I feel I need to respond to Chris Anderson, the Cornell professor who writes the blog Soccer by the Numbers. In his most recent post, he looks at whether a team fouling more is correlated with winning and finds that it is not (I also have to take issue with the title. Cheating is breaking the rules without being punished; fouling by definition is punished). He then looks at the same question on a team by team basis and finds that there are some teams with which fouling more is correlated with winning, including our beloved City. However, this analysis doesn't hold water if you take a deeper look at the statistics.
It's true that City fouling more has a slight correlation with earning City more points (emphasis on slight; the R-squared is .0214). However, the correlation is slightly stronger between City suffering more fouls and earning more points. It's even stronger between the total number of fouls in the match and earning more points. This suggests to me that City do not play better when they foul more, but rather the games in which they do well tend to have more fouls in them. Why would that be? One possible explanation could be refereeing differences. It's possible that City fare better when games are called rather tightly, protecting our creative players and allowing them to work. That solution doesn't make too much sense though, as we would expect the same to hold true for other talented offensive teams were that the case. A more compelling explanation is that City favor a game that is more fast-paced, i.e. a game in which possession changes hands more frequently. In such a game (although I have absolutely no evidence for this), I would posit that there are more fouls because the game is less settled. This would pass the sniff test, as City last season tended to labor when they had steady possession (one of the many reasons the recent comparisons between City and Barca, who are excellent at making possession count, are weak). They tended to do better in games with more fouls since they are indicative of a more fast-paced, counter-attacking game. Unfortunately, there's no way I can really test this hypothesis as possessions are not shown in the official statistics.