, in 2011 two new "big soccer city" teams were added to the league, Portland and Vancouver. Both cities are home to a passionate fan crowd and ever since belong to the teams that regularly sell out their home matches. Third, in 2011 a second huge increase in attendance was recorded (after a first jump that has been attributed to the arrival of David Beckham in 2007). Attendance increased by more than 7 percent compared to 2010, reaching an average value of 17,872 spectators per match. Finally, a new CBA was implemented in 2010 with the goal to grow attendance as well as TV ratings. At the same time the CBA was implemented, a new lucrative contract extension was signed with Fox Soccer Channel in 2011, next to the already existing broadcasting contract with ESPN. After the remarkable jump in 2011, the percentage of players for whom market values are available on transfermarkt.de increased only slightly up to 82 percent, a value that is comparable to the developments observed at Wikipedia by Spinellis and Louridas (2008) and fully in line with the predictions of the Bass model. After 2013, the value remains more or less constant. We can summarize the findings as follows. First, the development of crowd wisdom on transfermarkt.de is not unusual, but follows a predictable pattern: As the interest in MLS increased due to a series of exogenous shocks, the number of people contributing to the development of the website increased too. Second, and more generally, the Bass model appears to be well suited to predict and explain the emergence of crowd wisdom in online communities.

To answer the first research question (How precise are the transfermarkt.de estimates of players' market values?) we proceed in three different, yet closely related steps. First, we calculate Pearson correlation coefficients of market value and base and guaranteed salary separately for the two different time periods (2006 to 2010, and 2011 to 2015) and take a closer look at the corresponding scatterplots. Second, we estimate a simple OLS model with Market Value, Base, and Guaranteed Salary as the dependent variables. Third, we compare the Kernel density estimates of the three dependent variables.

The scatterplots and the correlation coefficients for the two sub-periods are displayed in Figures 6 and 7 below. It appears that the picture for Log (Market Value) and Log (Base Salary), is very similar to the one obtained for Log (Market Value) and Log (Guaranteed Salary).

For the season 2006-2010 the data shows a statistically significant positive correlation of r = 0.706 between market value and base salary. In the second half of the observation period (seasons 2011-2015) that value increased to r = 0.747, suggesting that the market value estimations on transfermarkt.de have already initially been good proxies for player salaries and that this quality has even increased following the increasing attention for MLS. To control for reverse causality, we also regressed salaries lagged by one year (in t-1) on market values (in t = 0) and obtained an [R.sub.2] of 0.22 only, suggesting that the market values available on transfermarkt.de are not driven by last year's salaries but reflect a player's skills instead. The correlation coefficient for the latter period is nearly identical to the one obtained for Italian "Serie A" in the 2014-15 and 2015-2016 season (1,075 player-season observations, r = +0.75) and quite similar to the one found for the German "Bundesliga" in the 2014-2015 season (500 players, r = +0.84). This is surprising insofar as MLS is the most regulated soccer league in the world and one would expect the correlation between market values and salaries to be higher in a market that is allowed to function more freely. (4)

Next, we present the results (see Table 2) of three OLS estimations with Log (Market Value), Log (Base Salary), and Log (Guaranteed Salary) as dependent variables to demonstrate that their determinants are indeed very similar as long as we consider the players' individual characteristics.

The coefficients of player age, position, designated player status, (5) footedness, and second nationality are surprisingly similar across the three models and are in line with previous research on either the determinants of player salaries (e.g., Bryson, Frick, & Simmons 2013 and Bryson, Rossi, & Simmons, 2014) or market values (e.g., Frick 2011). (6) Moreover, in all three models the variance explained by the same set of independent variables is comparable and exceeds 0.50, which increases our confidence in the results presented above. Finally, we compare the Kernel density estimates (see Figure 8) for Log (Base Salary), Log (Guaranteed Salary), and Log (Market Value) to document that their distributions are surprisingly similar, suggesting that in leagues where player salaries are not disclosed but remain private and confidential, market values can indeed be used as proxies for player remuneration. (7)

Discussion and Conclusion

Our results show that the availability of market values for MLS players on transfermarkt.de can be well explained with the widely used Bass model. The increasing availability and especially the substantial increase in the percentage of players covered by transfermarkt.de between the 2010 and 2011 seasons is due to a number of different factors, starting with a new CBA, a new TV contract, new teams that have been admitted to the league and the unexpected success of the U.S. soccer team in the 2010 World Cup tournament. These factors together spurred the public's interest in soccer and increased the popularity of soccer in general and MLS in particular.

As expected, the correlation of market values and player salaries (be it base or guaranteed pay) is close and increasing over time. Moreover, the determinants of market values on the one hand, and base and guaranteed salaries on the other hand are very similar: Any form of designated player status is associated with significantly higher market values and salaries. Age also has a statistically positive, yet nonlinear impact on market values and salaries, as does the ability to handle the ball with both feet and being a forward or a midfielder. Finally, our Kernel density estimates show a similar distribution of player market values on the one hand and player salaries on the other.

