PDA

View Full Version : New three point line



riverside6
11-21-2008, 09:32 AM
We just took a look at the new three point line (http://www.scacchoops.com/tt_NewsBreaker_External.asp?NB=1383) comparing 3P% this season to the past 5 seasons and also the percentage of 3 Point shots over the same timeframe.

The differences this season are pretty minimal it would appear.

1. Is it too early to tell?
2. What other factors should be considered?
3. Does this line make a difference?

Matches
11-21-2008, 10:18 AM
Biggest non-story of the year IMO. (And remember Guy Ritchie and Madonna got divorced this year.)

AtlDuke72
12-08-2008, 02:15 PM
I know that a lot of people, including Coach K, have said that the new line does not make a difference. I have to believe that it does make a difference. Does anyone know if there are any statistics out there yet which address this. I know Duke's numbers are down so far but that certainly doesn't prove anything.

riverside6
12-08-2008, 02:25 PM
we took a look at the numbers a couple weeks ago...

New 3 Point Line: Any Effect? (http://www.scacchoops.com/tt_NewsBreaker_External.asp?NB=1383)

We also have a poll running asking our readers their opinion as well.

tbyers11
12-08-2008, 02:26 PM
I know that a lot of people, including Coach K, have said that the new line does not make a difference. I have to believe that it does make a difference. Does anyone know if there are any statistics out there yet which address this. I know Duke's numbers are down so far but that certainly doesn't prove anything.

Ken Pomeroy is keeping track of this on his ratings site (http://kenpom.com/rate.php) (look at the top under the date). For those too lazy to look at the link, this season's 3PT% is 33.9 compared to 35.1 for all of last year. The percentage of 3PT attempts out of total FG attempts this year is 33.2 compared to 34.4 for all of last year.

So there is approximately a one percent decrease in both the 3PT shooting percentage and the amount of 3's being taken. Statistically, it doesn't seem like it is making much of a difference. I am also in agreement with Coach K and the others who don't think it makes a difference. We'll see how it plays out over the course of the season.

Scorp4me
12-08-2008, 02:30 PM
Following the Michigan loss I've tried not to post cause I just didn't want to deal with the non-sense on here, but I want to comment on this. And AtlDuke I'm not saying you've said any non-sense, just wanted to comment on it.

I don't necessarily know about Duke's shooting %'s, but I do know they have taken less threes. I think it has much less to do with that extra foot or 9 inches or whatever it was they added and much more to do with having an actual low post option. No it's not Brand or Battier or Williams, but it's an option. Not to mention having a multitude of play makers and slashers.

And yes we shot way too many 3's in the Michigan game. I would guess it had something to do with Michigan's game plan. But I know at one point in the game we were 1-11 from outside the arc and 11-14 from inside the arc.

So the number of outside jump shots was a concern in the Michigan game most certainly. But, and maybe it's just my perception, I would have to say on the year I've been very pleased with shot selection and lack of reliance on the outside shot.

weezie
12-08-2008, 03:02 PM
I agree w/scorp. It's nice to have this scoring option, something Duke hasn't been able to go to in a while. Everything will jell nicely in time. Seeing the confidence bloom on Zoubek (and LT's) face is worth the early miscues. This is a real team.

AtlDuke72
12-08-2008, 03:24 PM
Following the Michigan loss I've tried not to post cause I just didn't want to deal with the non-sense on here, but I want to comment on this. And AtlDuke I'm not saying you've said any non-sense, just wanted to comment on it.

I don't necessarily know about Duke's shooting %'s, but I do know they have taken less threes. I think it has much less to do with that extra foot or 9 inches or whatever it was they added and much more to do with having an actual low post option. No it's not Brand or Battier or Williams, but it's an option. Not to mention having a multitude of play makers and slashers.

And yes we shot way too many 3's in the Michigan game. I would guess it had something to do with Michigan's game plan. But I know at one point in the game we were 1-11 from outside the arc and 11-14 from inside the arc.

So the number of outside jump shots was a concern in the Michigan game most certainly. But, and maybe it's just my perception, I would have to say on the year I've been very pleased with shot selection and lack of reliance on the outside shot.


