Adjusting three point shooting statistics

[threrf23]

Hey guys,

Couple months ago I put together something to submit to a Houston Rockets internship contest on the subject of trying to predict each NBA player’s three point shooting percentage on a yearly basis. I’ve held back previously, and I might try to tweak this out maybe get it posted to 82games.com, but now I am sharing what I came up with - this will be in a series of a few posts. I found my findings to be pretty interesting.

A large part of what I did was find a way to adjust players’ three point shooting stats to account for the team they played on and its statistical ability to foster good looks from beyond the arc, the role they likely played for their team, and to a lesser extent, the quality of their shot selection. This way trends in three point shooting are more easily examined/understood/predicted. While you can take players’ scores and apply anticipated age adjustments and such, what I found very interesting is that many players’ three point shooting performances seemed to at times follow logical graphical patterns after their stats had been adjusted (although the graphical pattern often differed from player to player).

The scoring system I came up with approximately breaks down as follows:

.20 < : all time great
.16 - .20: elite shooter
.13 - .16: excellent shooter
.09 - .13: very good shooter
.07 - .09: good shooter
.05 - .07: above average shooter
.035 - .05: capable shooter
.02 - .035: below average shooter
.005 - .02: poor shooter
< .005: liability

What I came up with exactly, is posted right here:

http://www.criteriondynamics.com/prospectus.pdf

Some quick notes before you pull that up –

1.) My calculations for the second half of the ’07-08 season are slightly off due to a small error on my part. Players’ scores for the second half of that season may be skewed 10-20% in any direction unfairly.

2.) The “likely to decline” list for the ’07-08 season contains incorrect scores.

3.) For the ’06-07 season, I mixed up Josh Smith’s stat lines with Jason Smith (who wasn’t in the league)

I’ll fix that stuff eventually.

Some random player examples, which I feel make for the best validations:

Jason Terry:

’03-04 (ATL, age 26): .090
’04-05 (DAL, age 27): .108
’05-06 (DAL, age 28): .143
’06-07 (DAL, age 29): .105
’07-08 (DAL, age 30): .090

I think this is the best validation I could provide, because you have a guy who moved from a bad ATL team to a good Mavericks team, and was asked to play different roles for that Dallas team, and yet his three point shooting clearly seems to show an exact graphical pattern nonetheless. It would be easier to predict his next year’s performance if calculations were done for the ’02-03 season, but my guess is he continues to decline a little bit before leveling out somewhere around .06-.07 after he hits 32.

Ben Gordon:

’04-05 (CHI, age 21): .075
’05-06 (CHI, age 22): .092
’06-07 (CHI, age 23): .127
’07-08 (CHI, age 24): .137

The encouraging thing about Ben Gordon is that his shooting shows consistent year by year improvement. However, he is past the age of 23 (most improvement tends to occur then), and his margin of improvement seems to be getting smaller (his scores seem to fall on a curve). My guess is he continues improving for a few years though, and eventually peaks somewhere around .16.

[threrf23]

Celtics –

Ray Allen:

’03-04 (SEA, age 28): .135
’04-05 (SEA, age 29): .134
’05-06 (SEA, age 30): .203
’06-07 (SEA, age 31): .135
’07-08 (BOS, age 32): .109

As you can see Ray Allen declined slightly this past season – but that was to be expected after turning 32. Most players – particularly those who have not previously declined – tend to decline during the season at which they are 32 years old from the get go. Anthony Parker was another three point shooter who was 32 years old at the beginning of the season, and his score declined by a very similar amount as well this past season.

If you go beyond this past season – in ’05-06 Ray went bazonkas and set a .203 mark which serves as best in league over the past five seasons and probably beyond. Aside from that, his .135 performances in themselves were nothing amazing, but were very impressive considering the exact degree of Ray’s year by year consistency. He probably stays consistently around .11 over the next few seasons, making him fairly comparable to a current day Michael Redd.

Paul Pierce:

’03-04 (age 26): .074
’04-05 (age 27): .08
’05-06 (age 28): .075
’06-07 (age 29): .137
’07-08 (age 30): .089

His score in ’06-07 might be slightly skewed in his favor since year long team stats were used to adjust his stats, and our team absolutely sucked when he wasn’t playing due to injury. But it seems he peaked that year. Pre-2006, its possible he would have scored higher if he was more motivated playing for a better team, but his scores were still decent. Objectively, he probably posts a .08 somethin next season before falling down closer to .07 a year from now when he is 32.

