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Username Post: At Penn/Princeton        (Topic#13110)
Brian Martin 
Masters Student
Posts: 963
Brian Martin
Loc: Washington, DC
Reg: 11-21-04
02-20-12 01:10 PM - Post#121514    
    In response to Silver Maple

To measure three point defense you need a new hybrid stat that combines percentage, rate, and maybe other variables.
Harvard made 4 of 9 threes against Princeton but I consider that a very good job by Princeton because Harvard usually shoots and makes twice as many. I would say 4/9 is a better defensive performance than 8/20 even though the percentage is worse. Of course it also matters if a team is not shooting threes because they are getting easy twos. So maybe effective fg defense is the better stat and we should not isolate threes.

Three point stats can be tricky because of the variability and the sample size. Friday night Columbia was 2/10 while the outcome was in question but made 3 of 4 at the end in between Princeton free throws to end up a respectable 5/14. Last weekend McNally made a three at the buzzer to make an 11 point loss an 8 point loss and make Harvard's percentage 44.4 from 37.5.

In the league stats Pomeroy used, one game might have 30 threes attempted by an opponent while two or three games have less than 10 attempts, so the 30-attempt game overwhelms the 7-game sample.


 
Tiger69 
Postdoc
Posts: 2801

Reg: 11-23-04
02-20-12 01:13 PM - Post#121517    
    In response to Silver Maple

Thank you.

Any candidates for statisticians walking into a bar?

 
palestra38 
Professor
Posts: 32683

Reg: 11-21-04
02-20-12 01:38 PM - Post#121523    
    In response to Tiger69

3 statisticians sitting at a crowded bar on a busy Friday night talking, as they will, about the probabilities of succeeding with the opposite sex.

Gerard Butler walks in. Leaves 15 minutes later with two models. The statisticians all look at each other knowingly and say, "That was a 99% probability."

Jeremy Lin walks in. Women are all over him from the minute he enters the bar. He is polite, but leaves alone a half hour later. Each statistician nods and says, "I could have predicted that."

Finally, Jeff walks in. Walks out with a cute hipster chick after a little while. The statisticians all look at each other and shake their heads. The first one declares, "That's why you have to play the game." The other two nod and say, "I never would have believed it unless I saw it for myself."

 
1LotteryPick1969 
Postdoc
Posts: 2261
1LotteryPick1969
Age: 73
Loc: Sandy, Utah
Reg: 11-21-04
02-20-12 01:38 PM - Post#121524    
    In response to Tiger69

and say to the bartender:

"any chance we can get a drink?"

Bartender says...

"You tell me".

 
mrjames 
Professor
Posts: 6062

Loc: Montclair, NJ
Reg: 11-21-04
02-20-12 02:02 PM - Post#121528    
    In response to Brian Martin

A lot of those critiques are noise that would not obscure an effect, if one existed, over a large sample.

I am looking at 2PT% and eFG% now. Just taking a while because of work. Certainly seems like the next angle of attack here - specifically with the 2PT% to make sure there isn't a shift.

 
Brian Martin 
Masters Student
Posts: 963
Brian Martin
Loc: Washington, DC
Reg: 11-21-04
02-20-12 02:06 PM - Post#121530    
    In response to 1LotteryPick1969

Me: did you ever notice that if you drop a piece of toast it usually lands butter-side down?
Stats guy: No, it lands butter-side up just as often. You just remember the butter-side down times more because of the consequences.
Me: watch. (drops toast, it lands butter-side up)
Stats guy: see!
Me: obviously I buttered the wrong side.



 
1LotteryPick1969 
Postdoc
Posts: 2261
1LotteryPick1969
Age: 73
Loc: Sandy, Utah
Reg: 11-21-04
02-20-12 02:12 PM - Post#121531    
    In response to Brian Martin

Very good!

 
TheLine 
Professor
Posts: 5597

Age: 60
Reg: 07-07-09
02-20-12 02:20 PM - Post#121533    
    In response to palestra38

  • palestra38 Said:
"I never would have believed it unless I saw it for myself."


That's not what yo mama's stat sheet told me.


 
Brian Martin 
Masters Student
Posts: 963
Brian Martin
Loc: Washington, DC
Reg: 11-21-04
02-20-12 02:29 PM - Post#121535    
    In response to Brian Martin

To me, 3-point percentage and rate are only useful for analyzing a team's offensive or defensive efficiency and effective field goal percentage and understanding the variability in their performance. Some perimeter-oriented teams live and die on three-point shooting. Some teams (habitual zoners for example) are vulnerable to hot shooting by opponents. The overall percentages often are not as important as the variability and the distribution of the highs and lows.


 
mrjames 
Professor
Posts: 6062

Loc: Montclair, NJ
Reg: 11-21-04
02-20-12 03:02 PM - Post#121539    
    In response to Brian Martin

I ran through them all. Here's what I found...

As I said before, the R^2 on 3PT% allowed during the first half of the season and the second is 0.02. So, there's basically no correlation. The correlation between 3PT attempted rate is 0.42. So, teams allow opponents to shoot three pointers at pretty consistent rates, but don't show any consistent proficiency at affecting conversion rates.

Moving to 2PT%. The R^2 on first and second half 2PT% is 0.24. That's a decent, but not overly strong correlation, but shows that a team can affect its opponents' conversion rate from inside the arc to a decent extent.

Finally, FT% allowed. As we'd expect, the R^2 here is 0.02. We know teams have very little control over how their opponents shoot (other than who they send to the line, maybe), so it's no surprise that the results are pretty random. But at the same time, FTRates have an R^2 of 0.30, showing that teams are in pretty solid control of how many times they send opponents to the line.