I agree with this. My question went only to the difficulty of the shot. I agree that the post play has been a big improvement over last year and is the reason for fewer 3s being taken not counting the Michigan game. The shooting percentages are down a little bit and it would seem they should be improved. 2% nationally seems to bear out that the extra 9 inches does not make much difference.

ArnieMc
12-08-2008, 03:41 PM
From a (very) simple physics standpoint, the extra foot should reduce accuracy by about 5% of made shots or about 1.6 - 2.0% overall.

AtlDuke72
12-08-2008, 04:09 PM
From a (very) simple physics standpoint, the extra foot should reduce accuracy by about 5% of made shots or about 1.6 - 2.0% overall.

Ok, I'll bite. How is this "simple"?

SilkyJ
12-08-2008, 05:40 PM
I know that a lot of people, including Coach K, have said that the new line does not make a difference. I have to believe that it does make a difference. Does anyone know if there are any statistics out there yet which address this. I know Duke's numbers are down so far but that certainly doesn't prove anything.

I think its really obvious to me that several folks like Gerald and Jon and Nolan to an extent do a good job of getting as close to the line as possible. But Greg and and Kyle seem to be taking shots 3-4 feet behind the line (sometimes further) with no one near them and while they are capable of making that shot, I think if they took one step up it and close that gap to the line it would make a very tangible difference.

So i think its a touch of that combined with what has to be a small drop in % from everyone else just b/c its a foot further.


Ok, I'll bite. How is this "simple"?

I'd love to hear the explanation to this as well. Does someone record every shot and distance in college bball to come to an average for each distance?

Lulu
12-09-2008, 03:01 AM
Not to be too much of a geek but just thought I'd point out that even though both percentages (% attempts and % made) have dipped only 1.2% each, it actually comes out to only 93% as many total 3 pointers made in college this year. Assuming statistical significance of this year's numbers and ignoring year-to-year variance etc...

(0.339*0.332)/(0.351*0.344) = 93.2%

So that's not completely insignificant.


I also have to ask about the "simple physics" a previous poster referred to. I decided to look at this myself and, from a very simple standpoint as well, came up with this, which was a quite surprising result:

To determine the change in the % of made field goals due to the increased distance you could simply look at the equivalent size of a hoop at 19'9" compared to an 18" hoop at 20'9". (Imagine you're shooting a rifle at a circular target, and if you miss by x degrees, the maximum size of a circular target you'd still hit at each distance. Yes, it's greatly simplified.)

The truth is, all you have to do is take the ratio of the distances, and then square the ratio because we're actually comparing areas (of circular hoop targets), not lengths.

(237 inches / 249 inches)^2 = 90.6%


This might not be completely clear, so if we wanted to go ahead and compute the actual equivalent hoop sizes here's what we'd get:

An 18" hoop 249" away is equivalent to what size hoop at 19'9"?
Answer: (18/249)*237 = 17.133" diameter hoop
(I did notice this was 95.2% of 18", if that's what the other poster did to get their 5% result.)

Since we're talking about targeting a circular plane, what is the ratio of the areas of these hoops?
Answer: [pi*(17.133/2)^2] / [pi*(18/2)^2] = (17.133/18)^2 = 90.6%


It is worth noting that it doesn't matter what size we consider the appropriate "made basket" target to be; it's all just ratios. We would get the same answer if we wanted to know how many balls would "swish" through and not hit the rim. (A 9" ball through an 18" hoop implies there is a 9" diameter "swish" target at 20'9". At 19'9" the equivlant is 8.57".)

Of course, MANY factors are ignored here, such as energy, distributions, and further geometric considerations. (Most of which I would assume would actually decrease the % further, unless the geometric factors are truly more linear in nature.) In any case, if 90.6% fewer 3's dropped in this year we'd expect the 3pt% to drop to 35.1*0.906 = 31.8%. So the fact that it is 33.9% so far this year almost implies we've got better shooters putting up 3's this year.
Personally, I've always wondered if some shots weren't just mechanically "bad" with little chance of going in, and others that are mechanically "good" with an excellent chance. That's how I feel when I shoot anyway.