James Posey:

’03-04 (MEM, age 27): .101
’04-05 (MEM, age 28): .008
’05-06 (MIA, age 29): .087
’06-07 (MIA, age 30): .073
’07-08 (BOS, age 31): .054

Posey’s .008 in ’04-05 can be ignored as it was likely due to injury. However – even if my formula isn’t perfect – it seems clear that he has been on the decline for the past three seasons now, and he is coming up on the magical age of 32. There’s a decent chance he’s still a capable shooter over the next couple of seasons, and three point shooting isn’t close to being everything, but this would indicate that we did well to not match the Hornets’ offer.

Eddie House:

’03-04 (LAC, age 26): .01
’04-05 (SAC, age 27): .013
’05-06 (PHX, age 28): .028
’06-07 (NJN, age 29): .023
’07-08 (BOS, age 30): .04

In the past, House is possibly hurt by not playing many minutes per game, and possibly by injury (with NJ, at least). This is interesting though because it seems to indicate that while a respectable scorer persay, he has been an overrated three point shooter (by fans). That said he shows consistent year by year improvement for the most part. My best guess is he peaks next season around .05 before falling off considerably thereafter,

Tony Allen:

’04-05 (age 22): .006
’05-06 (age 23): .007
’06-07 (age 24): .017
’07-08 (age 25): .002

This basically tells us what we already know, but his .017 last season is enough to give us at least some hope, as he wouldn’t be expected to peak for another few seasons anyway.

FWIW, Rondo:

’06-07 (age 20): .0006
’07-08 (age 21): .0006

[threrf23]

Some interesting non-Celtic Examples:

Jason Richardson:

’03-04 (GSW, age 23): .044
’04-05 (GSW, age 24): .085
’05-06 (GSW, age 25): .132
’06-07 (GSW, age 26): .026
’07-08 (CHA, age 27): .197

His performance in ’06-07 must have been due to injury. This is interesting because the drastic improvement J-Rich has shown on a year by year basis would seem to indicate that he may work harder on his long range shot than anyone else in the league. Back in 2006, looking at his previous statistics, you may have guessed a score somewhere around .165 in ’06-07, and something around .20 in ’07-08 – and that is what happened. But there comes a point when you can no longer improve, and given how high his score was last season, there’s a decent chance he is at that point.

Tracy McGrady:

’03-04 (ORL, age 24): .172
’04-05 (HOU, age 25): .078
’05-06 (HOU, age 26): .026
’06-07 (HOU, age 27): .052
’07-08 (HOU, age 28): .015

The extent to which he has fallen off in recent years is interesting. Is it his knees? Or is he a lazy mofo? Or has he just been focusing on other parts of his game?

Jason Kapono:

’03-04 (CLE, age 22): .031
’04-05 (CHA, age 23): .042
’05-06 (MIA, age 24): .008
’06-07 (MIA, age 25): .11
’07-08 (TOR, age 26): .032

Kapono was penalized at least slightly his rookie season, and his first season in MIA, due to playing time. Nevertheless, his .11 performance seemed to come out of nowhere at the age of 25 in a contract year. This could have suggested a possibility that it was a fluke. Next year, we find out for sure whether that is the case.

Mike Miller:

’03-04 (MEM, age 23): .069
’04-05 (MEM, age 24): .12
’05-06 (MEM, age 25): .126
’06-07 (MEM, age 26): .164
’07-08 (MEM, age 27): .134

He seems to take a large step forward, then a small step forward or back, and low motivation due to playing on a bad team may kick in at times. Objectively, I think it would seem logical to expect him to peak somewhere around .17 or .18 over the next few seasons. This is partially why Pogue is so high on him.

JR Smith:

’04-05 (NOH, age 19): .034
’05-06 (NOH, age 20): .027
’06-07 (DEN, age 21): .145
’07-08 (DEN, age 22): .157

Back in 2006, JR Smith did not appear to be a great three point shooter. But as a less than physically developed guy under the age of 21, he wasn’t supposed to be one. In fact, in context, his .034 showing his rookie season was impressive (and coincidentally almost exactly equals what Kevin Durant posted this past season). The next season, he declined maybe due to injury or playing time, but significantly improved his FT% indicating he was working on his shot. When he hit 21 – the age when most players finally seem physically fit to contribute from long range – this translated into a surprisingly predictable (if you read the PDF) .145 the next season, and then he continued to improve the season after, posting close to a .20 in the second half of last season. If you were to adjust players’ scores based on their age and what they would have likely posted if they were in their prime or at their peak, JR Smith would be right up there with Reggie Miller, possibly head and shoulders above the rest of the league in recent years.

