Be forewarned, this is one of the most geeky posts ever to be written on this blog. I spent way too much time this evening trying to figure out why my advanced stats didn't mesh with a few different sites. Check out the updated chart after the jump, and feel free to skip the part where I explain the differences in the numbers if you aren't into it.

As you can see, the pace was way down last night, mostly because the Sixers were extending pressure at various times throughout the game, and neither team was in much of a hurry to run offense. The Sixers performed a little above their season average in offensive efficiency and held the Nets below their typical defensive efficiency rating, although you would've hoped they could've performed much better on the defensive end.

Two trends continue through the first five game: 1) When the Sixers beat their opponents in eFG, they win the game. When they don't, they lose. 2) The only area the Sixers are truly dominating right now is free throw rate. They're producing almost twice as much from the charity stripe as their opponents. This might be a mixed blessing stat. Getting to the line is obviously very good, and very important for this team. But on the other side, not sending the other team to the line could be a mixed bag. On the one hand, you aren't giving up free points. On the other hand, why aren't you fouling? Is it because you're playing sound fundamental defense, or is it because you're giving up a ton of uncontested shots? Too early to tell, but I'm leaning toward the latter.

And now for my battle with formulas. Here's the issue, I obtained the formula I use for possessions from Dean Oliver's book, Basketball On Paper. This is the same formula listed by basketball-reference.com, and this formula is the building block for Offensive and Defensive ratings as well. Somehow, the numbers I was coming up with, using the same formula they list in their glossary, were different than their numbers. I had 108.26 for offensive rating, they had 107.3. I had 111.4 for defensive rating, they had 110.4. I had 93.56 for pace, they had 94.4.

First, I checked, double checked and triple checked my formulas. I assumed I had simply made a mistake somewhere, maybe misplaced a parenthesis. That wasn't the problem, though. Then I thought maybe Basketball-Reference.com had made a mistake in their calculations, so I went to another source for pace and OR/DR ratings, Knickerblogger.net. Their results were exactly the same as B-R.com's.

At this point, I decided to look at methodology. The formula for possessions is basically an estimate, a fairly accurate estimate, but still, it's not perfect. Teams should have an equal number of possessions throughout the game (This is Oliver's assertion, but I think teams probably wind up a possession or two apart in most games, but that's neither here nor there), so what you do is run the formula for each team, then average the two numbers. They're never exactly the same. When I run my OR and DR numbers, I use this average number for both.

Let's use last night's Nets' game as an example:

The formula tells us the Sixers had 87.12 possessions, while the Nets had 90.46. The average of the two would be 88.79. To get the offensive rating for the Sixers, I then divide points scored (97) by possessions (88.79). This gives you the number of points per possession (1.0924). Then you multiply that number by 100 to get the offensive rating (109.24).

My first step in questioning methodology was to see if maybe B-R.com and Knickerblogger were using the raw formula for each team to determine the OR & DR. It can make a pretty big difference. If we use the number the formula gave us for the Sixers alone (87.12), their offensive rating would jump up to 111.34. So I plugged all of those numbers in to see if that made up for the difference. It did not.

At this point, I was completely at a loss, so instead of figuring out how what numbers they used to derive their formulas, I looked at their results and tried to reverse engineer the numbers. The only variable here is possessions. The points are a constant, no matter what math they used, the Sixers have still scored 517 points and allowed 532. So I used simple algebra to figure out how many possessions they were using. It looks like this:

**Offensive rating**

- (517/x) x 100 = 107.3

**Defensive rating**

- (532/x) x 100 = 110.4

**Sixers possessions:**473.15**Opponents possessions:**481.94**Average possessions:**477.55

Pace is possessions per 48 minutes, rather than possessions per game. It's an important distinction when you have an overtime game in your sample. There's a convoluted formula for it, using total team minutes, but you can easily get pace by dividing possessions by the number of minutes in a game (53 for a single overtime game), then multiplying by 48. The Sixers possessions/game (using the average of pos. and op. pos.) is 95.51. Their pace is 93.36, by my math, because of the overtime game in New York. Unfortunately, both B-R.com and Knickerblogger had their pace at 94.4. When you break out the algebra again, you find out they're both using opponent's possessions to calculate pace, again, rather than the average.

I can't explain why they're doing this, but that's the only way I can come up with their numbers. Personally, I don't like the methodology at all and I'm going to stick with the average number of possessions going forward.

This is just a long-winded explanation of why my pace, offensive rating and defensive rating numbers differ from those at B-R.com and Knickerblogger.