Disclaimer: All of the above might be bunk.

hughgs
12-09-2008, 07:24 AM
Ken Pomeroy is keeping track of this on his ratings site (http://kenpom.com/rate.php) (look at the top under the date). For those too lazy to look at the link, this season's 3PT% is 33.9 compared to 35.1 for all of last year. The percentage of 3PT attempts out of total FG attempts this year is 33.2 compared to 34.4 for all of last year.

So there is approximately a one percent decrease in both the 3PT shooting percentage and the amount of 3's being taken. Statistically, it doesn't seem like it is making much of a difference. I am also in agreement with Coach K and the others who don't think it makes a difference. We'll see how it plays out over the course of the season.

Neither analysis linked in this thread has shown that the changes are statistically significant. What are the odds that either change is just due to random variation of the percentages of 3 point FGs made? Until someone does that analysis I don't think you can say one way or the other that the line is having an affect.

AtlDuke72
12-09-2008, 08:57 AM
Not to be too much of a geek but just thought I'd point out that even though both percentages (% attempts and % made) have dipped only 1.2% each, it actually comes out to only 93% as many total 3 pointers made in college this year. Assuming statistical significance of this year's numbers and ignoring year-to-year variance etc...

(0.339*0.332)/(0.351*0.344) = 93.2%

So that's not completely insignificant.


I also have to ask about the "simple physics" a previous poster referred to. I decided to look at this myself and, from a very simple standpoint as well, came up with this, which was a quite surprising result:

To determine the change in the % of made field goals due to the increased distance you could simply look at the equivalent size of a hoop at 19'9" compared to an 18" hoop at 20'9". (Imagine you're shooting a rifle at a circular target, and if you miss by x degrees, the maximum size of a circular target you'd still hit at each distance. Yes, it's greatly simplified.)

The truth is, all you have to do is take the ratio of the distances, and then square the ratio because we're actually comparing areas (of circular hoop targets), not lengths.

(237 inches / 249 inches)^2 = 90.6%


This might not be completely clear, so if we wanted to go ahead and compute the actual equivalent hoop sizes here's what we'd get:

An 18" hoop 249" away is equivalent to what size hoop at 19'9"?
Answer: (18/249)*237 = 17.133" diameter hoop
(I did notice this was 95.2% of 18", if that's what the other poster did to get their 5% result.)

Since we're talking about targeting a circular plane, what is the ratio of the areas of these hoops?
Answer: [pi*(17.133/2)^2] / [pi*(18/2)^2] = (17.133/18)^2 = 90.6%


It is worth noting that it doesn't matter what size we consider the appropriate "made basket" target to be; it's all just ratios. We would get the same answer if we wanted to know how many balls would "swish" through and not hit the rim. (A 9" ball through an 18" hoop implies there is a 9" diameter "swish" target at 20'9". At 19'9" the equivlant is 8.57".)

Of course, MANY factors are ignored here, such as energy, distributions, and further geometric considerations. (Most of which I would assume would actually decrease the % further, unless the geometric factors are truly more linear in nature.) In any case, if 90.6% fewer 3's dropped in this year we'd expect the 3pt% to drop to 35.1*0.906 = 31.8%. So the fact that it is 33.9% so far this year almost implies we've got better shooters putting up 3's this year.
Personally, I've always wondered if some shots weren't just mechanically "bad" with little chance of going in, and others that are mechanically "good" with an excellent chance. That's how I feel when I shoot anyway.

Disclaimer: All of the above might be bunk.

Thanks for making it simple !

ArnieMc
12-09-2008, 09:28 AM
From a (very) simple physics standpoint, the extra foot should reduce accuracy by about 5% of made shots or about 1.6 - 2.0% overall.


Ok, I'll bite. How is this "simple"?I just assumed a constant aiming error. An error of 1% translates to 4.14 inches at the basket from 19'9" or 4.35" at 20'9", an increase of about 5% which implies that 5% fewer shots will go in. There's a similar relationship for force (If you shoot the ball 1% too hard, etc.) I think that the governing parameter is the linear distance from the center of the basket since the ball and rim retain their relative sizes.