And, this is taking into account that he played on a team conducive to getting good looks from behind the arc, and that some of his shot opportunities were likely to be as a result of being on the floor alongside Carmelo and AI, and to a lesser extent that his shot selection probably could have been at least slightly better.

Andre Iguodala:

’04-05 (PHI, age 21): .034
’05-06 (PHI, age 22): .044
’06-07 (PHI, age 23): .032
’07-08 (PHI, age 24): .076

Last year’s mark may or may not have been a fluke, but it does seem that he is an underrated shooter, and when viewing his percentages from last year, you must consider that he was a primary option on a team that lacked much of any inside or outside presence.

[threrf23]

League’s top 10 shooters, by season:

2007-08: Jason Richardson, JR Smith, Peja Stojakovic, Ben Gordon, Mike Miller, Rashard Lewis, Rashad McCants, Manu Ginobili, Andres Nocioni, Damon Jones

2006-07: Gilbert Arenas, Mike Miller, Brent Barry, Rashard Lewis, JR Smith, Paul Pierce, Ray Allen, Ben Gordon, Luther Head, Joe Johnson

2005-06: Ray Allen, Gilbert Arenas, Kyle Korver, Jason Terry, Chauncey Billups, Jason Richardson, Mike Miller, Kobe Bryant, Mike James, Peja Stojakovic

2004-05: Damon Jones, Kyle Korver, Donyell Marshall, Gilbert Arenas, Rashard Lewis, Peja Stojakovic, Ray Allen, Chauncey Billups, Jamal Crawford, Mike Miller

2003-04: Tracy McGrady, Peja Stojakovic, Eddie Jones, Ray Allen, Reggie Miller, Brent Barry, Mo Pete, Chauncey Billups, Donyell Marshall, Gilbert Arenas

[s1ickd]

Good stuff, very interesting.

surprised micheal redd is nowhere t be found on those lists.

Wheres Jiri Welsch, wasn't he supposed to be a "shooter?" lol

[threrf23]

Good stuff, very interesting.

surprised micheal redd is nowhere t be found on those lists.

Wheres Jiri Welsch, wasn't he supposed to be a "shooter?" lol

Redd's been top 20 for 4 of the past 5 seasons, and top 11 two of the past three seasons. He just hasn't hit the top 10. Definitely one of the league's best shooters if you factor in his consistency, just not in the top tier.

If you average each player's league rank over the past five seasons, you get a top ten of:

Ray Allen, Chauncey Billups, Peja Stojakovic, Mike Miller, Rashard Lewis, Brent Barry, Jason Terry, Manu Ginobili, Michael Redd, and Gilbert Arenas. If you extend to the top 15, you also get Steve Nash, Kobe Bryant, Paul Pierce, Damon Jones, and Jamal Crawford. Lebron comes in at #24, but he's a bit younger than those listed.

Jiri...ahaha..Jiri...he had mental issues, he was a good shooter when he wanted to be badly enough.

[crm0922]

How was Gilbert Arenas #1 in 06-07 with 42% FG and 35% 3p%? Those aren't even great numbers individually, let alone combined in some magical fashion.

I just don't understand how your system could have skewed it so that a guy chucking up 584 3-pointers at 35% is the top shooter in the league.

Your system seems to reward being a chucker. And I don't even have a problem with him as a player, but purely as a shooter, he only scares me about as much other shooters with similar stats.

C

PS - TRIVIA: Did you know that in 03-04 Gilbert Arenas attempted more 3's than FT's?

[threrf23]

I just don't understand how your system could have skewed it so that a guy chucking up 584 3-pointers at 35% is the top shooter in the league.

Your system seems to reward being a chucker. And I don't even have a problem with him as a player, but purely as a shooter, he only scares me about as much other shooters with similar stats.

It awards being a being a chucker - to some extent - but then it subsequently punishes those who are non-efficient offensive players (relative to their teamates at least). Arenas might take a lot of threes, but going by TS%, he is regularly the most efficient offensive option on his team. So statistically, by the formula used, it is assumed that a.) there is nothing wrong with his quantity because it was better him put up a shot than someone else on his team - i.e. he is deemed to have good shot selection, and b.) opponents are likely do their homework and more likely to be providing added defensive attention to him rather than his teammates - making it harder for him to maintain a certain percentage. And, even if Arenas could have shot a higher percentage, chances are the threat he presented by his shot helped create better scoring opportunities for his teammates.

