Atlético’s next match in the UEFA Champions League

Liverpool’s previous results:

Liverpool 2:2 Manchester City

Porto 1:5 Liverpool

Brentford 3:3 Liverpool

Norwich City 0:3 Liverpool

Liverpool 3:0 Crystal Palace

\(\rightsquigarrow\) How were goals scored? Build-up play? Counter attacks?

things to consider when analysing future opponents (among others):

• how are goal-soring chances created? \(\color{gray}{\text{(counter attacks?)}}\)

• style of play? \(\color{gray}{\text{(offensive?)}}\)

• how does a team defend? \(\color{gray}{\text{(pressing?)}}\)

\(\rightsquigarrow\) such questions are usually investigated via (time-consuming) video analysis

Here, we…

• … make use of high-frequency tracking data

• … aim at automatically detecting a team’s playing style

• for the analysis of soccer tracking data, studies focus on…
  • … pass/shot performance (Kempe et al., 2018; Fairchild et al., 2018)
  • … team formation (Memmert et al., 2019)
  • … space creation (Fernandez and Bornn, 2018)
• review paper on soccer tracking data by Goes et al. (2020)

• tracking data from a single match

• data provided by Metrica Sports
  (https://github.com/metrica-sports/sample-data)

• \((x,y)\) coordinates of all players + the ball

• sampling frequency: 25 Hz

• 22 players + the ball, 90 minutes of play, 25 obs. per second
  \(\rightsquigarrow\) 3M individual data points

• convex hull of all players (excluding goalkeepers)

• referred to as ‘effective playing space’ (EPS)
  (see Frencken et al., 2011; Goes et al., 2019)

• sampling rate of the EPS: 25 Hz

• 145,006 observations (\(\approx\) 97 minutes of play)

• we consider only those observations where the ball was in play

\(\rightsquigarrow\) 88,251 observations in total

• for the EPS \(y_t\), Gamma distribution is chosen
  (continuous-valued response with values \(>\) 0)
• Gamma distribution with mean \(\mu\) and standard deviation \(\sigma\)

model with two states fitted separately to the data from both teams:

Team A:

• state 1: \(\hat{\mu}_1 = 1251, \hat{\sigma}_1 = 224\)
• state 2: \(\hat{\mu}_2 = 704, \hat{\sigma}_2 = 176\)

Team B:

• state 1: \(\hat{\mu}_1 = 1234, \hat{\sigma}_1 = 200\)
• state 2: \(\hat{\mu}_2 = 714, \hat{\sigma}_2 = 182\)

• univariate modelling approach might neglect dependence between the two teams \(\rightsquigarrow\) bivariate model

• bivariate obs. of the EPS: \(\mathbf{y}_t = (y_{t,\text{teamA}}, y_{t,\text{teamB}})\)

• within-state correlation in \(\mathbf{y}_t\) is allowed by using a copula \(C\)

• bivariate Gamma distribution as state-dependent distribution:

  • \(F(\mathbf{y}_t\,|\,s_t) = C\Big(F_1(y_{t,\text{teamA}}\,|\,s_t), F_2(y_{t,\text{teamB}}|s_t)\Big)\)
  • \(F_1, F_2\): c.d.f. of the Gamma distribution (with \(\mu\) and \(\sigma\))
  • \(C\): copula

• we select the Frank copula with dependence parameter \(\theta \in {\cal R} \setminus \{ 0\}\)

  • \(\theta \approx 0\): independence
  • \(\theta < 0\): neg. dependence
  • \(\theta > 0\): pos. dependence

• how many states (i.e. different tactics) are there?

• we consider models with 2-5 states

• computational cost:

  • two-state model: \(\approx\) 7 minutes
  • five-state model: \(\approx\) 4 hours

\(\rightsquigarrow\) four states seem reasonable

• initial aim: provide classification of a team’s underlying tactics

• investigate decoded states
  \(\rightsquigarrow\) for each time point, we thus obtain an estimate on the most likely state

time spent in each state (in minutes):