Wealth inequality is bad news for a country’s growth prospects. Everyone’s favourite economist/football analyst/Argentinean wine expert Dan Altman takes up the story here in *The New York Times*. So how exactly is inequality calculated within a given dataset? Economists apply the Gini coefficient, which, in the omniscient words of Wikipedia “is a measure of statistical dispersion intended to represent the income distribution of a nation’s residents.” The Gini coefficient offers a score of between 0 and 1 for a set of data, with 0 representing perfect equality and 1 representing perfect inequality. To give you an idea, bastions of income inequality such as Lesotho, Botswana and Sierra Leone have Gini coefficients in excess of .6, whilst Slovenia, Hungary and Denmark lead the egalitarian end of proceedings in being able to boast Gini coefficients below .25.

Rather than being constrained to merely capturing income/wealth disparities, the Gini coefficient is an extremely useful tool for measuring inequality in all manner of instances. Indeed, any list of numbers can be pasted into this very handy tool which allows you to calculate your very own Gini coefficients. Applied to sports, for example, Gini coefficient analysis reminds us of the disparities in revenue inequalitybetween the Premier League (2012/13 Gini .35) and the collectivist revenue-sharing ‘socialist leagues’ of the USA (NHL .15, NBA .14, MLB .13, NFL .09). In football specifically, Sam Gregory used Gini coefficients here to capture whether teams rely on only a few, or many, players to create chances and take shots. Gini coefficients were also applied here by Dan Altman to argue that fatigue doesn’t seem to explain English teams’ poor performances in European competitions in recent seasons. Other than those two excellent pieces, however, I’m not actually aware of it having been applied elsewhere within the football analytics blogosophere – please correct me if you know of anything I’ve missed.

This is perhaps surprising given that an entire chapter of that oh so influential text for football analytics types, *The Numbers Game*, is devoted to the apparent importance of within-team equality. It is argued – via Zurab Khizanishvili being hung out to dry for costing Reading promotion to the Premier League in 2011 – that a team is better off replacing its weakest link, rather than seeking to improve upon their strongest player. If we imagine a team comprised of 10 3-star players and a 1-star left back with the arbitrary constraint of being able to make only one transfer per season, then the implication from *The Numbers Game* is that this imaginary team would do better to bring in a replacement 2-star left back than to take up the option on signing a 4-star striker. A cumulative star rating of 32, then, is not necessarily equal to another cumulative star rating of 32.

This has substantial ramifications for football analytics, specifically for those such as Goalimpact who sum player values to ascertain a team’s overall quality. For example, if we look at Liverpool’s players according to Goalimpact ahead of their epic 3-3 draw with Arsenal, we notice a team with an average rating of 131.

According to *The Numbers Game*, however, this is not the optimal manner in which to produce an overall team rating of 131. Liverpool’s configuration of 131, as above, is produced with a Gini coefficient of .07. Would they have been better off fielding Benteke and Lucas rather than Henderson and Ibe for a slightly reduced Goalimpact of 130.9, but a much greater level of equality in the shape of a .05 Gini coefficient? If this is indeed the case then it is certainly something for clubs to bear in mind when recruiting. Understandably, Goalimpact only selectively release player figures. It accordingly means, however, that I am unable to test whether teams with low Gini coefficients outperform what their overall Goalimpact score would expect. Instead, I’ve had to make do with a very poor substitute – player values according to Transfermarkt.

Interestingly there appears to be no relationship between the Gini coefficient of a club’s 20 highest value players and that same team’s overall quality according to clubelo.com. Market value is, however, a very poor barometer of playing ability, so this doesn’t tell us all that much.

The question remains: Is *The Numbers Game *wrong to seemingly suggest that teams should seek equality between the abilities of their playing staff? Or is Goalimpact wrong to believe that 32 (or 131, or whatever) is always equal to 32 (or 131, or whatever), regardless of how it is summed?

The GI-Scores compile into a very low Gini coefficient. I think you could help that by going -100 on every GI wich widens the gabs between the players.

100 because it’s the chose 0 in Goal diffference and at the moment the difference from Firminos score and Lallanas is 16% but in reallity it means that Lallana has twice the positive impact on the average teams goal difference that Firmino.

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Very nice work you do here. I like your focus on goalkeepers, I used to be one myself, on an amateur level.

With regard to the topic of this post: If a team can boast an eleven with GI values well above 100 on average I guess it doesn’t matter so much how equal the players are. If, however, you are managing a really bad team it makes intuitive sense to spend your money on improving the weak links.

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