[This is an expanded post of the one I published on HexagonalBlog today (11 March).  I've now bumped it to the top and added some more analysis to make it a one-parter in the end.]

Most people would say that CD Saprissa's artificial turf gives them a significant home advantage.  But Saprissa's stadium has always been intimidating to visiting teams in the days when it still had a grass surface.  Assuming everything else equal, how significant is the difference in match results from the natural and artificial pitch eras? 

To investigate this problem, I collected the home match results for Saprissa over the past ten seasons, from the 1998-99 season to the 2009 Invierno tournament.  (I disregarded matches played after the first of this year for reasons that I'll explain later.)  I divided the data into two parts: the period between 1998 and the spring of 2004, when Saprissa Stadium had a natural grass surface, and the period between the fall of 2004 and the end of 2010, when Saprissa had their first artificial surface.  A new surface was installed at the end of last year, but not enough matches have been played on it to allow meaningful analysis.  I further grouped matches that were played in the Primera División from those played in the UNCAF Nations Cup or the CONCACAF club competitions (Champions' Cup, Champions League, and Giants Cup).

So here are the home match statistics for Saprissa, before and after the conversion to a synthetic pitch:

Here are the goals scored/allowed, averaged by the number of games:

So in domestic competition, the transition from a natural playing surface to an artificial one has reduced Saprissa's goal differential from +1.52 to +0.97, a reduction of 36%.  In international competition, the goal differential has also been reduced, but slightly — from +1.14 to +1.08 (5% reduction).  So Saprissa on average are a goal better than their opponents at home, but they were more dominant when their stadium had a natural grass surface.

Now let's have a look at the goal distributions.  In domestic matches, here is how Saprissa's offensive and defensive goal distributions looked.  First, the natural grass field era:

  (I can't get the figures to appear on one line, apologies.)

And now the artificial field era:

The distribution of goals scored by Saprissa has shifted slightly to the left, which would account for the decrease in the number of goals scored per game, while the distribution of goals scored by the opposition has remained the same.  The skewness of the distribution toward the smaller goal totals is present, as it is in goal distributions for soccer teams and leagues around the world.  The number of clean sheets kept by Saprissa has increased substantially, which might account for the very slight decrease in goals conceded.

Here is how Saprissa's home record changed for international matches.  First, their record during the natural grass era:

And the artificial turf era:

As I said before, there were too few matches played against international opposition on natural grass to say anything meaningful, but on matches played on a synthetic pitch it is interesting to note that the percentage of clean sheets kept by Saprissa in international matches does not appear to be too different from that of domestic matches.  It is rare for Saprissa to concede more than two goals to a team at home, no matter what the field is.  But it appears that Saprissa no longer score as freely at home as they used to when they had a natural grass field.  At least that's how it looks from a visual inspection of the goal distributions.

To wrap up this study, let's find out whether Saprissa's home performances fall in line with their statistical expectations.  I answer this question using my own soccer Pythagorean formula.  Here are the results that I get, starting with domestic competition:

During the natural grass era Saprissa's home record in domestic competitions was for the most part in line with their statistical expectations (Pythagorean residual of +4).  It was during the artificial turf period that Saprissa's home record has suffered, and the Pythagorean residual of -8 indicates that they might have lost some matches that they shouldn't have.

Here's how their Pythagorean expectation looks in international competition:

Saprissa's international record on the grass field is bang-on what you'd expect out of a team that scored ten goals and allowed only two over seven matches.  (It's only seven matches, but I'm impressed with how well the Pythagorean estimator is!)  After the conversion to the plastic pitch, Saprissa continued to play in line with their expectations (Pythagorean residual of +2).  

So in conclusion, the effect of the artifical surface on Saprissa's home performances is much more pronounced in domestic league play.  My theory is that opposing teams in the Primera División have more opportunities to play on Saprissa's surface, and Saprissa are not the only side in Primera with a plastic pitch, so local teams have figured out a strategy for playing Saprissa in their stadium. In international play, the caliber of teams is higher but they are not as accustomed to playing on an artificial surface.

These results are astonishing when you consider that since the conversion to the artificial pitch, Saprissa have won six domestic league titles (two full-season titles and four short tournaments), won a CONCACAF Champions' Cup, and finished runner-up in the Champions' Cup in 2008.  It makes me think that Saprissa's away performance could have been what really propelled them to success in Costa Rica and beyond, but that's a study for another day.