I wrote about this for the NFL at Chase Stuart’s Football Perspective, and I hinted at it for the NBA in this ESPN Insider piece about why an 82-game basketball season is unnecessarily long, so after Kevin wrote today’s article on the reliability of early-season records, I figured I might as well touch on the topic of regressing NBA team records to the mean in-season.

The basic premise is rooted in True Score Theory, which assumes that any observed result is the sum of an underlying “true” skill and a random error component. Any single sporting contest is an imperfect measure of the relative strengths of the two opponents, but over a large enough sample we can assume the random error will subside and we’ll be able to separate signal from noise.

How big of a sample do we need, though?

Glad you asked. The answer to that question comes from this Tangotiger post about true talent levels for sports leagues. From 2005-2011, the NBA had 30 teams and played an 82-game schedule. Over that span, the yearly standard deviation of team winning percentage was, on average, 0.155. Since variance equals the standard deviation squared, this means the NBA’s observed variance of winning percentage, var(observed), is 0.155^2, or 0.024.

The random standard deviation of NBA records in an 82-game season would be sqrt(0.5*0.5/82), or 0.055, meaning var(random) = 0.055^2 or 0.003.

Going back to True Score Theory, we know that var(observed) = var(true) + var(random). Rewriting that in a way that solves for the true variance, we see that var(true) = var(observed) – var(random). In this case, var(true) = 0.024 – 0.003 = 0.021. The square root of 0.021 is 0.145, so 0.145 is stdev(true), a.k.a. the standard deviation of true winning percentage talent in the current NBA.

Armed with that number, we can calculate the schedule length a season would need in order for var(true) to equal var(random) using:

0.25/stdev(true)^2

In the NBA, that number is 12 (more accurately, it’s 11.84, but it’s easier to just use 12). So when you want to regress an NBA team’s W-L record to the mean, at any point during the season, take twelve games of .500 ball (6 wins, 6 losses), and add them to the actual record. This will give you the best estimate of the team’s “true” winning percentage talent going forward.

So far this season, that yields the following set of true WPct talents:

-------------------------------------------------------- Team W L W%(obs) W%(true) -------------------------------------------------------- San Antonio Spurs 4 0 1.000 0.625 New York Knicks 3 0 1.000 0.600 Milwaukee Bucks 2 0 1.000 0.571 Chicago Bulls 3 1 0.750 0.563 Dallas Mavericks 3 1 0.750 0.563 Miami Heat 3 1 0.750 0.563 Houston Rockets 2 1 0.667 0.533 Memphis Grizzlies 2 1 0.667 0.533 Minnesota Timberwolves 2 1 0.667 0.533 New Orleans Hornets 2 1 0.667 0.533 Orlando Magic 2 1 0.667 0.533 Cleveland Cavaliers 2 2 0.500 0.500 Golden State Warriors 2 2 0.500 0.500 Indiana Pacers 2 2 0.500 0.500 Los Angeles Clippers 2 2 0.500 0.500 Oklahoma City Thunder 2 2 0.500 0.500 Portland Trail Blazers 2 2 0.500 0.500 Atlanta Hawks 1 1 0.500 0.500 Brooklyn Nets 1 1 0.500 0.500 Charlotte Bobcats 1 1 0.500 0.500 Boston Celtics 1 2 0.333 0.467 Philadelphia 76ers 1 2 0.333 0.467 Denver Nuggets 1 3 0.250 0.438 Los Angeles Lakers 1 3 0.250 0.438 Phoenix Suns 1 3 0.250 0.438 Sacramento Kings 1 3 0.250 0.438 Toronto Raptors 1 3 0.250 0.438 Utah Jazz 1 3 0.250 0.438 Washington Wizards 0 2 0.000 0.429 Detroit Pistons 0 4 0.000 0.375 --------------------------------------------------------

It doesn’t really tell you anything about the relative order of teams that you couldn’t already know from regular winning percentage, but it does give a better estimate of future expected winning percentage if you plug the WPct talent numbers into, say, Bill James’ log5 formula.

Another benefit of this process is the ability to compare that “regress-halfway” number to other sports. In basketball, the number is 11.8 in an 82-game schedule (you regress halfway to the mean 14.4% of the way into the season); in the NFL over the same 2005-11 span, the number was 10.2 in a 16-game schedule (64% of the season), and in baseball it was 88.1 in a 162-game slate (54.4% of the season).

You can use those numbers to generate equivalent season lengths between sports. The NFL’s equivalent of an 82-game NBA season? 70.9 games. And baseball’s equivalent? A mind-boggling 610.4-game schedule!

One last way to frame the data. If you picked two teams at random, looked at their records, and knew their “true” talent levels, how often would the team we observed to be better via W-L actually be the better team? In baseball, 79.8% of the time. In the NFL, 78.5% of the time. But in the NBA? 88.4% of the time.

The moral of the story: there’s a lot more certainty in NBA records than other sports, and these types of formulas help us measure that, in addition to regressing a team’s W-L record to the mean for predictive purposes.

**Reading Material:**

- True Talent Levels for Sports Leagues (Tangotiger)
- The Distribution of Talent Between Teams (Chances Is…)
- The Tango method of regression to the mean — a proof (Phil Birnbaum)

*Email Neil at np@sports-reference.com. Follow him on Twitter at @Neil_Paine.*