"Virtually no correlation between payroll and win%" - wrong

[shrink]

Conclusion:
There is indeed a sizable correlation between winning % and salary. It persists year over year, as demonstrated beautifully several posts above. However, the confounding factor is that the same teams tend to be both winning and spending money year over year, raising the question as to whether increasing salary is significant on it own. Team salary is more closely correlated with last years winning percentage then this years, and last year's winning percentage is highly significant on this year's winning percentage. The end result is that while a positive coefficient is found on this year's salary, it isn't statistically significant.

Thanks for the hard work.

I don't think it's surprising that salary and last year's winning percentage is correlated. The NBA lifeline is:

1. Team gets a star (either from draft or FA)
2. Team pays star
3. Team gets close to a championship
4. Team pays for additional talent
5. Star declines or departs
6. "Additional talent" still gets paid on the rest of their guaranteed contract.

If the results we read earlier are right, the only two teams with high salaries last year that didn't make the play-offs were CLE and UTA. Both paid to combine players with their stars, and when both stars ended their seasons on other teams -- with the expensive other players still remain.

[HartfordWhalers]

So the teams that won last year win this year. And winning last year means you pay more this year typically. So paying more in salary is useful just a sign that you were good last year. Which is seen when you look at teams that increase spending (That last regression with a change variable) they typically don't increase winning that year.

This is pretty accurate. I think the biggest determinant of being a good team is landing a superstar. Most commonly you do this through the draft, occasionally there is a big time free agent signing, but the rookie scale and max contract rules make these players phenomenally efficient investments. Most of the big increases in payroll simply occur when you resign your own guys, so it should come as no surprise that doesn't make for a big increase in wins.

On the other hand, what happens if you are good, but you can't afford to pay more to resign your players? It seems to me like that's where the biggest component of economic advantage lies -- LA was able to retain Bryant, Gasol, and Bynum, even though that trio by itself puts you over the salary cap. Meanwhile, the Jazz were good, but they weren't able to retain Deron Williams and Wesley Matthews last year at least in part due to their inability to go up to the $85M payroll level.

This was my first thought. I re-ran the last regressions using only teams that dipped in salary, figuring paying more was needed just to keep up, but if your spending dropped it would be a sure sign you were throwing in the towel and tanking. It came back not significant which surprised me.

The boring details:

. xtreg WinPercentage SalaryPercentage LagWinPercentage if SalaryPChange < 0 & Year >=
> 2000, re

Random-effects GLS regression Number of obs = 154
Group variable: Team Number of groups = 29

R-sq: within = 0.2614 Obs per group: min = 2
between = 0.5752 avg = 5.3
overall = 0.3740 max = 8

Wald chi2(2) = 78.88
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
WinPercent~e | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
SalaryPerc~e | .0570239 .0573098 1.00 0.320 -.0553012 .169349
LagWinPerc~e | .5430779 .0684254 7.94 0.000 .4089665 .6771893
_cons | .1653271 .0542234 3.05 0.002 .0590513 .271603
-------------+----------------------------------------------------------------
sigma_u | .03512941
sigma_e | .11573706
rho | .08435733 (fraction of variance due to u_i)
------------------------------------------------------------------------------

.

Or:

. xtreg WinningPChange SalaryPChange if SalaryPChange < 0, re

Random-effects GLS regression Number of obs = 154
Group variable: Team Number of groups = 29

R-sq: within = 0.0148 Obs per group: min = 2
between = 0.1754 avg = 5.3
overall = 0.0021 max = 8

Wald chi2(1) = 0.32
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.5702

------------------------------------------------------------------------------
WinningPCh~e | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
SalaryPCha~e | .0603804 .1063532 0.57 0.570 -.148068 .2688288
_cons | .0043074 .0164357 0.26 0.793 -.0279061 .0365208
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .1366736
rho | 0 (fraction of variance due to u_i)
------------------------------------------------------------------------------

.

[Don Draper]

Nice work HartfordWhalers

[jambalaya]

I wrote Andrew Zimbalist advising him of the discussions here and at APBRmetrics and asking if he had any comment. He replied and asked me to post this comment:

"if one runs team payroll on team win pct in a given year, the correlation coefficient is rarely significant in the NBA (also true for the NFL). actually, Howard Beck lopped off part of my quote. I did say that in a few years there was a significant correlation at the .10 level."

[Wizenheimer]

I wrote Andrew Zimbalist advising him of the discussions here and at APBRmetrics and asking if he had any comment. He replied and asked me to post this comment:

"if one runs team payroll on team win pct in a given year, the correlation coefficient is rarely significant in the NBA (also true for the NFL). actually, Howard Beck lopped off part of my quote. I did say that in a few years there was a significant correlation at the .10 level."

so do I have it right:
a paid spokesman for the union is claiming that his analysis could either confirm or not confirm a specific correlation, depending on the data used, yet the responsibility for the narrative that there is no correlation is not his but a reporter's?

and that his analysis was only based upon isolating any single season, but not an analysis of a period of time encompassing several seasons?

is that what he's saying?

[HartfordWhalers]

I wrote Andrew Zimbalist advising him of the discussions here and at APBRmetrics and asking if he had any comment. He replied and asked me to post this comment:

"if one runs team payroll on team win pct in a given year, the correlation coefficient is rarely significant in the NBA (also true for the NFL). actually, Howard Beck lopped off part of my quote. I did say that in a few years there was a significant correlation at the .10 level."

