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acollard
Joined: 22 Sep 2010 Posts: 56 Location: MA
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Posted: Fri Oct 22, 2010 2:35 pm Post subject: Contract Incentive Study |
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This is to serve as a more thorough explanation and technical discussion of the regression I ran and the findings it gave from my post at DailyThunder . It takes some methodology from the article I asked about a couple weeks ago, Playing for Keeps by K. Stiroh.
From prosportstransactions.com I collected contract information for every player who played 500 minutes in at least two seasons from 1998-2010. I broke these down into 3 categories, unrestricted free agents, free agents, and post long contract. I ignored extensions for the pre-contract effects, because it is incomplete to include everyone who signed an extension, everyone who is eligible must be used instead. This gave 4106 player seasons with 1033 contract observations. (Thanks to DsMok1 for the spreadsheet he shared in the Advanced SPM thread).
The basic regression was dvar= ai*age+ai2*age^2+player+rfa+ufa+post
Where player is a dummy variable for each player, rfa is a dummy variable for if the player will enter restricted free agency at the end of the year, ufa is the same but for unrestricted free agents, and post is a dummy variable coding for the year after a contract is signed that is four years or more in length (If I had to guess, I probably didn't catch all of these). The results of these regressions for some dependent variables I picked are below. I didn't use dummy variables for team and year because although they helped improve the R-squared a little, they didn't change results besides WS much (because WS are tied a lot to team effects) and I worried that I might have been overfitting.
Sorry for the lack of table formatting, I don't have time to figure it out now. DT has it formatted nicely.
Code: | Win Shares Win Shares/ 48 Mins/game Usage TS% AST% ORtg DRtg
RFA .467 ** 0.0132*** 0.827 0.249 0.00345 -0.1015 1.123* -1.078***
UFA -0.018 0.00438** -0.745*** -0.203* 0.00125 0.0397 0.348 -0.492***
Post .638 ** 0.00827*** 1.095** 0.4402** 0.00143 0.6963** 0.3956 -0.6342*
Age 2.53 *** 0.0356*** 7.612*** 2.68*** 0.02606*** 2.518*** 4.903*** 0.2104
Age2 -0.0472*** -0.00066*** -0.1412*** -0.052*** -0.000451*** -0.0483*** -0.0838*** 0.00331
R-squared 0.6418 0.6145 0.6474 0.8148 0.5588 0.9029 0.5471 0.6055
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What pops out is that restricted free agents have a significantly significant contract incentive in terms of win share, but unrestricted free agents do not. It looks like this is not due to a change in efficiency (as ws48 is still positive), but probably due the statistically significant reduction in minutes. Going on the rough $2mil per win in free agency, the restricted free agency effect looks like it worth almost $1mil. That's kind of cool.
Another strange thing is that the Drtg is correlated well with both types of free agency (over -1 improvement for restricted free agents???) but not well for Ortg. It doesn't really make sense given that Drtg is a noisier number, but it would at least imply that dudes are hustling more in their contract years.
I'm aware there is a lot of potential for selection bias. One bias I could think of is the fact that restricted free agents are often the same age and the same place in their development. I tried to test that, by finding the mean age of an RFA (24.2) and coding all 24 year olds as a variable called twentyfour, replacing rfa. twentyfour was not statistically significant.
Also, the fact that rarely was there a negative post contract effect was surprising, but thinking about it now, even most signing flops take a couple years to snowball, and its often that they just seem to age faster than expected, not
I wanted to try to scale the factors for player talent, because I thought that maybe the free agency effect would be proportional to the initial value of each stat, but it didn't seem to work well, even though I tried it a couple different ways.
Please let me know what you think of my methods, and what you think of the results. I've got the spreadsheets here, but I had to do the regressions in Stata because of all the dummy variables, so there's not much to look at besides the raw data.[/url] |
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Jon Nichols
Joined: 18 Aug 2005 Posts: 370
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Posted: Fri Oct 22, 2010 3:47 pm Post subject: |
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A long time ago, using PER and much less sophisticated methods, I found similar results. However, I did find that average PER decreased in the year after signing a new contract. Here's a link:
http://basketball-statistics.com/playingforthemoney.html |
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acollard
Joined: 22 Sep 2010 Posts: 56 Location: MA
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Posted: Fri Oct 22, 2010 5:08 pm Post subject: |
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Thanks for the link, John.
