A Look at Fouls and Defense
Perhaps I am incorrect to do, but I sometimes get the impression that Tom Soehn believes you can evaluate the toughness of a team by how willing they are to foul. Now, I am somewhat skeptical of this idea, but my skepticism should not be taken as Truth. So I'd like to examine this question in a little more detail.
Let's call this the Theory of Hack'em. I'm thinking the rational is that the closer your mark and the more frequently you challenge an attacker. As a result of this, you may have more free kicks conceded to the opposing team, but the overall effect is to blunt your opponent's attacks. When worded this way, it doesn't sound as ludicrous as a surface reading might suppose.
Now, as I said, I'm not sure I believe this theory at all. To me, fouls are far more likely to be a indication that a players is beating you on the ball, and so fouls indicate a weak defense, not a strong one. But this is a hypothesis that we should be able to test. I don't think I do so here, but I wanted to at least provide the overview before we went further, to give people an opportunity to say "I think you're barking up the wrong tree here."
Let's look at 2008. We have a full season's worth of statistics, so let's compare Goals Allowed per game against Fouls Committed per game. If we plot that, we get something that looks like this:
United, for your reference, committed 12.63 fouls per game (7th most in the league) and allowed 1.57 goals per game (2nd most in the league). Chivas led the league with over 16 fouls a game, and LA of course let in the most goals. Now, from this look, there doesn't seem to be any correlation between fouls committed and goals allowed. If anything, there's a weakly positive correlation.
So on a league wide basis, at least confined to the 2008 season, this seems to be bunk. But here's how I propose to really look at this (and it will take me some time, so if you think this is a fool's errand, speak now): This could be something we can only see in a season. Let's take a look at United's games only. We know that, on arithmetic average, they committed 12.63 fouls per game. So on games where they did more than that, did they allow fewer goals? This allows us to control for just the Tom Soehn system, plus we should be able to pull out 30 or so good data points for 2008. Make sense to you? Any takers on what we will find? Because honestly, part of me hopes I am wrong about thinking this entire theory is bunk.