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The dependent variables throughout the analyses conducted in this chapter were the result obtained by the home team, HTRESULT and the result obtained by the away team, ATRESULT, expressed as the number of points gained in the match. In the games of football covered in this analysis the reward for a win is 3 points, with 1 point for a draw and 0 points for a loss (Carmichael et al 2001)24. In previous studies on team performance in European football, team performance has often been measured using the match result as the output. For example, Carmichael et al (2000) measured team performance using match results expressed as goal differentials, with positive differentials representing wins, negative differentials representing losses and 0 differentials representing drawn games. Similarly, in a follow up study on team performances, Carmichael et al (2001) used aggregated points attained as a percentage of total points available (over the course of the season) as their output. Table 5.2.1 below reveals a list of all Bundesliga teams that were included in the sample (team-game observations), which covered the seasons from 2007-08 to 2010- 11. The established teams that regularly compete in European competition and battle for domestic honours such as FC Bayern Munich, Werder Bremen, Hamburger SV, VfL Wolfsburg, VfB Stuttgart, Bayer Leverkusen, Hannover 96, Eintracht Frankfurt and Borussia Dortmund all featured the maximum 136 times each. Each of these teams played in 68 home fixtures and 68 away fixtures over the four season sample period.

Other teams present for only three of the four seasons played in 51 home fixtures and 51 away fixtures and were therefore observed a total of 102 times and these teams included Hertha BSC, VfL Bochum, FC Nuremburg, Borussia Monchengladbach and TSG 1899 Hoffenheim. Some teams including Karlsruher SC, FC Energie Cottbus, Arminia Bielefeld, SC Freiburg and FSV Mainz 05 spent only two seasons in Bundesliga 1 and hence only amassed 34 home games and 34 away matches, totalling 68 team-game observations. Some teams only played in the Bundesliga for a solitary

24_{Theoretically, one might argue that the dependent variable used throughout the analyses is of an ordinal nature,} however throughout the analyses in this chapter (and again in chapter 7) linear estimators were adopted for two main reasons. Firstly, the use of linear estimators ensure that the interpretation of coefficients is much more straightforward (Downward et al 2014). Secondly and more importantly, estimators to control for endogeneity are much better developed and defined (Downward et al 2014). It is this latter issue that is of great significance for the analyses as a

season throughout the four season sample period and played only 17 home games and 17 away games such as Hansa Rostock, MSV Duisburg and FC Kaiserslautern, totalling 34 observations each.

One of the fixtures, involving the teams FC St Pauli and FC Schalke 04 played on the 1st of April 2011 was excluded from the sample as data for this fixture was only partially complete as the match was abandoned part way through the game and the result was awarded to the away side who were leading by a score of 0-2 at the time of abandonment. As a result the eventual sample size consisted of a total of 1,223 match fixtures and 2,446 team-game observations.

Table 5.2.1: Table listing all teams represented throughout the four season sample period and how often each team was observed.

Team Represented in Final Sample Number of Recorded Team-Game

Observations Bayern Munchen 136 Werder Bremen 136 FC Schalke 04 135* Hamburger SV 136 VfL Wolfsburg 136 VfB Stuttgart 136 Bayer Leverkusen 136 Hannover 96 136 Eintracht Frankfurt 136 Hertha BSC 102 Karlsruher SC 68 VfL Bochum 102 Borussia Dortmund 136 FC Energie Cottbus 68 Arminia Bielefeld 68 FC Nuremberg 102

Hansa Rostock 34 MSV Duisburg 34 Borussia Monchengladbach 102 TSG 1899 Hoffenheim 102 FC Koln 102 SC Freiburg 68 FSV Mainz 05 68 FC Kaiserslautern 34 FC St Pauli 33*

Notes: * Fixture between FC St Pauli and FC Schalke 04 played on 1st April 2011, excluded as match was abandoned part way through.

Table 5.2.2 below provides a list of all variables and their definitions. The dependent variables represent the output, the number of points gained in each match (match result). The endogenous variables represent the opponents’ player performance measures (aggregated team-match totals). The instrumental variables consist of variables unique to each team and help to identify the causal relationship between the dependent and endogenous variables. Finally, the control variables consist of variables used to control for team effects such as the relative quality of teams, the relative form of teams and other effects that impact the quality of football played within the league in-between seasons such as promotions, relegations, player transfers and managerial changes.

Table 5.2.2: List of all variables used throughout the analysis and their definitions

Variable Name Definition

Dependent Variables

HTRESULT Home Team Match Points Acquired

ATRESULT Away Team Match Points Acquired

Endogenous/Performance Variables

GLSAWAY Number of Goals Scored by Away Team

SOTIGLSAWAY Number of Shots on target (inc goals) by Away Team

TSPAWAY Number of Total Successful Passes by

Away Team

TWAWAY Number of Tackles Won by the Away

Team

SMAWAY Number of Saves Made by the Away

Team GK

GLSHOME Number of Goals Scored by Home Team

SOTIGLSHOME Number of Shots on target (inc goals) by Home Team

TSPHOME Number of Total Successful Passes by

Home Team

TWHOME Number of Tackles Won by the Home

Team

SMHOME Number of Saves Made by the Home

Team GK

Instrumental Variables

AVHGHTAWAY Average Height of the Away Team in

Metres

RFOOTAWAY Number of Right Footed Players in the

Away Team

BFEETAWAY Number of Two Footed Players in the

Away Team

TPLAPPAWAY Total Number of Previous Bundesliga

Appearances by the Away Team

AVAGEAWAY Average Age of the Away Team (Nearest

Year)

AVHGHTHOME Average Height of the Home Team in

Metres

RFOOTHOME Number of Right Footed Players in the

Home Team

LFOOTHOME Number of Left Footed Players in the

Home Team

BFEETHOME Number of Two Footed Players in the

Home Team

TPLAPPHOME Total Number of Previous Bundesliga

Appearances by the Home Team

AVAGEHOME Average Age of the Home Team (Nearest

Year)

Control Variables

SEASON1 Season 1 dummy variable (2007-08)

SEASON2 Season 2 dummy variable (2008-09)

SEASON3 Season 3 dummy variable25 (2009-10)

GDHOME Accumulated Goal Difference of Home

Team (at time t-1)

GDAWAY Accumulated Goal Difference of Away

Team (at time t-1)

PERPTSHOMETEAM % Points of the Home Team (at time t-1) PERPTSAWAYTEAM % Points of the Away Team (at time t-1)