So, the system rewards being a chucker to some extent - after all the more shots one can afford to pass up, the easier it is to maintain a certain percentage. Statistically, Gilbert Arenas shouldn't be passing up so many shots because its better he plays his offensive game than his teammates - because on average more points result. The system rewards chucking - but it doesn't reward Antoine Walker by any means. Looking back to 02-03, 04-05, I forget his exact rank, but even if you adjusted TS% based on MP and GP, he ranked I think maybe 7th/8th on our team. So for Antoine, it was assumed he was very likely to be on the floor with three or four other players that were more efficient than him, and therefore opponents were more likely to let him get good looks (and it was deemed that his quantity was bad quantity).

FWIW, JR Smith in this system would appear to already be an all time great or close to it if he wasn't knocked down for ranking third on his team in overall adjusted efficiency this season, and fourth the season before.

Antoine, despite being a chucker, regularly scored as a below average borderline poor three point shooter by this system, except for two seasons I think 04-05 and 05-06 when he peaked just very slightly above average. Its all not perfect but for the most part I feel it seems to work pretty well.

[Rocky5000]

So it sounds like you assume somewhere in your analysis, that the other team will be more likely to stay with the most efficient player and leave the lesser shooters open. I don't know if that is always true, a variety of teams do "try to make the other guys beat" them, but some teams with good individual defenders will only give a star single coverage and stay home on the other players, otherwise known as the "he can't beat us himself" approach to defense.

How did you derive your model? Did you start with the data and find a model?

[threrf23]

So it sounds like you assume somewhere in your analysis, that the other team will be more likely to stay with the most efficient player and leave the lesser shooters open. I don't know if that is always true, a variety of teams do "try to make the other guys beat" them, but some teams with good individual defenders will only give a star single coverage and stay home on the other players, otherwise known as the "he can't beat us himself" approach to defense.

How did you derive your model? Did you start with the data and find a model?

Well, players' TS% (adjusted for minutes/games played) is compared with their teammates' TS% as part of the overall formula. Yes, it is assumed that their team rank indicates a likelihood of how much defensive attention they were likely to receive.

But, the other main thing this accomplishes, and this is initially how I came to this part of the formula - is it provides a simple enough - and for the most part an effective enough - way to judge a player's shot selection tendencies. This accomplishes two things: first and foremost, it helps discriminate the bad quantity (Antoine Walker, Willie Green), against the good quantity (Ray Allen, Kyle Korver, etc). It would not be fair to not adjust player's statistics based on quantity, IMO, and I felt something needed to be done to this extent to not reward the Antoine Walker's of the league for their quantity.

Moreover, its like this - if you take a player from the Knicks and trade him to the Suns, he should be able to shoot a better percentage. But if he has bad shot selection, he might not be able to take full advantage of the new team/scenery. Theoretically.

So, this is done to judge a player's shot selection as well as to estimate the type of defense a player may have had to deal with.

Really, I just started with a base formula accounting for percentage and quantity of attempts, and found a logical way to adjust results based on team statistics (obviously, I don't think anybody really thinks Joe Johnson fell off big time when he left the Suns, he just moved to a team that lacked a post presence, lacked other outside shooters, and had not other major scorers to detract defensive attention).

After that, I wanted to throw in some measure to judge a player's shot selection quality, especially after realizing Antoine Walker sometimes scored nicely as the formula had then existed. That offended me. I figured shot selection could not be judged without comparing a player's stats to his teamates', and then used Joe Johnson as an initial case example, and experimented a slight bit so that he and other players' scores would seem to follow logical enough patterns.

Its imperfect in theory. But it seems to work well enough in practice if you consider general perception of the league's best shooters, and considering the fact that so many player's scores seem to follow logical patterns according to their age and such - I made no effort to see that happen, its just something that I considered to be something of a validation. And really, while imperfect in theory, it is for the most part logical in theory

I'm sure the formula (or method or whatever) can be improved upon, but after a lot of examination myself, I think it would be rather challenging to come up with something much better unless maybe you had access to some comprehensive and/or proprietary databases.

Quick sidenote, when talking about Jason Kapono above - I misread my spreadsheet - he scored tops on MIA in 06-07 in terms of overall efficiency. He just didn't score all that high partially because he only took so many shots (easier to shoot a good percentage if you are extra selective, plus the more you shoot the more defensive attention you are likely to get if you have good shot selection), and then you consider that he was playing on a team that was elatively conducive to his ability to get good looks from beyond the arc to begin with. I'll have to edit that out above

[celticfan42487]

This is okay stat for trying to seperate 3 point shooters.

But no matter how you adjust the shot stat for 3 pointers, it isn't going to tell us who is the better player even if a 35% 3 point shooter averages a higer point per made shot then a 50% fg shooting Center.

Although it looks like you did a lot of work putting up the original 5 posts in this thread.