Plus-minus stats in MLS

Most analytically inclined sports fans are aware of plus-minus metrics and what they mean. For those new to the concept, Plus-minus metrics combine the individual and the team. For soccer, it represents the goal differential for a player's team only while he was playing. I was going to provide a plus-minus chart for players in MLS going back to 2011, but as I'm going to explain, it's mostly useless. Even when using expected goal differential (xGD) instead of actual goal differential to create xPlusMinus, not much can be gleaned from the metric.

Here is a chart of the top 25 MLS players in 2014 by xPlusMinus. It is followed by a brief discussion on its current lack of meaningfulness, and then some foreshadowing as to what adjustments will be made in the future to create a worthwhile plus-minus metric. These metrics are on a per-96-minute scale.

Player	Team	Starts	Appearances	Minutes	xPlusMinus	PlusMinus
Todd Dunivant	LA	5	7	390	1.58	1.72
Alan Gordon	LA	5	14	566	1.53	1.70
Omar Gonzalez	LA	22	22	2014	1.12	1.10
Robbie Rogers	LA	15	19	1466	1.05	0.98
Marcelo Sarvas	LA	25	28	2338	1.04	1.07
Gyasi Zardes	LA	26	32	2541	1.02	1.21
Landon Donovan	LA	30	31	2870	0.95	1.07
Jose Leonardo Ribeiro da Silva	LA	20	24	1949	0.95	1.28
Dan Gargan	LA	27	29	2580	0.94	1.19
Chance Myers	SKC	7	7	609	0.87	1.26
Vitor Gomes Pereira Junior	LA	31	34	2906	0.86	1.06
Baggio Husidic	LA	26	34	2298	0.84	1.17
Robbie Keane	LA	28	29	2696	0.78	0.85
Jaime Penedo	LA	29	29	2768	0.77	0.90
A.J. DeLaGarza	LA	28	29	2642	0.76	0.80
Oriol Rosell Argerich	SKC	7	7	641	0.76	0.45
Helbert (Fred) da Silva	PHI	3	11	389	0.72	0.99
Clint Dempsey	SEA	23	26	2268	0.70	0.42
Zach Scott	SEA	16	16	1478	0.69	0.71
Rob Friend	LA	4	10	408	0.67	-0.24
Stefan Ishizaki	LA	22	30	1994	0.65	0.91
Obafemi Martins	SEA	29	31	2811	0.58	0.55
DeAndre Yedlin	SEA	25	25	2362	0.57	0.33
John Berner	COL	5	5	479	0.55	0.20
Chad Marshall	SEA	31	31	2967	0.50	0.49

Here's an example of how to interpret the chart. During Omar Gonzalez's 2,014 minutes on the field, the LA Galaxy recorded an xGD of +1.12. Since the Galaxy as a team recorded a league-best xGD of 0.88, one could come to the conclusion that Omar Gonzalez is one of the best players on the best team. That particular conclusion probably isn't too far from the truth, but what about the rest of the table?

Control for a player's team

Basically, this statistic reiterates that the LA Galaxy were the best team in the league. 16 of the top 25 players are from LA, while five of the remaining nine play for the Seattle Sounders. There are fewer lineup combinations in soccer than in basketball and hockey because of the restrictions on substitutions, and this leads to a mostly redundant plus-minus metric. However, by looking at this table, we can start to figure out how to make it better, and the first thing we need to do is control for a player's teammates.

Control for strength of opposition

If we focus just on Galaxy players, we still see some weird things. Todd Dunivant and Alan Gordon are not LA's best players, so why did they end up on top? It's very possible that when these two were on the field, it also independently happened to be when LA's other players were playing exceptionally well. Neither player has a large sample size of minutes with LA, and that can lead to additional random variance in any metric. 

But there is a more concrete factor that likely influenced their plus-minus metrics: an individual's strength of schedule. Weighted by minutes, Dunivant and Gordon played against teams with expected goal differentials of -0.23 and -0.15, respectively. Compare that to Landon Donovan and Robbie Keane's -0.05. Those discrepancies don't make up the whole difference in xPlusMinus, but show that even players on the same team may face different opponents. 

Control for home/away and gamestate

Two other key components to adjust for are whether or not a player's team is at home, and the gamestate in which he typically plays. Robbie Rogers is probably not more valuable than Donovan or Keane, but he did play 54% of his minutes at home and 69% of his minutes while tied or losing. That compares to Donovan's 50% and 63% figures and Keane's 49% and 63%. I know that was a smattering of strange numbers, but the point is that Rogers was given both a home-field advantage and a gamestate advantage relative to many of his teammates. We must also adjust for these factors.

We hope to create a refined plus-minus statistic such as the one ESPN uses for NBA players that controls for specific lineups at any given time. For now, I have put up some of the aforementioned plus-minus metrics in our Plus-minus tab in the upper right. Or just click this link. Proceed with caution.