Hmm.

Year by year is a pain, but again using that basketball-reference data I get the following correlations: Starred for 10% level, and with the significance following it:

99: 0.4879* 0.0073
00: 0.5721* 0.0012
01: 0.3694* 0.0486
02:0.1327 0.4927
03: 0.3103 0.1013
04: 0.2072 0.2809
05: 0.1512 0.4250
06: 0.0179 0.9253
07: 0.1002 0.5985
08: 0.1561 0.4101
09:0.4289* 0.0180
10: 0.4835* 0.0068
11: .5425* .0020

So, 6 of 13 years it is significant at the 10% level and 1 year and it is significant at the 10.13% level.
That is a lot closer to a tie then Vietnam was.

Oh, yeah, and splitting a data set into lots of smaller data sets, and then finding something not insignificant in the smaller data set where you only have 30 observations, isn't exactly compelling when you can aggregate the data and use a more powerful test. Take a look at 04. A .2 correlation, but not enough for significance.

If you email him back, feel free to ask if he meant in close to half years instead of in a few, and ask him why he didn't feel it was appropriate to aggregate the dataset.

[HartfordWhalers]

Or you could just tell him I said that while his pants appear to be in a state of combustion, the evidence cannot confirm if the belt (or left pocket) are on fire and as such I think it is safe to keep wearing them.

[jambalaya]

I think one e-mail to him will be the extent of my outreach. I carried back one response. I thought he might post directly but I guess he wasn't inclined at that moment to register and do so. If he sends other comments I'll post them. If any want to discuss fine points with him further finding his e-mail address is pretty straight forward.

[mid-post]

Based on the statistical breakdown done by RealGMers, it looks like this particular economist bent the truth in addressing/presenting this point to the media (on behalf of the NBAPA). And some of these experts seem to know how to play the media like a fiddle.
On the whole, a lot of the coverage and reporting on the lockout has been less than comprehensive. News outlets have been typically naive (perhaps lazy and biased even) in breaking down a lot of these minor points that make up the debate as a whole.

[shawngoat23]

Using that basketballreference data. Focusing on winning %, and salary%.

Quick note: Salary Percentage is measured off the average salary per team per year. It is constructed as such to be less time sensitive then a straight salary or a straight monetary gap between the team salary and the average salary that year, as an extra 5 million in 2000 means way more then in 2010.

Correlation:
A 25.8% correlation between winning % and salary %. Hard to deny that existing (used from 2000 to get the lags in there).

Can you rerun it normalizing salary a different way? The Charlotte Bobcats weren't a team until 2004-05, so the salary % from 1999-2004 will appear to be slightly higher than from 2005-11 (by a little bit). I think this would show an even higher correlation if you made this adjustment.

[Agenda42]

This was my first thought. I re-ran the last regressions using only teams that dipped in salary, figuring paying more was needed just to keep up, but if your spending dropped it would be a sure sign you were throwing in the towel and tanking. It came back not significant which surprised me.

That's very interesting. Worth more detailed study, I think. Can you print out a list of the (team, year) tuples that matched your query?

I wonder if there's anything interesting in restricting the list to teams that shed a significant amount of salary. For example, looking at teams that were tax payers in year X-1, but are no longer tax payers in year X?

[jambalaya]

Dr. Zimbalist made some further replies:

here are the results, for instance, from 2008-09:

Team winpct09 payroll09
Atlanta 0.573 68.17
Boston 0.765 78.74
Charlotte 0.427 68
Chicago 0.5 71.49
Cleveland 0.805 90.79
Dallas 0.61 93.21
Denver 0.659 67.07
Detroit 0.476 77.05
Golden State 0.354 63.29
Houston 0.646 68.76
Indiana 0.439 69.62
LA Clippers 0.232 61.88
LA Lakers 0.793 80.75
Memphis 0.293 75.82
Miami 0.524 50.03
Milwaukee 0.415 70.22
Minnesota 0.293 63.53
New Jersey 0.415 61.98
New Orleans 0.598 67.09
New York 0.39 97.09
Oklahoma City 0.28 61.53
Orlando 0.72 74.86
Philadelphia 0.5 74.43
Phoenix 0.561 75.45
Portland 0.659 56.15
Sacramento 0.207 71.51
San Antonio 0.659 68.4
Toronto 0.402 95.36
Utah 0.585 66.27
Washington 0.232 70.56

r(d,e)= 0.203089




oh, one other thing. it is appropriate to aggregate the data for some purposes. if one wants to see the long-term advantage of having a high payroll, then pooling the data makes perfect sense. if one wants to predict who is going to do well in a given season (which is the only thing I was alluding to in my comment to Howard Beck), then it does not.


He said a bit more but it was unclear if he wanted that posted. I'll just say that I raised Hartford Whalers' questions and he stuck with .10 statistical significance levels for just a few of the years he checked and suggested the difference findings might be from different salary databases.

[Agenda42]

Or you could just tell him I said that while his pants appear to be in a state of combustion, the evidence cannot confirm if the belt (or left pocket) are on fire and as such I think it is safe to keep wearing them.

You sir, owe me some coffee. And a clean keyboard.

[jambalaya]

The discussion continued here
http://apbr.org/metrics/viewtopic.php?f ... da0863b8be

[Archerbro]

there's a correlation. But correlation=/= causation. Ask any statistician or economist.

Plus there brings the question, do good teams spend more ? or do teams that spend more become good?

Hard to come up with an answer.