We all have different ways of viewing the game, of trying to determine what went right, who did wrong, and the crucial factor that decided the winner. For instance, I think that a big part of what makes the Blazers' defense at least passable most nights and occasionally superb is their ability to generate more shot attempts than their opponents. The Blazers average 5.1 more FGA then their opponents, while giving up less than one more free throw attempt. This allows the Blazers to shoot poorly, or give up a high percentage, and pull out wins.

On Blazer's Edge, however, the story always seems to come down to rebounding. From today's recap,

 As we've been saying all season, you can tell how well a game is going simply by looking at the rebounding numbers.  When Portland stays even or pulls ahead on the boards they have enough other things going for them that they will edge the opposition.  When the opponent is dominating the boards they're probably making a ton of shots.  Plus they're controlling the ball when either team misses.  In those cases the Blazers have to play too much defense and don't get the same running opportunities, the energy goes away, and Portland becomes less than ordinary.

As noted, this has been a theme on Blazer's Edge throughout the season. Every time the theory holds, the game is given as proof of this trend, while when it doesn't, this is noted as an unlikely exception.

For my part, I'd always been a bit skeptical about this line of reasoning, as I am about most causal arguments. The write-up of the Mavs' game finally irked me enough to do some investigating, as watching the game I didn't really see the rebound battle playing a decisive role, compared to all the other factors Dave mentioned. Here are my basic findings:

First, if you count the number of times a Blazer game was won by the team with the most rebounds, you get that this occurs about half of the time, holding true in 39 games and false in 37.  The full breakdown for the for scenarios is as follows:

Thus, the Blazers have won the rebounding battle in exactly half of their wins, while doing somewhat poorer in games that they lose. Thus, their would seem to be some evidence of the rebounding theory.

However, as we all hopefully know, correlation does not imply causation, so a little more digging seems prudent. Recall that, in general, the winning team is making more of their shots, while the losing team is missing more of theirs. Thus, the winning team will have more opportunities to get defensive rebounds. This pans out in the case of Portland. Let DRC stand for Defensive Rebound Chances, which is calculated by adding a team's total defensive rebounds to their opponent's offensive rebounds. Then, in Portland's wins, they have the edge in DRC by a margin of 38.9 to 35.6. Furthermore, in the Blazers' losses, their opponents claim victory with 44.8 DRC to Portland's 35.6, a margin of 9.2. This is the real culprit behind any correlation between rebounding and wins and losses.

The skew introduced by the differential in DRC can be adjusted for by looking at rebounding rates. Again, we see that rebounding isn't a determining factor, as Portland has Off/Def rates of 67.5/29.3 in wins and 67.1/29.9 in losses.

The real culprit in losses, unsurprisingly, is field goal percentage. The Blazers outshoot their opponents by 2.1% in wins, but are outshot by 7.5% in losses.

Some final notes: First, statistics aren't the end of the discussion, especially not these statistics. There are numerous ways in which rebounding could still play a part, but wouldn't reveal itself in this area. For instance, it could be that the Blazers, when not rebounding well adjust their style of play, either with different lineups or more people crashing the glass. While this may allow them to pull even in the rebounding battle, this could be at the cost of more efficient strategies, such as fast breaking. Being able to handle the glass with just two players will produce a better result than if you need 4 or 5 guys to go in in order to secure a defensive rebound.

Secondly, I hope I don't come off too hard on a Dave. I love Blazer's Edge, am a little addicted, and it is currently my most visited site. I just think that we all interface with the outside world through a particular lens, and this can affect how we see things and interpret causes. Thus, it is important to try to look at things objectively, although this may come at the cost of constructing a cohesive narrative. I read this article a couple of weeks ago when the Heat were on a losing streak, in which the author labeled himself a basketball agnostic. His basic point was that sometimes teams just lose a bunch of games in a row, that unlikely things happen, and there isn't necessarily a good reason why everything happens in a game of chance. I guess I'd put myself in his camp (if anyone can find that article, I'd be greatly appreciative; also, any comments or critique).

