For the EPL and MLS in recent complete seasons, here are the standard deviations of the point totals and the percent of points earned at home: EPL 2012-2013: 606/1,032 = 58.72% of points earned at home, standard deviation of 17.37 points EPL 2011-2012: 606/1,047 = 57.88% of points earned at home, standard deviation of 17.00 points EPL 2010-2011: 648/1,029 = 62.97% of points earned at home, standard deviation of 12.46 points EPL 2009-2010*: 675/1,044 = 64.66% of points earned at home, standard deviation of 17.69 points EPL 2008-2009: 616/1,043 = 59.06% of points earned at home, standard deviation of 17.77 points MLS 2012: 578/892 = 64.80% of points earned at home, standard deviation of 11.99 points MLS 2011: 505/812 = 62.19% of points earned at home, standard deviation of 10.28 points MLS 2010: 406/662 = 61.33% of points earned at home, standard deviation of 10.45 points MLS 2009: 390/606 = 64.36% of points earned at home, standard deviation of 7.40 points MLS 2008: 375/573 points = 65.45% of points earned at home, standard deviation of 6.60 points For the EPL seasons: Regression line: Standard deviation = -0.476*% of points earned at home + 68.49 Correlation = -0.3608 For the MLS seasons: Regression line: Standard deviation = -0.353*% of points earned at home + 66.93 Correlation = -0.4499 For all the seasons: Regression line: Standard deviation = -0.417*% of points earned at home + 67.52 Correlation = -0.6440 The correlation was almost 20% stronger for MLS than for EPL. The coefficient in the regression line was over a third higher for the EPL while the constant terms were very close. For all the seasons, the regression line was near the average the EPL regression line and the MLS regression line. What surprised me was that the correlation for all the seasons was much stronger that for either subset of five seasons. I didn't make a hypothesis in advance, but after doing the calculations the negative correlation makes sense because if the clubs are more balanced (have a lower standard deviation), the home club should get a greater percentage of the points because there are fewer games where the better club is so much better that the site of the game becomes mostly irrelevant. MLS had an unbalanced schedule for some of the seasons, meaning that A and B would not be equal like in the EPL if: To get A, take the point gap between every pair of clubs and calculate the mean To get B, take the point gap for every game played and calculate the mean The correlation was negative and far enough away from 0 in all three cases, that I am confident that even if MLS had a balanced schedule every season the correlation would still be negative. *In 2009-2010, I gave Portsmouth credit for the 28 points they earned, not the 19 points they had after a 9 point penalty for entering administration.
Home advantage can go up or down, when looking at in on an individual club basis - usually per league it averages out at around 0.35 goals per game (I haven't done any work with the MLS in fairness so I don't know how this compares). For some clubs it can vary up to + or -1 goal per game (the thing is that it seems to do that rarely for seasons in a row - e.g. consistently above or below league average, e.g. so you can do the standard deviation of the difference and "z" score thing, to find out if it is significantly different). There's an interesting paper here that you may find to be of help: http://researchbank.swinburne.edu.a...y/swin:694?f0=sm_creator:"Clarke,+Stephen+R." I do the least squares thing - and saw where this was going, and could use it for other things (e.g. I have a particular interest in HFA in the NFL where I do believe the Seattle Seahwaks HFA is significantly different in a positive way, and hence believe that they are overrated when on the road - with one of the factors being travel).
I'm not interested in measuring home field advantage in terms of goals per game, and the paper's abstract wrote about home field advantage compared to the distance between stadiums which I don't care about either. Given that more balanced leagues have more home field impact (measured by percentage of points earned at home), I could then study if clubs in the middle of their leagues have the most home field impact. I could break the Premier League into elite (1-4), good (5-8), average (9-12), bad (13-16), and worried about relegation (17-20 of which three of them get relegated). MLS wouldn't be as simple to divide into groups.
Figured it might not have been quite what you were after (and I can see what you are doing) but thought it may have been of interest. I've totally looked at Home Field Advantage the other way but I do believe what the paper says and that the value of HFA is rarely consistent to the point where it would be significant. This is more of an interest to me in other sports but do think it can definitely be applied in football, anecdotally one of the consistently better HFA's in the EPL is supposed to be Norwich which would make sense given their location. The chaps from DTech ran a study on this and found a key distance, and that Home Teams in the EPL, that were 180km apart or less won 45% of the time, for teams that were at least 380km apart the home team won 48% of the time (it isn't much but it's something).
Most pairs of clubs in MLS are more than 380km apart, so even if that works for England, I don't know if it is applicable to MLS. Another factor is how much money the clubs have to spend on travel and whether the travel is done by plane, train, or bus.
For the most recent five complete EPL seasons (100 data points), I calculated the absolute value of the z-score of each club's points per game relative to all 20 clubs that season. I calculated the correlation between that and the percent of points earned at home. The correlation was negative like I expected but weak at -0.2065.
Home field advantage can be a Big advantage. We played on astro turf for 8 years here at Brooklyn college. The touch line was leaning down toward into metal drains for drainage. All our opponents hated playing on it. We did to, but I made up my mind we were going to learn to play on that crap and make it an advantage for us and we did. We won 8 league championships in those 8 yrs. We became experts on playing on that field. Plus we were real good. Plus we would constantly build on the game we already had. If you have an organized defense and you can get your players believing if they can put 5 passes together you can score you will find yourselves very hard to beat. Fans can also make the home field an advantage. Intimidating players can help make the home field an advantage. Let's say you have three top teams in your league. Each one of those teams can on a given day beat the other teams. Then it goes to who matches up better. It is possible team A can beat team B most of the time. Team B can beat team C most of the time. It is also possible that team C can beat team A most of the time if C matchup well against team A. All three teams can beat all the other teams most of the time. So there are those advantages and crazy work hard practices can make one of those teams win most of the championships in league play. Then the losing teams mistakenly think the winning team was just lucky the harder you work on the practice field the luckier your team seems to get.