I find it very hard to believe that 3PT% allowed being as inconsistent as FT% allowed and far less consistent that 2PT% allowed means little to nothing. Especially, when at the same time, the rates (which could potentially vary wildly) are solidly correlated as well.

The 2PT% and the rates are the clinchers for me. Not necessarily that opposing 3PT% is totally uncontrollable, but that there is a huge luck factor there beyond what the defense can force. I'm going to start testing an adjusted defensive rating (that awards teams their weighted opponents averages from FT and 3) to see if it has somewhat better predictive ability than the normal Pomeroy numbers.

 
Brian Martin 
Masters Student
Posts: 963
Brian Martin
Loc: Washington, DC
Reg: 11-21-04
02-20-12 03:09 PM - Post#121541    
    In response to mrjames

  • mrjames Said:
A lot of those critiques are noise that would not obscure an effect, if one existed, over a large sample.




I get that, but that is my complaint that Pomeroy discredits the results of a large sample because he cant resolve the substantial noise in 7 or 8 game samples.

 
mrjames 
Professor
Posts: 6062

Loc: Montclair, NJ
Reg: 11-21-04
02-20-12 03:32 PM - Post#121548    
    In response to Brian Martin

I understand what you're saying, but if it was all noise then we wouldn't see anything.

The fact that I see correlations some places and no correlations others leads me to believe that if there was an effect, we'd still be able to discern it. At least slightly.

In other words, if everything showed up with an R^2 only trivially different from zero, then I'd agree that it's all noise. But that some factors are showing up with a correlation and others aren't leads me to believe that it's less of a sample size issue and more of an issue of there not actually being a correlation.

Often, I wonder if the resistance to the possibility of such findings is that people refuse to admit how much of the game is truly luck (and by extension, how much of life is really luck).

 
1LotteryPick1969 
Postdoc
Posts: 2261
1LotteryPick1969
Age: 73
Loc: Sandy, Utah
Reg: 11-21-04
02-20-12 03:43 PM - Post#121552    
    In response to mrjames

Proving conclusively that an Ivy league education is a waste of time, since life is just luck. Damn, wish I had known. Could had more money and more fun at my local U, and maybe learned how to bet on Ivy basketball, which apparantly is very remunerative.

 
mrjames 
Professor
Posts: 6062

Loc: Montclair, NJ
Reg: 11-21-04
02-20-12 03:47 PM - Post#121554    
    In response to 1LotteryPick1969

  • Quote:
since life is just luck.



I never said THAT. I merely said that life is more dominated by luck than most people give credit for.

 
1LotteryPick1969 
Postdoc
Posts: 2261
1LotteryPick1969
Age: 73
Loc: Sandy, Utah
Reg: 11-21-04
02-20-12 04:15 PM - Post#121563    
    In response to mrjames

Robert Pirsig left the natural sciences (so I have read) because he was frustrated by the thought that he could never prove anything, since he could never refute all hypotheses to the contrary, or something like that. So he moved into the philosophy of "quality".

We need a book like "Zen and the Art of 3-point Defense."

 
mountainred 
Masters Student
Posts: 509

Age: 57
Loc: Charleston, WV
Reg: 04-11-10
02-20-12 07:18 PM - Post#121594    
    In response to mrjames

  • mrjames Said:

...
I find it very hard to believe that 3PT% allowed being as inconsistent as FT% allowed and far less consistent that 2PT% allowed means little to nothing. Especially, when at the same time, the rates (which could potentially vary wildly) are solidly correlated as well.

The 2PT% and the rates are the clinchers for me. Not necessarily that opposing 3PT% is totally uncontrollable, but that there is a huge luck factor there beyond what the defense can force. I'm going to start testing an adjusted defensive rating (that awards teams their weighted opponents averages from FT and 3) to see if it has somewhat better predictive ability than the normal Pomeroy numbers.



Thanks Mike. My other message boards would never understand how interesting I find this stuff. Please don't tell them, or it will be middle school all over again.


 
IvyBballFan 
Masters Student
Posts: 479

Age: 77
Loc: Central Florida
Reg: 11-19-09
02-20-12 10:53 PM - Post#121615    
    In response to mrjames

  • mrjames Said:
  • Quote:
since life is just luck.


I never said THAT. I merely said that life is more dominated by luck than most people give credit for.


but... "Chance favors the prepared mind." - Louis Pasteur

and... it sure is nice that when you are lucky enough to have the guy watchin' you slip and hit the deck right in front of you 21 feet from the basket, that you know have made 25 in a row from that spot every day in practice for the past four months.

 
SRP 
Postdoc
Posts: 4894

Reg: 02-04-06
02-21-12 09:38 PM - Post#121736    
    In response to IvyBballFan

Let's make the simplifying assumption that each team has only a "true" season-long 3pt% defense parameter tau. Then one could test the hypothesis that tauA and tauB were statistically indistinguishable at some confidence level by performing a difference-of-means t-test. You'd have nA+nB-2 degrees of freedom, where nA is the number of treys shot against A and nB for B, which should be enough to accept or reject the joint hypothesis that the modeling assumption is true and the means are the same.

More complex models, with game-specific shocks to tau, say, would have fewer d.f.and might not work with the data available.

 
mrjames 
Professor
Posts: 6062

Loc: Montclair, NJ
Reg: 11-21-04
02-24-12 04:52 PM - Post#121956    
    In response to SRP

This is certainly the right thought if we're worried about true randomness - that over a seven to 10 game span the posted 3PT% will differ from what is "true."

I wonder if proving out whether the subset's mean is truly different from the full set's mean is necessary though (or, somewhat by extension, that there is no "true" 3PT shooting mean). The point seems much simpler than that. Three-point field goals are somewhat random, and they can be the catalyst for strange results.

I do agree with the general point of the test, though, if I were seeking to prove the point of whether the means are truly different over that small of a sample.

 
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