Summarizing, our results suggest that player market values generated by the wise crowd on transfermarkt.de are very good proxies of current as well as future player salaries and will, therefore, play an increasing role in the sports economics literature. (8)

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(8) We acknowledge, however, that the correlation of base and guaranteed salaries with market values is significantly higher for players with above median market values (300,000 [euro]; r = +0.74 and r = +0.73 respectively) than for players with a below median market values (r = +0.47 and r = +0.43 respectively). Since the former are significantly older than the latter (29.7 years vs. 25.6 years) this suggests that market value estimations are better for more experienced players.c

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Franziska Prockl (1) and Bernd Frick (2,3)

(1) McKinsey & Company

(2) Management Department, Paderborn University

(3) Department of Sport Marketing and Sport Economics, Seeburg Castle University

Franziska Prockl is a management consultant at McKinsey & Company. She completed her PhD at Paderborn University. Her research interests include labor and sports economics with a special focus on Major League Soccer. She lives in Munich and very much enjoys exploring the Alps as well as the nearby lakes, and cheering for Bayern Munich.

Bernd Frick is Professor of Organizational Economics at Paderborn University and Professor of Sports Economics at Seeburg Castle University. His research interests are in personnel and organizational economics as well as in sports and cultural economics. When younger, he was a competitive long-distance runner. Although somewhat slower today, he continues to be a dedicated athlete.

(1) Transfermarkt.de Mediadaten 2017, retrieved from https://www.mediaimpact.de/dl/23855437/Transfermarkt.de_Mediadaten.pdf

(2) The only other football league for which individual player salaries are available on a regular basis is Italian "Serie A." For this league, sports newspaper Gazzetta dello Sport publishes base salaries (net of individual and team bonuses) each year in early September (this data has been used by Bryson, Rossi, & Simmons (2014) to estimate a hedonic wage model similar to the one we present below). For the 2014-15 season, base salaries of some 500 players under contract by one of the 18 teams in the German "Bundesliga" have been made available too. Unfortunately, this source has not been updated since then.

(3) The upload of any type of terroristic, harassing, or pornographic content is strictly forbidden. Violating one of the 11 commandments is sanctioned with point deductions. Compare http://www.transfermarkt.co.uk/intern/elfGebote

(4) The correlation between team values (obtained by aggregating individual player values) and team wage bills is even closer: Using team wage bills from French club accounts for all 1st and 2nd division clubs and the pre-season market values of these clubs over an eleven-year period (2006-2007 through 2016-2017 with 440 team-season observations) the correlation coefficient is r = +0.96).

(5) Regular designated player (= DP). A transfer designated player (= TDP) receives a special status due to the amount of transfer fee paid while a young designated player (= YDP) is a player under 23 earning more than the maximum but due to his age is not considered as a DP yet.

(6) We include in our results table the coefficients of the team dummies to demonstrate that--contrary to results presented in studies using data from European leagues (e.g., Bryson, Rossi, and Simmons 2014, Frick, 2011)--few of the coefficients are statistically significant. This is not surprising insofar as the labor market in MLS is highly regulated, while in Italy and Germany large market teams are able and allowed to pay much higher salaries than small market teams. This, in turn, is ruled out in MLS due to the strict salary cap.

(7) Quantile regression estimates, the results of which are available from the authors upon request, demonstrate that for each of the three dependent variables, the pattern of coefficients is remarkably similar across the .10, .25, .50, .75 and .90 quantile.

Table 1: Descriptive Statistics

              count  mean          sd          min         max

base salary   2542   235,307      608,829     12,900      6,660,000
log base      2542        11.7          0.88       9.46          15.7
salary
guar. salary  2542   261,760      673,175     12,900      7,167,500
log guar.     2542        11.8          0.90       9.46          15.8
salary
market value  2542   560,102      1,183,815    5,000     19,800,000
log market    2542        12.6          1.03       8.52          16.8
value
age           2542        26.3          4.28      16             40
DP            2542         0.069                   0              1
TP            2542         0.012                   0              1
YDP           2542         0.006                   0              1
position      2542                                 1              4
footedness    2542                                 0              3
nationality   2542                                 1             91
2nd           2542         0.34                    0              1
nationality
team          2542                                 1             21
season        2542                              2006           2015

Table 2. Regression Results: Determinants of Transfer Values,
Guaranteed Salaries and Base Salaries in MLS, 2006-2015

