By Benamin Bellman (@beninquiring)

I’ve been wondering for some time about soccer teams’ reliance on star power and top statistical producers. Is it really a good strategy? Are teams with one main goal scorer or playmaker easier to “figure out”? When the game is on the line, is a singular threat easier to neutralize than a team with a plethora of attacking options? And would this kind of reliance actually hamper a team’s success across a season?

My skepticism must seem foolish to European executives, given the huge fees Gonzalo Higuain and Paul Pogba went for this summer. But the conventional wisdom is different in the American sports landscape. In our most popular sports, one person simply can’t do it all. Here, Defense Wins Championships. The San Antonio Spurs, the best NBA team of the past two decades, emphasize team play over everything. Peyton Manning was completely underwhelming in both of his Super Bowl wins, needing his incredible teams to carry him to glory. One star pitcher or one star hitter is simply not capable of winning a World Series on their own. The anecdotal evidence even appears in MLS. Chris Wondolowski’s 27 goals in 2012 didn't get the Earthquakes past the first round of MLS playoffs; MVP Sebastian Giovinco and 2015’s Toronto FC didn't have much else to offer.

More and more, the conventional European wisdom is coming under fire. Money-ballers, regardless of continent, will tell you that 100 million quid is better spent on several great players instead of one Pogba. This piece takes a similar stance; if one player can make all the difference for a team, I want rigorous empirical evidence using on-the-field production and results.

This analysis uses two different data sets. To track patterns in Europe, I’ve collected information for all teams in six leagues for the 2011/12 through 2015/16 seasons: English and Scottish Premier Leagues, Ligue 1, Serie A, La Liga, and Bundesliga. This data set has each team’s point total at the end of each season, and the total goals and assists each player contributed in that season. I also use ASA’s shot database for the 2011 through 2015 MLS seasons, tracking scored goals as well as expected goals. Results from these data are not comparable to other leagues, but help us understand patterns in the quality of actual events rather than opaque (and possibly fluky) goal totals.

To track how statistical production is distributed across a team’s players, I’m pulling from my demography background and using Theil’s Entropy Index of diversity (or “E”). This index comes from information theory, and is often used by segregation scholars to understand the diversity of an area’s population across ethnic or economic groups. In my analysis, the population is a team’s goals in a season, and the groups are the team’s goal scorers (or assisters). E is smaller for teams where few players account for a large proportion of a team’s goals, and increases as those goals are spread more evenly across players. For example, take this year’s Colorado Rapids and Portland Timbers (as of August 24). Fanendo Adi (12 goals) and Diego Valeri (10 goals) account for about 60% of Timbers goals this season, while the top two Rapids scorers, Shkelzen Gashi (4 goals) and Kevin Doyle (4 goals), make up 30% of their team’s total. According to my formula, the Timbers’ goal E is 1.93, while the Rapids’ goal E is 2.36. Note that these teams both have 12 goal scorers; E also increases with the number of players that have scored at least one goal, reflecting that increased diversity, making it a very useful metric for describing lots of different goal distributions. Message me (@BenInquiring) if you’d like some more information (and lots of nerdiness) about these calculations. I use loess curves to visualize the relationships between the various E scores and teams’ season points totals, and validated my interpretations with linear regression models, which I’ll discuss, but won’t present.