There are other factors, of course, such as the speed of the ball from longer distances would make the rims less forgiving, and the extra effort for a longer shot would probably increase the aiming error.

vick
12-09-2008, 01:44 PM
Neither analysis linked in this thread has shown that the changes are statistically significant. What are the odds that either change is just due to random variation of the percentages of 3 point FGs made? Until someone does that analysis I don't think you can say one way or the other that the line is having an affect.

I doubt that it is. My statistics is a little hazy, and I might well be in error, but this is probably a pretty rare result. Assuming the following:

340 teams
7 games per team
40 shots per game
1/3 of shots are threes (I'm estimating the percentage made, not percent of shots that are threes, but the basic point is similar)

gives you ~32000 three pointers attempted so far. Under the old percentage (35.1%), this would lead to 11232 made three pointers. The standard deviation of this is, I think, (32000*35.1%*(1-35.1%))^(1/2), or 85.38.

Under the 2008-09 percentage (33.9%), the number of made three pointers is (32000*33.9%), or 10848.

So the "z" on this is (10848-11232)/85.38, or -4.50. That is, having this few made three pointers on a sample size that large, if the underlying percentage was the same, is a 4.5 sigma event. It's sometimes difficult to even find that rare an event in normal distribution tables, but I believe the odds on the percentage being this low are something like 0.00034%.

Now, that doesn't necessarily mean the new three point line caused this--the underlying assumption is that the sample (that is, 2008-09 percentage) is a fair sample of 2007-08, which of course it is not--conference season hasn't even started. I'm not certain which way this effect goes, to be honest--I don't know if percentages go up as the season progresses (as shooters are in a groove and freshmen are more acclimated) or go down (as teams play tougher defenses). What I believe we can say is that this variance in three point shooting isn't likely pure chance.

UrinalCake
12-09-2008, 01:59 PM
It's tough to compare stats from ALL of last season to stats from this year's partial season... there are more out-of-conference mismatch type games, early season jitters, freshmen who haven't played in college yet, etc. And there's naturally going to be an adjustment period. I think we need at least a full season's worth of data before drawing any conclusions. That said, I'll be curious to learn the impact on TWO-POINT shooting percentage as a result of the line being moved back, as well as any change in overall points scored.

Lulu, I found your mathematical analysis to be intriguing, but I think you've simplified the problem a little too much. A basketball is not shot directly at a round hoop, it follows a parabolic arc and then drops through. And the release point is going to be lower than the hoop (unless you're Gerald Henderson 8-)), complicating the mathematics even further. My instinct tells me that the amount of change imposed by the farther distance to the hoop is lessened because of this.

nyr484
12-09-2008, 02:11 PM
Just a thought... the 3 point percentage dropping from about 35% the last few years to 32.14% this year may not be statistically significant, but it is basketball(y) significant. Here's why... Coaches will tell you that a team is successfully shooting the 3 if they make 1/3 of their 3's. This is because if you shoot the same number of 2's and 3's, and make 50% of your 2's and 1/3 of your 3's, you end up with the same number of points. Still with me? Ok, so if you are above 1/3 on 3's, then the 3 point shooting is paying off. If you are below 1/3, then the 3 point shooting is not paying off. FWIW, Duke is shooting about 31%.

Lulu
12-10-2008, 07:58 PM
It's tough to compare stats from ALL of last season to stats from this year's partial season... there are more out-of-conference mismatch type games, early season jitters, freshmen who haven't played in college yet, etc. And there's naturally going to be an adjustment period. I think we need at least a full season's worth of data before drawing any conclusions. That said, I'll be curious to learn the impact on TWO-POINT shooting percentage as a result of the line being moved back, as well as any change in overall points scored.

