Box-Out%

This is fun:
http://dl.dropbox.com/u/241759/boxoutpercent.pdf - for all NBA players in 2010 with 25+ minutes per game, who have played 40+ games.

I created a stat that shows us some representation of the % of the time a player gets a rebound, versus the % of the time their man gets the rebound.

Their man is assumed to be an average player whose rebounding percent (offensive reb% while player in question is on defense, etc) is ~80% the rebounding percent at the player's position, and 20% the average rebounding percentage of all other players. For example:

Oklahoma City's Russell Westbrook (great offensive rebounder for a point guard) collects 6% of all available rebounds while he is on offense. His 'man' is likely to be a point guard, but there is a chance (here estimated to be 20%) that his man will be a different player.
Point guards collect ~10.2% of all available defensive rebounds, while the rest of their team gets on average around 16%. So, (80%*.102)+(20%*.16)=.1016, or ~10.2%.
His 6% versus his 'man's' 10.2% gives him an offensive boxout% of 37.1% by dividing like this:

Westbrook's 6% Offensive rebounds / (His 6% Offensive Rebounds + 'Man's' 10.2% offensive rebounds) = 37.1%

Finally, the two are averaged. This gives us the total percent of rebounds the player gets, versus their 'man' (a weighted average does not do this).

Adjusted Offensive Efficiencies

Here we estimate each player's Adjusted (against average competition) Offensive Efficiencies

(The formula is simply (Raw Offensive Efficiency x Average Team Efficiency)/ Opponent's Defensive Efficiency. This is based on the assumption that Raw Team & Player Offensive Efficiency can be described as Real Offensive Efficiency x Real Opponents' Defensive Efficiency / League Efficiency average).

The results above 20% of possessions used are here: http://dl.dropbox.com/u/241759/adjusted%20offensive%20efficiencies.htm

Monte Carlo Methods

Since my blog is so ugly, I don't really like updating it. But here's a quick rundown of my monte carlo simulation method.

1) The Ken Pomeroy simulation.
https://dl.dropbox.com/u/241759/bracket_simulation.htm

Ken Pomeroy has set up his statistics in a simple way to find point margin (see one of my way old posts). For several reasons that I have mentioned on this site, I do not agree with his % chance of win statistic, and so instead I stick to Dean Oliver's (the one I learned in statistics class). Simply, in excel, I tell it to look at the normal distribution of the expected outcome of the two teams. Assuming a standard deviation of 10.9 points (which is roughly what we find from most teams in Pomeroy ratings, and the number found by the LRMC paper), we tell the computer:

=Normdist(x, 0, 10.9, 1)
where X is the expected point margin.

Then, we tell the computer to create one random tournament. For each game, the computer generates a random number between 0 and 1. If the value surpasses the better team's win%, (i.e., if it chose .91 while the better team's win% was .9) -- the worse team moves on.

Then by setting up a macro, I record the number of times each team makes it to which round. Then we simply divide the number of times each team makes it to any given round and divide it by the total number of trials to get % chance that a team will make it to whichever round of the tournament.

2) The LRMC simulation

http://dl.dropbox.com/u/241759/lrmc_montecarlo.htm

This uses the same computer program, but different statistics.
Unfortunately, the LRMC does not post anything that we can convert to point margin or win probabilities. So we have to estimate point margin from each team's ranking. I took Jeff Sagarin's predictor rating of all 347 teams by ranking, and used the LRMC's ranking order. While this certainly has some inaccuracies, I should say that this method was by far my best for the vast majority of the tournament. Then, we just convert his numbers into a win probability by subtracting one rating from another (this gives us predicted point margin).

Hope that answers any questions!