Has the free kick spray in soccer an effect? Binomial Testing In Germany a referee supported the use of the free kick spray introduced on the World Cup 2014. He reported some statistics. His data supported the assumption using the spray leads to more goals after free kicks.
I wonder how to calculate a inference test to test the hypothesis of the referee. I was considering to conduct a binomial test.
For this test I would e.g. calculate the likelihood of scooring with a free kick in Worldcup 2010 and count the averall number of free kicks in WC2014 and the number of goals occured after a free kick. With a binomial test I would get a probability I could test the hypothesis of the referee.
Is this approach appropriate and did I interpreted the binomial test right?
 A: You need to find an economist knowledgeable about natural experiments to work on this. Essentially, you need to find identical situations that only differ by whether the free kick spray was applied vs. not applied. The positions of the free kicks would have to be the same; the strength and accuracy of the kicker would have to be the same; the experience of the goalkeeper would have to be the same; etc. This will likely be extremely difficult to ensure. If the referees were to flip a coin at every free kick, then we'd have a randomized experiment. But we don't: all of the referees, the attacking team and the defending team adapt to the new rules, subtly changing the flow of the game. E.g., if the foam is indeed helping the attacking team, then the defending team would become more cautious in committing the fouls, as they will know they will be punished more heavily. As a result, there will be fewer free kicks per game; or the spatial distribution of fouls leading to free kicks may change, with fewer committed within 10 or so meters right in front of the box (when the free kick taker is the most likely score). So the effects may be far more reaching than the mere productivity of free kicks.
If you don't have good economists by your side, you can read Mostly Harmless Econometrics instead to get acquainted with the difficulties in teasing out the causal effects.
