Cultural Evolution Of Football Tactics: Strategic Social Learning In Managers Choice Of Formation

Cultural Evolution Of Football Tactics: Strategic Social Learning In Managers Choice Of Formation
Media summary: When selecting formations, football managers draw on their own and others’ past use of and success with those formations

Introduction
When solving problems or making decisions, people use a combination of personal information acquired directly from the environment (individual learning) and social information acquired by copying others (social learning) (Boyd & Richerson, Reference Boyd and Richerson1985, Reference Boyd and Richerson1995; Enquist, Eriksson, & Ghirlanda, Reference Enquist, Eriksson and Ghirlanda2007; Kendal et al., Reference Kendal, Boogert, Rendell, Laland, Webster and Jones2018; Laland, Reference Laland2004; Perreault, Moya, & Boyd, Reference Perreault, Moya and Boyd2012; Rogers, Reference Rogers1988). The strategic combination of individual and social learning is adaptive when decisions or problems are challenging, such as when environments change over time such that social information may become outdated (Boyd & Richerson, Reference Boyd and Richerson1995; Enquist et al., Reference Enquist, Eriksson and Ghirlanda2007; Rogers, Reference Rogers1988), or when solutions are causally opaque or multidimensional, such that they cannot be acquired by individual learning alone and require the social learning of accumulated past solutions (Boyd & Richerson, Reference Boyd and Richerson1985, Reference Boyd and Richerson1995). People show this strategic mix of individual and social learning in the laboratory (Kameda & Nakanishi, Reference Kameda and Nakanishi2003; McElreath et al., Reference McElreath, Lubell, Richerson, Waring, Baum, Edsten and Paciotti2005; Mesoudi, Reference Mesoudi2008; Morgan, Rendell, Ehn, Hoppitt, & Laland, Reference Morgan, Rendell, Ehn, Hoppitt and Laland2011; Toelch, Bruce, Newson, Richerson, & Reader, Reference Toelch, Bruce, Newson, Richerson and Reader2014; Toelch et al., Reference Toelch, Delft, van, Bruce, Donders, Meeus and Reader2009) and the real world (Beheim, Thigpen, & McElreath, Reference Beheim, Thigpen and McElreath2014; Miu, Gulley, Laland, & Rendell, Reference Miu, Gulley, Laland and Rendell2018) (although sometimes imperfectly: Mesoudi, Reference Mesoudi2011). When combined appropriately, individual and social learning can generate cumulative cultural evolution at the population level, where innovations generated via individual learning are preserved and accumulated over generations via social learning (Mesoudi & Thornton, Reference Mesoudi and Thornton2018).

Beheim, Thigpen & McElreath (Reference Beheim, Thigpen and McElreath2014) provided an innovative demonstration of the strategic use of social and individual learning in the real world. They analysed decades of professional matches of the board game Go to understand the spread of an opening move, the ‘Fourfour’. This move increased rapidly in frequency from 1968 onwards. Beheim et al. showed that Go players’ use of Fourfour is predicted by both personal information, i.e. the past use and win rate of Fourfour by that player, and social information, i.e. the past use and win rate of Fourfour in the entire population of Go players. They also showed considerable between-player variation, with some players using predominantly social information (e.g. Lee Sedol) and others using mostly personal information (e.g. Takemiya Masaki, the originator of the modern Fourfour).

Here I apply the methods and approach of Beheim et al. to another competitive real world sport, football (soccer). Football is enjoyed by millions of people worldwide, and European leagues alone have a revenue of almost €30 billion (Barnard, Boor, Winn, Wood, & Wray, Reference Barnard, Boor, Winn, Wood and Wray2019). Football has been subject to historical analyses of tactics (Wilson, Reference Wilson2013b) and increasingly, by providing a wealth of fine-grained quantitative data, statistical analyses (Tamura & Masuda, Reference Tamura and Masuda2015).

The equivalent in a football match to a Go player's opening move is a manager's starting formation. This describes how the 10 outfield players are initially organised on the pitch. Formations are typically defined by three or four numbers specifying the number of players in each segment of the pitch. For example, 442 comprises four defenders, four midfielders and two attackers. While formations may change during matches in response to player substitutions or other in-game events, all managers select one of a finite and, in practice, relatively small set of starting formations. Formations are a key component of overall tactics. For example, 541 is more defensive than 343.

The history of football tactics, crystallised in the use of different formations, is a fascinating case of cultural evolution, involving cumulative change over more than a century driven by numerous innovators from across the world, each modifying what had gone before to achieve success within the tightest of margins. The following is the briefest of narrative histories (for book length treatment, see Wilson Reference Wilson2013b). After the codification of the sport in Britain in the nineteenth century, football teams played in something like a 235, a very attack-heavy formation known as the ‘pyramid’. In 1925 the W-M was developed by the Arsenal manager Herbert Chapman in response to changes in the offside rule. This was 3223, which on the pitch looks like a capital W above a capital M. The Italian manager Vittorio Pozzo developed the WW (2323) in the 1930s, after which the 424 emerged seemingly independently in Brazil and Hungary in the 1950s. Alf Ramsay in England developed a 433 or 4132 formation, winning the 1966 World Cup in the process. The first ‘modern’ formation, the 442, was developed by the Russian Viktor Maslov and later used to great success by Italian managers such as Arrigo Sacchi of AC Milan in the 1980s and 1990s. Concurrently, Rinus Michels and Johan Cruyff brought considerable success to Ajax, and later Barcelona, with a modern 433. These gave way to the 4231 in the 2000s (Wilson, Reference Wilson2008), which in turn is being replaced (Wilson, Reference Wilson2013a). For example, Antonio Conte is credited with introducing a back three to the English Premier League at Chelsea in 2016–2017, to great success (Wilson, Reference Wilson2017).

