Goal Differential and Balance In Various CONCACAF Leagues

[EvanJ]

http://www.bigsoccer.com/forum/showthread.php?t=813764 is a topic I started entitled "Goal Differential and Balance In Various Leagues," in which the league I selected from CONCACAF to post was the Honduran Clausura 2008. For each team, I took the absolute value of their goal differential. Then I added that number for each team up to get a league value and divided that by the total number of goals scored in the league that season. The higher the value, the more uneven the teams are in terms of goals scored and allowed. Here are values for different CONCACAF leagues:

Honduran Clausura 2008 (10 teams, 18 games each): 0.358
Costa Rican Verano 2008 (12 teams, 16 games each): 0.227
Belize 2007-2008 (9 teams, 16 games each): 0.243
El Salvador Clausura 2008 (10 teams, 18 games each): 0.361
Nicaraguan Apertura 2007 (10 teams, 18 games each): 0.512 (I didn't use the Clausura 2008 because one team didn't show up for 3 games)
Guatemalan Clausura 2008: 0.380

So in UNCAF, Costa Rica and Belize are about equally balanced and the most balanced; Honduras and El Salvador are almost exactly equally balanced; Guatemala is a little less balanced than El Salvador; and Nicaragua is by far the least balanced. Panama is an UNCAF country that RSSSF didn't have listed.

Cuba 2006-2007 (10 teams that qualified from a previous round, 18 games each): 0.497
Guadeloupe 2007-2008 (14 teams, 26 games each): 0.338
Jamaica 2007-2008 (12 teams, 33 games each, the additional 5 games between the top six and between the bottom six that make 38 total games are not included): 0.211
Martinique 2007-2008 (14 teams, 26 games each): 0.586
Bermuda 2007-2008 (8 teams, 14 games each): 0.602
Aruba (10 teams, 18 games each): 0.841 (4 teams scored more than double the goals they allowed and the bottom 2 combined allowed over five times as many goals as they scored)
Antigua and Barbuda 2007-2008 (10 teams, 18 games each): 0.556 (exactly 5/9ths)

5 of these 7 leagues are almost as unbalanced or more unbalanced than the most unbalanced of the 6 UNCAF leagues I posted. RSSSF only had a limited amount of CFU countries/territories.

Mexican Clausura 2008 (18 teams, 17 games each): 0.344

Maybe I'll post MLS after the season ends.

[MoRado]

http://www.bigsoccer.com/forum/showthread.php?t=813764 is a topic I started entitled "Goal Differential and Balance In Various Leagues," in which the league I selected from CONCACAF to post was the Honduran Clausura 2008. For each team, I took the absolute value of their goal differential. Then I added that number for each team up to get a league value and divided that by the total number of goals scored in the league that season. The higher the value, the more uneven the teams are in terms of goals scored and allowed. Here are values for different CONCACAF leagues:

Honduran Clausura 2008 (10 teams, 18 games each): 0.358
Costa Rican Verano 2008 (12 teams, 16 games each): 0.227
Belize 2007-2008 (9 teams, 16 games each): 0.243
El Salvador Clausura 2008 (10 teams, 18 games each): 0.361
Nicaraguan Apertura 2007 (10 teams, 18 games each): 0.512 (I didn't use the Clausura 2008 because one team didn't show up for 3 games)
Guatemalan Clausura 2008: 0.380

So in UNCAF, Costa Rica and Belize are about equally balanced and the most balanced; Honduras and El Salvador are almost exactly equally balanced; Guatemala is a little less balanced than El Salvador; and Nicaragua is by far the least balanced. Panama is an UNCAF country that RSSSF didn't have listed.

Cuba 2006-2007 (10 teams that qualified from a previous round, 18 games each): 0.497
Guadeloupe 2007-2008 (14 teams, 26 games each): 0.338
Jamaica 2007-2008 (12 teams, 33 games each, the additional 5 games between the top six and between the bottom six that make 38 total games are not included): 0.211
Martinique 2007-2008 (14 teams, 26 games each): 0.586
Bermuda 2007-2008 (8 teams, 14 games each): 0.602
Aruba (10 teams, 18 games each): 0.841 (4 teams scored more than double the goals they allowed and the bottom 2 combined allowed over five times as many goals as they scored)
Antigua and Barbuda 2007-2008 (10 teams, 18 games each): 0.556 (exactly 5/9ths)

5 of these 7 leagues are almost as unbalanced or more unbalanced than the most unbalanced of the 6 UNCAF leagues I posted. RSSSF only had a limited amount of CFU countries/territories.

Mexican Clausura 2008 (18 teams, 17 games each): 0.344

Maybe I'll post MLS after the season ends.


Costa Rica got the minimum score... and that means...? we got the most even league?

[EvanJ]

Costa Rica got the minimum score... and that means...? we got the most even league?

Yes, but I would say "lowest" score, not "minimum" score. The minimum score would be 0 if every team had a goal differential of 0. The most extreme goal differential in the 2008 Costa Rican Verano was -12 for AD Carmelita and the best goal differential was +9 for LD Alajuelense.

[MoRado]

Yes, but I would say "lowest" score, not "minimum" score. The minimum score would be 0 if every team had a goal differential of 0. The most extreme goal differential in the 2008 Costa Rican Verano was -12 for AD Carmelita and the best goal differential was +9 for LD Alajuelense.

understood, very interesting

[EvanJ]

MLS 2008 was much more balanced than Costa Rica. MLS 2008 was 0.146. 5 out of 14 teams had positive goal differentials and half the 8 playoff teams had negative goal differentials. With each team having played 30 games, only 3 teams had a goal differential in the positive or negative double-digits and nobody had a goal differential of +0.5 goals per game or better or -0.5 goals per game or worse.

[SJJ]

...and divided that by the total number of goals scored in the league that season...

And right there is your damping effect. More games in the league will mean a higher divisor, and ending up in a lower final value. You should use a value that does not depend on the number of goals overall: standard deviation, which says, more or less, how "spread out" a data set is.

So for MLS 2008, just completed regular season, the raw goal differentials are: Columbus 14, Houston 13, Chicago 11, Dallas 4, Salt Lake 1, Chivas -1, Colorado -1, Kansas City -2, New England -3, New York -6, San Jose -6, Los Angeles -7, D.C. -8, Toronto -9

Taking the absolute values, the mean (average) value is 6.143 and the standard deviation is 4.435

What would the other leagues be in standard deviation? (You didn't post the raw GD numbers, so I'm not going to go looking for them.)

(Just a quick note: for a data set to be considered statistically-significant, you need enough data points. Generally, thirty is considered a good enough number, and MLS of course has only 14 teams, so any calculation for this could be questioned. There are tests that you can prove that a lower-number of data points is valid, though. But in virtually no league will you get close to 30, except if you combine multiple seasons.)

[EvanJ]

You can't simply use the mean of the absolute values. The English League Championship 46 game season would produce goal differentials much farther from 0 than a Costa Rican 16 game season even if the Costa Rican league was somewhat more unbalanced. As for the sample size, I'm not trying to do a statistical study worthy of an award. I know the values for each country will vary from year to year, and I don't know if combining years would be good because teams get promoted and relegated (and MLS doesn't do that but has expansion teams).