Saturday, February 16, 2013

Playoff Seed Projections - Updated Daily

I have added a new feature to the daily NBA team rankings.  On the far right, there are two additional columns.  The first column, labelled "Prob", represents each team's probability of making the playoffs.  The second column, "Proj. Seed", is a bar graph displaying the team's playoff seeding probability distribution.

Each bar graph is scaled identically on the horizontal axis, from seed 15 to seed 1.  In addition, the bars are color coded, with blue bars for seeds 1-8 (playoff teams) and red bars for seeds 9-15 (lottery bound).  You can also mouseover the bar graphs to get the actual probabilities.  See below for some examples:


The Lakers



The Lakers have a 18.6% chance of making the playoffs at this point, which is represented by those tiny blue bars on the right.  But the most likely outcome is a 9 seed, with a 39% probability.

The Pacers




The Pacers have the playoffs locked up, it's just a matter of seeding.  Nobody is catching the Heat, but the Pacers have about an equal probability of a 2, 3, or 4 seed.  The probabilities drop dramatically after that, most likely due to the NBA's convoluted seeding methodology, which guarantees the top 4 seeds to the three division winners plus the team with the best non-division winning record.

The Heat



Like I said, nobody is catching the Heat.

Methodology

I first randomize the team rankings for the remainder of the season by adding an error term to the team's current GPF (Generic Points Favored) rank.  Team strength is not static and can be affected by trades, injuries, coaching etc.  This needs to be factored into the projection, otherwise the projection will be overconfident.  John Hollinger applies a similar adjustment for his playoff projections.  I calibrated the standard deviation of the error term to match average GPF movement from seasons past.

After randomizing the rankings, I calculate a projected point spread for all future regular season games.   I then convert the point spread into a win probability using the following formula:

win probability = 1 / (1 + exp(line/6.5))

A negative line implies the team you are calculating the win probability for is favored.  The 6.5 factor maximized the log-likelhihood of the point spread's accuracy in picking winners in past seasons.

Armed with those probabilities I then simulate the remainder of the season, apply the various tiebreaker rules, and output the seeding results.  This process is rerun 10,000 times and summarized in order to arrive at the probabilities shown in the ranking table.

I am only aware of two other sites which produce daily playoff projections: Team Rankings and ESPN (the Hollinger projections).  My overall playoff probabilities look roughly in line with Team Rankings.  The Hollinger projections at ESPN seem to have more spread amongst the teams (e.g. Hollinger has the Raptors at a 20% chance of making the playoffs, while my projection only gives them a 9% chance).

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