Of course, the preceding linear narrative is highly simplified, and reality contains numerous dead-end lineages, failed experiments, ignored co-innovators and reversions to previously popular formations, just as in any evolutionary process. There have also been parallel non-formation-related innovations, from passing to pressing to improved nutrition. However, formations have remained a key part of football tactics, so much so that leading football magazines, such as FourFourTwo (Future Publishing, 1994 to present), are named after them. Given this, the drivers of changes in formation use is a promising subject of study for cultural evolution research.

The key question addressed here is therefore the extent to which managers use personal and social information to decide on their starting formation. This is a challenging decision, as defined above. The success of a formation depends partly on what formation the opposing manager plays, making payoffs of the same formation temporally variable and frequency dependent. Various other factors, from squad strength to luck, determine match outcomes in addition to formation, making the true contribution of the latter difficult to determine. And in the high stakes of football management (the median tenure of English Premier League managers as of August 2019 was 1 year, 158 days), there are limited opportunities to directly trial formations, especially if those trials are unsuccessful.

To maintain tractability and comparability to Beheim et al., I examine a manager's choice of whether to play the 4231 formation or not. During the period of study 4231 was the dominant formation (see Figure 1 and Wilson Reference Wilson2008): in the top five European domestic leagues from 2012 to 2017, it was used 37% of the time, more than double the next most common formations (18% for 433 and 14% for 442). However, 4231 also showed a clear decline in frequency during this period, from 47% in the 2012/13 season to 28% in the 2016/17 season. This decline was more extreme in some leagues than others; for example, the Spanish La Liga saw a decline in 4231 use from 78 to 37%.

Figure 1. Frequencies of initial formations across all leagues (large image) and in the five separate leagues (right panels). The three most common formations are shown: 4231 (orange), 433 (blue) and 442 (green). Other less common formations are shown in grey. Frequencies are calculated as the proportion of all matches in consecutive 30-day bins that started with that formation. ‘Days’ are consecutive match days across five seasons from 2012 to 2017, omitting days on which no matches were played. EPL, English Premier League.

Here I use a 5-year dataset of all games (n =9127, 2012–2017) in the five top European leagues (English Premier League, German Bundesliga, Spanish La Liga, French Ligue 1 and Italian Serie A) to test the following hypotheses, derived from the above theory and the results of Beheim et al. (Reference Beheim, Thigpen and McElreath2014). All hypotheses and analyses were preregistered before running any analyses on the original data (/er4dx), and all data and code are available at /amesoudi/football.

* • H1: A manager's choice of whether to play 4231 is determined by a combination of personal and social information.

* • H2: On average, there is greater reliance on social than personal information, as found by Beheim et al. for Go players.

* • H3: There is more variation between managers in both personal and social information use compared with randomised data.

* • H4: There is an n-shaped relationship between the ratio of population:personal information use and a manager's success, indicating that an overreliance on either form of information is less effective than strategically combining the two.

Methods
Data
The original dataset was downloaded from the website Kaggle, originally compiled by Jemilu Mohammed from various online sources including whoscored.com, dated 6 July 2017 (version 3) and with licence CC0: Public Domain. There are 9127 games in the dataset, which gives 18,254 starting formations (two per game, one for each team). The downloaded dataset is available as Supplementary Material.

Data was preprocessed to correct inconsistent spelling of manager names (e.g. Arsène Wenger and Arsene Wenger were merged, as were Gus Poyet and Gustavo Poyet), add one missing formation and one missing manager, add season indicators using official season start and end dates, and create predictor variables (see analysis scripts in Supplementary Material for preprocessing code).

It is important to consider the provenance and accuracy of all large secondary datasets such as this one, especially how the starting formations were coded. Opposing managers in each match officially announce their team lineups simultaneously, typically an hour before match kickoff. While they do not specify their starting formation, it is relatively straightforward to derive the formation from the announced lineup. For example, if four defenders are playing, there must be four at the back, giving a 4xxx formation. The dataset used here was compiled from whoscored.com, which in turn obtains its data from sports analysis companies such as Opta, who inform broadcasters, journalists and professional clubs in recruitment. These companies employ hundreds of analysts who are responsible for coding formations in this way. Given the importance to these companies of providing accurate data, standardised definitions of formations are used which hopefully means that the data used here reliably represents the actual formations used. Nevertheless, bias or error can never be completely avoided in large datasets that ultimately involve some human interpretation, so r