Two things are different between our studies. I included one-year links, because the one year qualifying offer is considered a new contract and it includes some significant players, and i figure the minutes/season restriction would be good enough. I
i also only included those on longer length contracts (+3 years) because I don't think people often view 2 or 3 year contracts as albatrosses. Here's what my regression gives for PER:
Code: | per | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
rfa | .7828513 .2223881 3.52 0.000 .3468214 1.218881
freeagent | .1825745 .1020244 1.79 0.074 -.0174617 .3826106
post | .5006318 .1752594 2.86 0.004 .1570058 .8442578
age | 3.054301 .1277551 23.91 0.000 2.803815 3.304787
age2 | -.0590878 .0022954 -25.74 0.000 -.0635883 -.0545874
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acollard
Joined: 22 Sep 2010 Posts: 56 Location: MA
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Posted: Sat Oct 23, 2010 5:03 pm Post subject: |
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perhaps this table is a little clearer Code: | Win Shares Ws/48 Mpg Usage TS% AST% ORtg DRtg
RFA .467 ** 0.0132*** 0.827 0.249 0.00345 -0.1015 1.123* -1.078***
UFA -0.018 0.00438** -0.745*** -0.203* 0.00125 0.0397 0.348 -0.492***
Post .638 ** 0.00827*** 1.09** 0.440** 0.0014 0.6963** 0.3956 -0.6342*
Age 2.53 *** 0.0356*** 7.61*** 2.68*** 0.0260*** 2.518*** 4.903*** 0.2104
Age^2 -0.0472*** -0.00066*** -0.141*** -0.052*** -0.000451*** -0.0483*** -0.0838*** 0.00331
R^2 0.6418 0.614 0.647 0.814 0.558 0.902 0.547 0.605
| about a 5-10% effect on ws/48, but no effect on TS% or AST%... DRtg effect being so significant is still really interesting to me... |
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Ed Küpfer
Joined: 30 Dec 2004 Posts: 786 Location: Toronto
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Posted: Sat Oct 23, 2010 6:31 pm Post subject: |
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Code: | Win Shares Ws/48 Mpg Usage TS% AST% ORtg DRtg
RFA .467 ** 0.0132 *** 0.827 0.249 0.00345 -0.1015 1.123 * -1.078 ***
UFA -0.018 0.00438 ** -0.745*** -0.203 * 0.00125 0.0397 0.348 -0.492 ***
Post .638 ** 0.00827 *** 1.09** 0.440 ** 0.0014 0.6963 ** 0.3956 -0.6342 *
Age 2.53 *** 0.0356 *** 7.61*** 2.68 *** 0.0260 *** 2.518 *** 4.903 *** 0.2104
Age^2 -0.0472 *** -0.00066 *** -0.141*** -0.052 *** -0.000451 *** -0.0483 *** -0.0838 *** 0.00331
R^2 0.6418 0.614 0.647 0.814 0.558 0.902 0.547 0.605 |
I have found TABS2spaces to be really useful.
Also, you said DRTG is noisier than ORTG -- is this true? I haven't looked, but I can think of several a priori reasons why this would not necessarily be the case. _________________ ed |
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acollard
Joined: 22 Sep 2010 Posts: 56 Location: MA
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Posted: Sun Oct 24, 2010 8:40 pm Post subject: |
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Thanks for the link, I'm sure I'll find that extremely useful.
I'm sorry that I made that conjecture about individual offensive rating vs individual defensive rating without explanation. My reasoning is that individual offensive rating just being ortg= (pts scored by player)/ ( 100 possessions used by player) would show individual player improvement more than defensive rating, which is affected a lot by the teammates around the player in question. |
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acollard
Joined: 22 Sep 2010 Posts: 56 Location: MA
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Posted: Sun Mar 06, 2011 9:20 am Post subject: |
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[quote="Ed Küpfer"] Code: | Win Shares Ws/48 Mpg Usage TS% AST% ORtg DRtg
RFA .467 ** 0.0132 *** 0.827 0.249 0.00345 -0.1015 1.123 * -1.078 ***
UFA -0.018 0.00438 ** -0.745*** -0.203 * 0.00125 0.0397 0.348 -0.492 ***
Post .638 ** 0.00827 *** 1.09** 0.440 ** 0.0014 0.6963 ** 0.3956 -0.6342 *
Age 2.53 *** 0.0356 *** 7.61*** 2.68 *** 0.0260 *** 2.518 *** 4.9,.03 *** 0.2104
Age^2 -0.0472 *** -0.00066 *** -0.141*** -0.052 *** -0.000451 *** -0.0483 *** -0.0838 *** 0.00331
R^2 0.6418 0.614 0.647 0.814 0.558 0.902 0.547 0.605 |
Man... Really wish I had submitted this. I'm not saying it was as good as Arup's or anything, he had a really good presentation, but its interesting that we got somewhat different results with a pretty similar methodology. |
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