Some Lazy Blogging While I Grade

Posted on May 5, 2009 by


Later today I might post something on the LeBron, Kobe, and the MVP award.  Then again, I have a pile of grading to finish by tomorrow.  So my comments on this award might have to wait.

In the meantime, let me do some lazy blogging.  Specifically, rather than write something original, let me re-post two comments with a Wages of Wins theme.  The first is from Stacey Brook (co-author of The Wages of Wins).  Stacey has a wonderful blog that he calls Hawkonomics, and recently he commented on the link between NBA payroll and performance:

NBA Payroll and Performance for 2008-2009

Recently the USA Today ran a story on NBA team payrolls. The story seemed to conclude that NBA teams that have the highest paid players do the best and thus teams that have lower paid players do not perform so well. They make their point by using player salaries from the LA Lakers and the Boston Celtics as examples. This is a variant on the argument that teams with high payroll will perform better than teams with lower payroll, and I have to disagree that NBA (or for that matter NHL, MLB or NFL) teams that have high payrolls result in higher winning percentages; nor am I the first to say this.

In essence, the main premise of Michael Lewis’ book, Moneyball was to examine how the Oakland A’s did so well with one of the lowest payrolls in Major League Baseball. Additionally, as we state in The Wages of Wins, team payroll does not explain a high degree of team performance. How do we back up this statement statistically? We analyzed team performance and relative team payroll data (to account for increasing overall payrolls over multiple seasons), and calculated the coefficient of determination, also called r-squared or R2. We use R2 since we are interested in the proportion of variance that is in common between NBA team payroll and NBA team performance. Since R2 is between zero and one, the number is the percentage of the variance that is in common between NBA team payroll and NBA team performance. What we find is that the proportion of variance that is in common between NBA team performance and NBA team payroll is rather small.

Some have argued – incorrectly – that we use the wrong statistical measure. They say the true measure is the correlation coefficient – also called r. Why is this incorrect? As I explained in this post on The Wages of Wins Journal, the correlation coefficient does not measure how much of the variation between NBA team payroll and NBA team performance is in common, but rather whether NBA payroll and NBA performance change together or change oppositely.

Sometimes correlations can lead us astray. For example my blog about there being is a high positive correlation between vocabulary and corporate success. If we use correlation as our guide to the importance that one variable has on another, we would conclude that studying the dictionary (or watching The Daily Show) will allow us to climb higher on the corporate ladder. While I do not have the data, my guess is that the R2 is rather low, since the amount of variation that is common between these two variables is most likely tiny. These cases where you get very high correlations (positive or negative) are referred to as spurious correlation.

So with the stats stuff briefly discussed, let me show you why I disagree with the USA Today’s inferences about NBA payroll and team performance. If we calculate the coefficient of determination (R2) for NBA team payroll – using the USA Today’s NBA salary database and the NBA’s final season team performance the R2 is 0.041. What this means is that the proportion of variance that is common between NBA team payroll and NBA team performance is 4.1%. Just to be clear, the correlation coefficient is 0.202.

Not only that, but I also tested to see if the correlations between this past years NBA team payroll and team performance were related, and using the test statistic: ((n-2)*R2)/(1-R2)) for 1 degree of freedom and 30 degrees of freedom, found that the calculated test statistic was less than found at the 5% probability level in the F Distribution, so we would accept the null hypothesis, which is that the correlations between the two variables (NBA payroll and NBA performance) are unrelated. So not only the proportion of variance that is common between the two tiny, but here I am able to show that the correlation coefficient between the two populations (NBA payroll and NBA performance) for the 2008-2009 season is statistically zero.

Now since I am only looking at the 2008-09 NBA season, I did not calculate relative payroll as we did in The Wages of Wins. If I were to calculate relative payroll – like we did in The Wages of Wins – we will get the same answer since relative payroll is a monotonic transformation of total payroll.

Earlier this year, an unnamed NHL executive and I looked at NHL payroll (using their data) and NHL team performance, and we found in essence the exact same result – which was a surprise to him, but not to me.

Bottom line: team payrolls are poor gauges in measuring team performance.
Click here for more information on correlation.


The next stolen comment is from Matthew Yglesias.  What he states is both a) obvious and b) as he notes, generally missed by many sportswriters.

Rebounds are in the Box Score

My baskeblogging has gotten pretty lame around here. So lame that I didn’t even watch the Rockets upset the Lakers last night. Huge mistake. That said, this seems like a good time to revisit a classic theme of Yglesias NBA commentary—a lot of times you hear that guys are making awesome contributions that don’t show up in the box score when, in fact, their contributions show up in the box score. Thus this from J.A. Adande:

And Chuck Hayes? Well, you couldn’t even find a box score by his locker. He said he doesn’t even bother to read them anymore, because they don’t reflect his contributions. “What he does, it does show up … just in winning and losing,” Morey said.

My copy of the box score shows that Hayes only played 6 minutes. Obviously, under the circumstances he didn’t make that huge an impact. But it also shows that during those six minutes he grabbed three rebounds and a steal while taking zero shots and committing zero turnovers. A guy who played 30 minutes and grabbed 15 rebounds and five steals should, I think, be seen as making a huge contribution to his team as long as he plays defense well even if he doesn’t score many points. The key thing is that your possession monster can’t be missing tons of shots. Hayes used to be a modest scorer whose field goal percentage was consistently over 50 percent. Add that to great rebounding, and you have a very effective player whose contributions are very much being captured by the box score. This season, however, Hayes’ FG% and FT% are both way down which makes him less useful.

All this, however, is right there in the box score. The box score has its limits—most notably it’s hard to draw any conclusions about defense from box scores—but unless by “box score” you mean “raw point total without considering shots taken or minutes played” then it really is a very informative thing.


Again, I should have something original posted on the MVP award soon.  At least, as soon as I get done with all this grading.

– DJ

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