Arturos’ Awesome Primer: Everything you need to know about the 2011-2012 NBA Season

“If you thought that science was certain – well, that is just an error on your part.”
— Richard P. Feynman

Well, it’s been an interesting season so far. Teams bubbling up. Teams crashing down. As always, it’s human nature to rush off and make dramatic pronouncements particularly when you want to tell a good story.

Reality is a good deal more complicated than that.

The  law of large numbers (LLN) describes the result of performing the same experiment a large number of times. It’s a simple enough theorem, the average of results obtained from a large sample (or number of trials) will get closer and closer to the real value of something the larger the sample. Conversely, the error (or more accurately  the possibility of it) gets larger and larger the smaller the sample . What does this mean?

Let’s not get ahead of ourselves. Rushing to judgement based on a small sample is premature. A larger sample size is called for before we can make any definitive conclusions.

We can however use what we know to maximize what we can actually learn from the current sample. And that is precisely what I’ve been doing with my time.

We are going to have some fun today.

Because, today is the day when we I put it together all that I’ve learned about point margins, the homecourt advantage, strength of schedule and give you Team Rankings.

Let’s start with recapping what we know.

Warning: Science ahead!

Point Margin (The Win Cheat Sheet and Point Margin Produced Rev 1.1 (originally seen Here))

I’ve previously shown that on a game to game basis Wins produced correlates at a 99.8% with point margin (Point Margin for a game = 0.0377 + 15.5 Wins Produced for that game) and for the season a 95% correlation has been shown repeatedly (the difference is down to blowouts).The gist of it is that Wins Produced for a team correlates to a teams average point margin which correlates strongly with games won.

Do some additional maths and you can come up with some nice and nifty equations:

Expected Avg Point Margin for Team (season) = 31*(Wins Produced (team for the season) -41 )/82

Wins Produced (team for the season) = (Expected Avg Point Margin for Team (season)*82)/31 +41

Team Win % = Team WP48= (Avg Point Margin for Team (season))/31 +.500

Wins Produced (team for the season) = (Expected Avg Point Margin for Team (season)*82)/31 +41

And

+1 Points per game = 2.645 wins over .500 (43.645 wins)

+3.1 Points per game = 10% increase in Winning %

+10 Points per game= 26.45 wins over .500 (67.45 wins)

+1 WP = +.378 Points per game

+10 WP = +3.78 Points per game

And for Players:

Point Margin Produced per 48= (WP48-.099)* 31.1

Homecourt Advantage (The Unfair Advantage (originally seen Here))

The basic equation goes something like this:

Probability of Home team winning a game (Win %)

= (Projected Wins Home Team-Projected Wins Road Team)/82 +.606

=Win %: (Proj. Home Team Win% – Proj. Road Team Win%) +Homecourt Advantage(.606)

This is the simple equation I came up with for the home team winning a single game. The base assumption being that based on the data set (all regular season games from 1999 thru 2008 ) the home team wins 60.6% of time) and this was good and worked fairly well. As I got older and wiser (or at least more creaky), I then decided to add some more factors in:

  • Add in the effect of rest days and back to backs.
  • Add in the effect of altitude

I did some maths and figured the homecourt advantage in each scenario over playing at a neutral site. For this post I went even further and figured out the value of that advantage in points (using the handy-dandy equations in the previous section):

In summary, both, altitude and rest days affect the Homecourt advantage (HCA) and they interact with one another. Average HCA is at 59.9%. Altitude is directly proportional to HCA. Rest days are a little stranger. Altitude directly interacts with rest. Denver and Utah kill teams at home if they have a rest edge but they get killed themselves if the other team is coming in with at least a two day rest edge.

It just so happens that this kinda adds up. Apply that to a regular season played by identical clones and you get:

So if I assume all teams are equal, Utah and Denver both get a 10% boost in winning percentage when they play at home. This is good for four extra wins a season versus the average.

Strength of Schedule

Simple logic here. The Washington Wizards (hi Ted!!) are not the Miami Heat, or even the Chicago Bulls, or the Sixers for that matter. Wait, I’m getting a little ahead of my self.

All wins are not created equal. Opponents matter. We will account for that. A typical NBA schedule (I used 2010 here) confers Home court as follows over the course of a whole season:

So Utah and Denver get a four point edge over the Lakers,Clippers,Mavs, Rockets,Wizards, Warriors and Celts. This advantage goes away for the most part in the playoffs.

Some of those playoff losses make a wee bit more sense

The Rankings as of 1/11/2012

So, Point Margin, check, Homecourt check, Strength of schedule check. Are we missing anything?

Of course, the game data. God Bless Basketball Reference.

Now let’s put this all together an make a ranking. I will wok out the following numbers:

  • Point Margin per Game: Pts scored by team -Pts scored by opponent divided by games played
  • Home court Point Margin per Game: Point Margin per game due to the schedule and homecourt advantage.
  • Adjusted Point Margin per Game: Point Margin per Game -Home court Point Margin per Game. Schedule independent point margin (neutral site at sea level)
  • Adjusted Opponent Point Margin: The average Point Margin per Game of a teams opponents.
  • Real Point Margin (RPM): Point Margin per Game -Home court Point Margin per Game +Adjusted Opponent Point Margin. Expected Point Margin at a neutral site against perfectly average opposition. This is the Number I use to rank.
  • Neutral Site Win % : RPM/31 + .500

This is meant as a measure of just how strong each team projects based on the data of the season to date . We still need to account for injuries and incorporate what we know of player historical performance. We will address this in a, say it with me, future post.

A few notes:

  • The Sixers look totally legit by any definition. They in fact form a tight group of three (Philly, Chicago and Miami) at the top that must be considered the favorites for the title at this point.
  • Atlanta is the only eastern team in the 2nd tier with Portland, the Lakers, Clippers, Nuggets and Thunder in a logjam out west. Denver, with their unfair advantage, has a stellar shot at the #1 seed out west (barring acts of god or George Karl).
  • The bottom of the East is putrid. Memphis, the second worse team in the West would be the 7th in the East.
  • Some playoff teams from 2011 that look cooked: Hornets, Grizzlies and my beloved Celts.

And before we go, let’s attempt to add the effect of schedule back in to the equation:

As always, the schedule breaks greatly in favor of the Nuggets who look good for the #1 seed in the West. Keep in mind I’m using older schedules for this. Special accounting will have to be done for this season.

In the future, of course. The very uncertain future.

A future where this just might be a critical playoff matchup.

-Arturo

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