Measuring a Player's Contribution to His Team

The goal I had when starting this blog was to analyze soccer statistically, "Bill James-style".  My focus so far has been on team stats.  I'm now going to take a crack at player stats.  Unlike baseball or football, soccer is not a sport that lends itself well to statistical analysis.  This is because of the fluid nature of the game.  Baseball has discrete events, such as pitches or plate appearances, that serve as the foundation of sabrmetric research.  Advanced football statistics are based on analysis of plays.  Soccer does not have many discrete events.  Although there are set pieces such as corner kicks, free kicks and throw-ins, these are a small part of the game.  Most of the action consists of the passing and dribbling and heading that is constantly happening.  Each touch of the ball can be considered a discrete event, but there are few meaningful statistics that can be calculated from this data at this point in time.

What I'm trying to do here is determine how valuable a player is to his team using a rather simplistic method - measuring the difference between goals scored and goals allowed for a team when a particular player is on the pitch.  This is roughly equivalent to the Plus/Minus stat used in hockey.  I'll be using Real Salt Lake as an example.  Here are their stats for MLS matches through 6/26:

Player	Minutes	GS	GA	GS90	GA90	GD90	MGS90	MGA90	MGD90
Kyle Beckerman	1287	16	9	1.119	0.629	0.490	-0.071	0.041	-0.112
Ned Grabavoy	1244	18	8	1.302	0.579	0.723	0.112	-0.009	0.122
Nat Borchers	1170	15	7	1.154	0.538	0.615	-0.036	-0.050	0.014
Tony Beltran	1030	13	8	1.136	0.699	0.437	-0.054	0.111	-0.165
Chris Wingert	1013	13	8	1.155	0.711	0.444	-0.035	0.123	-0.157
Jamison Olave	958	12	6	1.127	0.564	0.564	-0.062	-0.025	-0.038
Will Johnson	780	8	4	0.923	0.462	0.462	-0.267	-0.127	-0.140
Fabian Espindola	760	12	6	1.421	0.711	0.711	0.231	0.122	0.109
Andy Williams	719	10	7	1.252	0.876	0.376	0.062	0.288	-0.226
Robbie Russell	625	8	4	1.152	0.576	0.576	-0.038	-0.012	-0.026
Collen Warner	615	9	2	1.317	0.293	1.024	0.127	-0.296	0.423
Alvaro Saborio	594	5	2	0.758	0.303	0.455	-0.432	-0.285	-0.147
Jean Alexandre	539	7	4	1.169	0.668	0.501	-0.021	0.080	-0.101
Chris Schuler	450	6	3	1.200	0.600	0.600	0.010	0.012	-0.002
Javier Morales	405	6	2	1.333	0.444	0.889	0.143	-0.144	0.287
Arturo Alvarez	396	3	1	0.682	0.227	0.455	-0.508	-0.361	-0.147
Luis Gil	323	5	5	1.393	1.393	0.000	0.203	0.805	-0.602
Paulo Araujo Jr.	194	7	0	3.247	0.000	3.247	2.058	-0.588	2.646
Nelson Gonzalez	174	3	1	1.552	0.517	1.034	0.362	-0.071	0.433
Artur Aghasyan	98	0	1	0.000	0.918	-0.918	-1.190	0.330	-1.520
Rauwshan McKenzie	90	2	0	2.000	0.000	2.000	0.810	-0.588	1.398
Total	13464	178	88	1.190	0.588	0.602	0.000	0.000	0.000

Minutes = minutes played by each player. 

GS = goals scored by the team during the time that player was on the pitch. 

GA = goals allowed by the team during the time the player was on the pitch. 

GS90 = GF per 90 minutes. 

GA90 = GA per 90 minutes. 

GD90 = GF90 - GA 90. 

MGS90 is Marginal Goals Scored per 90 minutes = Player's GS90 - Team's GS90.
MGA90 is Marginal Goals Allowed per 90 minutes = Player's GA90 - Team's GA90.
MGD90 is Marginal Goal Differential per 90 minutes = Player's GD90 - Team's GD90.

The key figures are the "Marginal" stats which measure the player's contribution over and above the team's performance.  For example RSL averages 1.190 goals scored per 90 minutes.  A player with a GS90 below 1.190 is not performing at the same level as his teammates so is actually hurting the team offensively.  If the player's GS90 is greater than 1.190 he is performing above the level of his teammates and is helping the team.  In the above table higher MGS90 scores are better while lower (negative) MGA90 scores are better.  MGD90 captures a player's total performance (offense plus defense) and higher scores are better.

The marginal scores of the players at the top and bottom of the table are affected by low amounts of playing time so tend to be extremely high or low.  Of those that have played over 1000 minutes, midfielder Ned Grabavoy has the highest MGD90 score of 0.122.  When Grabavoy is on the field, RSL's goal differential is 0.122 better than when he isn't playing.  Grabavoy's contributions can't be explained by goals and assists.  In fact he has none of either.  But as a midfielder he is contributing via tackles, passes, free kicks, headers, etc.  The effect of all these touches is subtle and hard to measure directly so I'm using marginal stats to infer the impact of the player's performance.  His MGD90 rate of 0.122 goals is worth just over 4 additional goals in a 34-game season.

The 1000-minute player with the worst MGD90 score is Tony Beltran at -0.165.  His MGS90 is -0.054 which means he is hurting the team offensively.  His MGA90 of 0.111 hurts the team defensively (remember that negative MGA scores are better).  His MGD90 means that the team's goal differential is 5.6 goals worse over a full season when he is on the pitch.

So let me know what you think in the comments about my methods.  I plan on adding other teams to this analysis.  Let me know which teams you would like to see!