Numbers taken from Basketball Reference and ESPN, calculated before the Mavs game.

So, as detailed in many places, the Blazers will likely end up as the 6th seed, and the Mavericks will most likely be the 2nd seed (I assume they will beat the Spurs). If this is a case, then the 3rd seed will be determined by the two Phoenix games, under the following permutations:

-Phoenix is 3rd if they win both games.

-Utah is 3rd if Phoenix beats Denver and Utah beats Phoenix

-Denver clinches 3rd if they beat Phoenix tonight. (I also assume that Utah beats the warriors tonight)

With these caveats in mind, the situation is this:

If Denver wins tonight, we play them. If they lose, then the 3rd seed will be the winner of the Phoenix/Utah game. So, my question is, who would you rather have win tonight? Denver, which locks our matchup, or Phoenix, in which case we both the best and the worst matchups of the three are still possible. (This is right to the best of my knowledge, but let me know if I'm mistaken.)

I myself, being an eternal optimist, will be rooting for the Suns.

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                There seems to have been quite a bit of discussion lately about the value of various statistical evaluations of NBA teams, especially the Blazers. This most likely is due to the Blazers 2nd best point differential, despite their slow pace. This usually leads to observations about strength of schedule and general doubt about what the future holds.

                As has been observed by many people, point differential is a flawed metric. Most other metrics have similar problems, or are shrouded in such mystery (Hollinger), that it is impossible to tell what is going on. Being a mathematically inclined individual, I've been working on devising a metric that meets several standards:

1)   Predictive: Ratings are great, as are a myriad of statistics. However, if we are searching for some single number, it would be best if it allowed us to give a prediction of future games. That is, if given the ratings for two teams, the system would calculate an expected margin.

2)   Sensitivity To Games: Once a game's margin is predicted, a team will either exceed this margin or not. If it does exceed it, then the team is better than expected, and the rating should adjust itself upward. The same idea applies to not meeting the margin.

3)   Dependent on Strength of Schedule: This is really the whole point of this post. If everyone knows that the metric needs to be viewed through a SOS lense, then why not just incorporate SOS into the metric in the first place. Note that if the 1st two characteristics are incorporated, this one should be taken care of as well.

4)   Pace-Adjusted: This is true of almost all basketball statistics. The Blazers play slowly, and we really want to know how a team performs over 100 possessions, not 48 minutes.

With these in mind, I proceeded to construct a theory of skill as relates to basketball. The metric encompasses the first 3, but is not paced adjusted, as I was unable to find pace calculations for individual games (if you have any tips, please let me know). The basic idea is that each team has a given rating, and the expected margin is merely,

TeamOneRating-TeamTwoRating = Margin,

where, since this is time based, the margin would be the expected margin after 48 minutes. However, I noticed that, on average, home teams outscore visiting teams by a margin of about 3.8. Thus, the margin that the Home team is expected to win by, MarginExpected, is given by

MarginExpected = 3.8 + HomeRating-VisitingRating.

From this formula and the scores of the last 221 basketball games, I was able to compute the ratings for all 30 teams. This was done using a least squares approximation. For each game, there is an error given by

Error = ExpectedMargin-ActualMargin.

The least squares method finds the values of the ratings such that the sum of the errors is minimized. Additionally, because all of the values are relative to each other, you can constrain them so that the average rating is 0. Then it becomes a constrained minimization problem in a quadratic of 30 variables, which computer software can solve quite easily.

                The following table shows the calculated ratings, both with and without home-court advantage factored in. As you can see, this does move some teams around, such as the Lakers, who have only played 3 road games, but it leaves the general ordering unchanged, and the Blazers at number 2.

If you have any questions about methodology, math, thought-process or anything else please just post a response. This is my first post, so I will be watching it closely. Hope you enjoy it.

To read the table, just subtract the visiting team rating from the home team and add 3.8. Thus, we expect the Blazers to win by roughly 6.372-(-5.5607)+3.8 = 15.7 pts. Go Blazers.