Dep.              Log                 Log                 Log
Variable         (Transfer           (Guaranteed         (Base
                  Value)              Salary)             Salary)

age              -1.071 (***)        -1.005 (***)        -0.859 (***)
                 (0.236)             (0.193)             (0.181)
age2              0.0469 (***)        0.0403 (***)        0.0363 (***)
                 (0.00878)           (0.00718)           (0.00675)
age3             -0.000611 (***)     -0.000498 (***)     -0.000463 (***)
                 (0.000108)          (0.0000879)         (0.0000826)
[DP.sup.3]        1.426 (***)         1.964 (***)         1.920 (***)
                 (0.0616)            (0.0503)            (0.0473)
[TP.sup.3]        0.952 (***)         0.325 (***)         0.277 (***)
                 (0.136)             (0.111)             (0.104)
[YDP.sup.3]       1.055 (***)         0.832 (***)         0.876 (***)
                 (0.200)             (0.163)             (0.153)
position                             (ref.:
                                      goalkeeper)
defender          0.131 (**)          0.0627              0.0387
                 (0.0583)            (0.0476)            (0.0448)
midfielder        0.222 (***)         0.107 (**)          0.0780 (*)
                 (0.0581)            (0.0475)            (0.0446)
forward           0.397 (***)         0.234 (***)         0.191 (***)
                 (0.0600)            (0.0490)            (0.0460)
footedness                           (ref.:
                                      no info)
right foot        0.248 (***)         0.130 (***)         0.145 (***)
                 (0.0462)            (0.0378)            (0.0355)
left foot         0.270 (***)         0.124 (***)         0.146 (***)
                 (0.0554)            (0.0453)            (0.0426)
both feet         0.325 (***)         0.364 (***)         0.364 (***)
                 (0.0657)            (0.0537)            (0.0504)
2nd               0.148 (***)         0.0709 (***)        0.0570 (**)
nationality      (0.0312)            (0.0255)            (0.0240)
team                                 (ref: CHI)
CHV               0.0162             -0.214 (***)        -0.186 (***)
                 (0.0917)            (0.0750)            (0.0704)
CLB               0.0941             -0.0412             -0.0586
                 (0.0857)            (0.0700)            (0.0658)
COL               0.0723             -0.0360             -0.0307
                 (0.0855)            (0.0699)            (0.0657)
DAL               0.0708             -0.0874             -0.0960
                 (0.0866)            (0.0708)            (0.0665)
DC               -0.0751             -0.0383             -0.0440
                 (0.0869)            (0.0711)            (0.0668)
HOU               0.265 (***)         0.157 (**)          0.156 (**)
                 (0.0912)            (0.0746)            (0.0701)
KC                0.0227              0.0687              0.0769
                 (0.0869)            (0.0711)            (0.0668)
LA                0.0677              0.0603              0.0759
                 (0.0834)            (0.0682)            (0.0641)
MTE               0.0976             -0.0133             -0.0332
                 (0.0984)            (0.0804)            (0.0756)
NE                0.122               0.00877             0.00487
                 (0.0907)            (0.0742)            (0.0697)
NYC               0.147 (*)           0.0553              0.0705
                 (0.0879)            (0.0718)            (0.0675)
NYCFC            -0.146              -0.174              -0.164
                 (0.168)             (0.137)             (0.129)
ORL               0.147              -0.124              -0.113
                 (0.158)             (0.129)             (0.121)
PHI               0.192 (**)          0.123               0.123 (*)
                 (0.0932)            (0.0761)            (0.0715)
POR               0.0828             -0.102              -0.0729
                 (0.0910)            (0.0744)            (0.0699)
RSL              -0.00508             0.00646             0.0131
                 (0.0896)            (0.0732)            (0.0688)
SEA               0.0254             -0.188 (***)        -0.158 (**)
                 (0.0868)            (0.0710)            (0.0667)
SJ               -0.0493             -0.148 (**)         -0.124 (*)
                 (0.0868)            (0.0709)            (0.0666)
TOR               0.190 (**)          0.0868              0.0758
                 (0.0860)            (0.0703)            (0.0660)
VAN               0.182 (*)           0.0371              0.0456
                 (0.0935)            (0.0764)            (0.0718)
season                               (ref.:
                                     2006)
2007              0.0149             -0.185              -0.166
                 (0.175)             (0.143)             (0.134)
2008             -0.0713             -0.106              -0.0916
                 (0.172)             (0.141)             (0.132)
2009             -0.0231             -0.150              -0.137
                 (0.166)             (0.136)             (0.128)
2010             -0.0911             -0.164              -0.170
                 (0.156)             (0.128)             (0.120)
2011             -0.562 (***)        -0.242 (**)         -0.268 (**)
                 (0.149)             (0.122)             (0.114)
2012             -0.377 (**)         -0.200 (*)          -0.232 (**)
                 (0.148)             (0.121)             (0.114)
2013             -0.191              -0.160              -0.179
                 (0.148)             (0.121)             (0.114)
2014             -0.262 (*)          -0.0633             -0.0781
                 (0.149)             (0.122)             (0.114)
2015             -0.195               0.0404              0.0354
                 (0.149)             (0.122)             (0.114)
constant         19.06 (***)         19.13 (***)         17.42 (***)
                 (2.086)             (1.705)             (1.602)
N of          2,542               2,542               2,542
Observations
[R.sub.2]        50.2                56.7                60.1
(*) 100

Note: Standard errors in parentheses, (*) p < 0.10, (**) p < 0.05,
(***) p < 0.01.