Lulu, I found your mathematical analysis to be intriguing, but I think you've simplified the problem a little too much. A basketball is not shot directly at a round hoop, it follows a parabolic arc and then drops through. And the release point is going to be lower than the hoop (unless you're Gerald Henderson 8-)), complicating the mathematics even further. My instinct tells me that the amount of change imposed by the farther distance to the hoop is lessened because of this.

Agree fully, all part of the considerations when I said it was very simplistic. It would be interesting to know the average length of the arc traveled by a shot, but I don't really know how much loft the average player puts on a shot. Really don't even want to start down that road on these boards though, not to mention all the other simplifications and factors that were ignored.

Still, I was surprised. I should have known that when you have a 18" rim and a 20' line, the trade off is approx 1" of rim per 1' of increased distance (ignoring path length again), but I just hadn't considered it. I thought the new distance would be insignificant to shooters, aside from *perhaps* having to relearn their step patterns to get behind the new line.

Of course, when our guys were already shooting 2-3 ft behind the line anyway...

pfrduke
12-10-2008, 10:48 PM
Just out of curiosity, has anyone checked whether last year's 3pt% was representative? When we're talking about differences within two percentage points, it would be useful to know whether last year was in any way aberrant.

BlueintheFace
12-10-2008, 11:47 PM
... only on DBR

tbyers11
12-13-2008, 02:58 PM
Just out of curiosity, has anyone checked whether last year's 3pt% was representative? When we're talking about differences within two percentage points, it would be useful to know whether last year was in any way aberrant.

As a follow-up on this topic, here is an article by John Gasaway on Basketball State (http://www.bbstate.com/features/15) about the effect that an extra foot is having on the 3 point-shot. (I think that you should be able to get to this article without a subscription, but if you can't the data is in the free link below.)

Linked within that article is this website (http://statsheet.com/mcb/beyondthearc) that answers pfrduke's question about how representative the 2007-08 data was to previous years. It goes back to the 1996-97 season and is sortable by each conference and team as well as for Division I as a whole. Some really fine work here shows that the 1.2% YTD decrease may be a little more meaningful than I previously thought, at least from a statistical sense.

pfrduke
12-13-2008, 03:41 PM
Thanks for the link. One interesting thing to note from Duke's page - as much as people here complain about "live by the three, die by the three," the one season in the past 10 during which we shot (and made) the most 3s per game was 00-01. And it's by a lot, too - at least two more attempts for game than any other season.

hughgs
12-13-2008, 05:33 PM
I doubt that it is. My statistics is a little hazy, and I might well be in error, but this is probably a pretty rare result. Assuming the following:

340 teams
7 games per team
40 shots per game
1/3 of shots are threes (I'm estimating the percentage made, not percent of shots that are threes, but the basic point is similar)

gives you ~32000 three pointers attempted so far. Under the old percentage (35.1%), this would lead to 11232 made three pointers. The standard deviation of this is, I think, (32000*35.1%*(1-35.1%))^(1/2), or 85.38.

Under the 2008-09 percentage (33.9%), the number of made three pointers is (32000*33.9%), or 10848.

So the "z" on this is (10848-11232)/85.38, or -4.50. That is, having this few made three pointers on a sample size that large, if the underlying percentage was the same, is a 4.5 sigma event. It's sometimes difficult to even find that rare an event in normal distribution tables, but I believe the odds on the percentage being this low are something like 0.00034%.

Now, that doesn't necessarily mean the new three point line caused this--the underlying assumption is that the sample (that is, 2008-09 percentage) is a fair sample of 2007-08, which of course it is not--conference season hasn't even started. I'm not certain which way this effect goes, to be honest--I don't know if percentages go up as the season progresses (as shooters are in a groove and freshmen are more acclimated) or go down (as teams play tougher defenses). What I believe we can say is that this variance in three point shooting isn't likely pure chance.

I agree with your math (and having the book near me certainly helps). But, I don't agree with your attempt to ascertain the number of successful three point shots. I think a better idea would be to simply use the percentages from the previous years as a baseline. Then, use that data to find the standard error and resultant z-score. That would avoid the issue of whether last year was a "normal" year (as noted in another post) and would also avoid any of the assumptions you made above. And if someone is worried about the differing number of shots between different year you could weight the percentages.

