# Regressing to the Mean

Posted on 02/02/2011 by

“There’s only one thing more beautiful than a beautiful dream, and that’s a beautiful reality.”-Ashleigh Brilliant

Something is coming. That something is one of those posts that’s gonna get crossed of my bucket list. I’ve thrown hints about it on twitter and the thing is done.

But I’m not quite ready to talk about it yet and I’m short on time so instead I’m keeping it simple.

Simple (Image courtesy of xkcd.com)

You’re getting a short post on regression to the mean and what it could mean for the rest of the NBA season.

First a shoutout, this post is Powered by Nerd Numbers (now with next day game splits) . Second, if you need to hit the Basics for further explanations.

Remember this? There where some fun equations there:

Point Margin for a game = 0.0377 + 15.5 Wins Produced

To convert WP to expected Point Margin (and vice versa) for the team I have to account for the fact that for a single game half the win credit goes to the victor and half get charged to the loser so the equations for conversion become:

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

Marginal Wins Produced (team for the season) = Expected Avg Point Margin for Team (season)*82/31 = PM*2.645

Point Margin = 31/82 * Marginal WP = .378 *WP

So:

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

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

+1 WP = +.378 Points

+10 WP = +3.78 Points

If I use these equations and combine with the Power Rankings from this week as well as each teams average margin of victory I can forecast team records for the rest of the season. Like so:

What does the table mean? The table is meant to reflect expected performance for each team based on their average point margin and Wins Produced.A team that has exceeded their numbers is expected to fall back to the predicted value for wins (and vice versa) barring a significant improvement to their performance. We call this regression to the mean and at this point in the season (where the sample size is no longer small) it can be very telling.

To give an example, Miami’s had some bad luck and is expected to pick it up (as are LA and Orlando). San Antonio, Atlanta , Dallas, OKC  and Utah have outstripped their point margin and are headed for a fall. Philadelphia, Memphis and Houston may play themselves into playoff slots. Minnesota and Sacramento will play themselves out of the relegation zone.

I hope you have fun kids, and remember all predictions are true or your money back 🙂

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