We will come back to Yao Ming's direct impact on the Rockets in a second.  For now, let's look at the changes that his absence has indirectly caused:

1. Pace

Without a solid post option such as Yao to build an offense around, the Rockets have had to up the tempo.  Common sense tells us that pace and points allowed most likely share a positive correlation, meaning that the more we run, the more points we allow.  Statistics prove common sense to be correct, as teams with a lower pace, such as Portland, Detroit, Charlotte, Miami, Boston, Cleveland, Orlando, and San Antonio, give up fewer points per game.

If you look at defensive efficiency, you notice that the same correlation exists for the most part, but there are plenty of outliers.  Detroit's defensive efficiency is up around 106.1, meaning that they give up 106 points per 100 possessions.  Every other team in the group that I listed above is between 101.2 and 95.4.  This means that Detroit doesn't do a great job defensively.  Instead, they give up less shots per game than most teams do.

That's your introduction to pace.  So, where do the Rockets fit in?  Currently, this is where we stand:

Pace: 97 possessions used per game -- 9th overall.

Points Allowed: 101.3 points allowed per game -- 20th overall.

Defensive Efficiency: 104.1 points allowed per 100 possessions -- 18th overall.

Here are the same statistical categories, but from 2008-2009 (along with where they would rank this season):

Pace: 92.8 possessions used per game -- 18th overall (tied for 25th in 2009-10)

Points Allowed: 94.4 points allowed per game -- 6th overall (6th 2009-10)

Defensive Efficiency: 101.4 points allowed per 100 possessions -- 4th overall (11th in 2009-10)

The game itself has sped up, too.  Even Golden State, leaders in pace each of the past two seasons, are up to 104.7 possessions per game this season, as opposed to 100.9 last season.  Yet, what's odd is that the defensive efficiency of the league is down this year (treat it like golf, lower is better).  What can we attribute that to?  Most likely the OTOR, or Opponents Turnover Rate.  Turnovers are up, at 13.84 in 2009-10 compared to 13.256 in 2008-09.  It's not a gigantic difference, but it could help explain the paradox before us.

Anyway, the whole point of the statistics is to show that without Yao, our pace has increased, thus making it tougher for us to defend.  Yao impacts our defense when he's on the court, but his role on offense indirectly affects our defense as well.  Remove Yao from the offense, and it hurts the defense that much more.

2. Yao's Direct Impact in the Paint

Above are screenshots of Hoop Data's "Shot Location" tab under the team statistics bar.  Here, we are looking at shots around the rim, i.e. dunks, lay-ups, and tip-ins.  The first statline is from the current season, and the second is from last season.

From left to right, the bar shows the following per game statistics: Shots made, shots attempted, field goal percentage, and percent of assisted field goals on shots made at the basket.  Clearly, there is a distinction from last season to this season.  Not to say that Chuck Hayes isn't a good defender, but Yao's ability to help and force shot adjustments is near-impossible to replace.  It is this statistic that effectively illustrates Yao's importance on defense, as opposed to rebounds or blocked shots per game.

3. Yao's Impact Elsewhere

Talented NBA shooters have their limits, at least statistically.  In the previous segment that dealt with offense, we learned the most efficient places to shoot from on the floor (three-pointer, at rim, and then jump shots from closest to farthest).  When it comes to forcing opponents to take inefficient shots, the Rockets are in the top quarter of the league (8th, in fact).  According to Hoop Data's OXeFG% (Opponent's Expected Effective Field Goal Percentage, based on where the opponent is being forced to shoot from), opponents should be shooting around 49% from the floor against us.  It's not the greatest statistic, but when paired with shot locations, it does make sense.  

However, this season opponents are shooting 51% against us, placing us in the bottom quarter of the league in Defensive Ratio (OXeFG% / OeFG%).  Last season, we were in the top quarter of the league in Defensive Ratio, but had the same OXeFG% at 49 percent.  We held our opponents below their expected effective field goal percentage, as they shot 47%.  This season, as I have pointed out, opponents are making more shots than they are expected to make.  Blame this on defensive rotations and closing out.

Without Yao in the middle of the paint, perimeter defenders are forced to show more help, thus delaying rotations and leaving opponents more open.  So, despite the fact that opponents are taking the same amount of bad shots as last season, they are having a much easier time making them this season.  It's probably due to poor closeouts and rotations.  With Yao, everything becomes much easier.

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While the dumbed-down analysis is actually correct, seeing as Yao Ming's absence has severely hurt our defense, isn't it nice to see exactly what has been affected?  I think so.  But really, who cares what I think?