But, since noone has done that analysis (and I'm too lazy to do it) I will concede that you are correct. At least until someone else addresses my concerns :).

gep
12-22-2008, 07:45 PM
Got this from the goduke.com link on DBR with post-game quotes...

From Coach K:

"It was a court that had one (three-point) line; they had Duke in one Xavier in another (lane). It was really classy. I told my staff I said you know what, it’s like going to the best restaurant. It was done well. They had an NBA game last night and they have one tonight. They have to bust their rear ends to make that happen. I just think that extra attention sets the stage for some good things. They have always done that. They have always done that. It’s always been an honor for us to be here. Having that one damn line is better, it’s just better."

http://www.goduke.com/ViewArticle.dbml?DB_OEM_ID=4200&ATCLID=3636199

Seems like Coach K doesn't like the two 3-point lines, and maybe it does have an effect on 3-point shooting? Or is he just tallking about how the court looks?

-jk
12-22-2008, 08:28 PM
I don't think any college coach likes an NBA 3 pt line. I doubt two college lines is a problem since most everyone has one.

- jk

gep
12-22-2008, 11:34 PM
I thought Coach K was specifically talking about the two college 3-point lines... that are usually on college game arenas... :) One college 3-point line, like the Xavier game, and no NBA 3-point line, did look "clean" on the court. I'm not sure, but I thought I even saw a college game with three 3-point lines on the court... but could definitely be mistaken:rolleyes:

gofurman
02-13-2009, 03:36 PM
Here is what everyone is shooting this year (ytd -

1. North Carolina 24 176 453 .389
2. Miami 23 177 468 .378
3. Clemson 23 174 468 .372
4. NC State 22 138 377 .366
5. Boston College 26 169 496 .341
6. Virginia Tech 23 134 397 .338
7. Duke 24 166 494 .336
8. Florida State 24 144 433 .333
9. Wake Forest 22 90 273 .330
10. Maryland 23 120 394 .305
11. Virginia 20 109 369 .295
12. Georgia Tech 23 99 336 .295

Does anyone have what the teams shot last year? THANKS!

CDu
02-13-2009, 05:42 PM
Here is what everyone is shooting this year (ytd -

1. North Carolina 24 176 453 .389
2. Miami 23 177 468 .378
3. Clemson 23 174 468 .372
4. NC State 22 138 377 .366
5. Boston College 26 169 496 .341
6. Virginia Tech 23 134 397 .338
7. Duke 24 166 494 .336
8. Florida State 24 144 433 .333
9. Wake Forest 22 90 273 .330
10. Maryland 23 120 394 .305
11. Virginia 20 109 369 .295
12. Georgia Tech 23 99 336 .295

Does anyone have what the teams shot last year? THANKS!



Here's the stats from last year (and I apologize if this doesn't turn out right):

BC 184 511 .360
Clem 271 728 .372
Duke 308 816 .377
FSU 234 665 .352
GT 214 575 .372
UMd 182 539 .338
UM 236 613 .385
UNC 216 580 .372
NCSU 176 505 .349
UVa 274 748 .366
VT 192 570 .337
WF 189 518 .316

CDu
02-13-2009, 05:53 PM
So by comparison, some teams' 3pt fg% have gotten worse:

GT -.077
UVa -.071
Duke -.041
UMd -.033
FSU -.019
BC -.019

Some have gotten better:

UNC +.017
NCSU +.017
WF +.014
UM +.007

Clemson and VT are at basically the same percentage.

gofurman
02-13-2009, 11:10 PM
So by comparison, some teams' 3pt fg% have gotten worse:

GT -.077
UVa -.071
Duke -.041
UMd -.033
FSU -.019
BC -.019

Some have gotten better:

UNC +.017
NCSU +.017
WF +.014
UM +.007

Clemson and VT are at basically the same percentage.

even as stated that is 6 worse, 4 better and 2 even,,

but also look at how much those are better are better - avg .014
as opposed to how much the worse are worse - avg .043 ! That's significant. Tough on Duke as we like to go outside a lot