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2011 APBRmetric All-Stars

Posted by Neil Paine on February 9, 2011

Just as we did last season, let's take a look at which players would have made the All-Star teams if various advanced stats were the only criteria in the voting. To pick teams, I used the official positional designations from the 2011 ballot; each team must have 4 guards, 4 forwards, and 2 centers, with room for 2 wild cards from any position to fill out the roster. Players in bold are starters; "*" designates the player as a member of the real-life All-Star team.

Win Shares

Eastern Conference Western Conference
Guards Guards
Dwyane Wade* MIA 7.9 Chris Paul* NOH 11.0
Derrick Rose* CHI 7.3 Kobe Bryant* LAL 7.2
Ray Allen* BOS 6.9 Manu Ginobili* SAS 7.1
D.J. Augustin CHA 5.3 Deron Williams* UTA 6.8
Forwards Kevin Martin HOU 6.4
LeBron James* MIA 9.7 Forwards
Paul Pierce* BOS 7.7 Pau Gasol* LAL 9.2
Elton Brand PHI 6.3 Kevin Love* MIN 8.5
Chris Bosh* MIA 6.1 Kevin Durant* OKC 7.2
Amare Stoudemire* NYK 5.8 Lamar Odom LAL 7.2
Luol Deng CHI 5.6 LaMarcus Aldridge POR 6.5
Center Center
Dwight Howard* ORL 8.6 Tyson Chandler DAL 6.5
Al Horford* ATL 7.5 Nene Hilario DEN 6.3

Adjusted +/- (minimum 751.58 minutes)

Eastern Conference Western Conference
Guards Guards
Keyon Dooling MIL 12.68 Earl Watson UTA 14.98
Derrick Rose* CHI 11.70 Deron Williams* UTA 13.61
Landry Fields NYK 8.88 Steve Nash PHX 13.47
Dwyane Wade* MIA 7.61 Mike Conley MEM 12.88
Forwards Manu Ginobili* SAS 11.11
Paul Pierce* BOS 11.04 Stephen Curry GSW 11.10
LeBron James* MIA 10.96 Forwards
Kevin Garnett* BOS 10.42 LaMarcus Aldridge POR 15.26
Thaddeus Young PHI 10.14 Dirk Nowitzki* DAL 13.63
Gerald Wallace CHA 9.50 Paul Millsap UTA 13.54
Josh McRoberts IND 9.23 Pau Gasol* LAL 11.69
Center Center
Roy Hibbert IND 14.15 Emeka Okafor NOH 9.19
Brook Lopez NJN 10.62 Nene Hilario DEN 7.53

Statistical Plus/Minus (minimum 752 minutes)

Eastern Conference Western Conference
Guards Guards
Dwyane Wade* MIA 6.35 Chris Paul* NOH 11.53
Rajon Rondo* BOS 5.12 Manu Ginobili* SAS 7.15
Derrick Rose* CHI 4.71 Kobe Bryant* LAL 6.06
Ray Allen* BOS 2.77 Deron Williams* UTA 5.04
Forwards Russell Westbrook* OKC 4.38
LeBron James* MIA 8.60 Kevin Martin HOU 4.25
Kevin Garnett* BOS 5.90 Forwards
Paul Pierce* BOS 4.85 Dirk Nowitzki* DAL 5.26
Carlos Boozer CHI 4.20 Kevin Love* MIN 5.17
Andre Iguodala PHI 3.93 Kevin Durant* OKC 4.94
Center Pau Gasol* LAL 3.57
Dwight Howard* ORL 6.66 Center
Al Horford* ATL 4.86 Nene Hilario DEN 4.29
Joakim Noah CHI 4.27 Tyson Chandler DAL 3.24

PER (minimum 752 minutes)

Eastern Conference Western Conference
Guards Guards
Dwyane Wade* MIA 25.2 Chris Paul* NOH 26.0
Derrick Rose* CHI 22.9 Kobe Bryant* LAL 24.8
Joe Johnson* ATL 18.8 Russell Westbrook* OKC 24.0
Louis Williams PHI 18.6 Steve Nash PHO 23.3
Forwards Deron Williams* UTA 22.8
LeBron James* MIA 27.0 Kevin Martin HOU 22.7
Amare Stoudemire* NYK 24.1 Forwards
Carlos Boozer CHI 21.5 Kevin Love* MIN 24.5
Kevin Garnett* BOS 21.1 Kevin Durant* OKC 24.2
Paul Pierce* BOS 20.0 Dirk Nowitzki* DAL 23.9
Elton Brand PHI 19.6 Pau Gasol* LAL 23.6
Center Center
Dwight Howard* ORL 25.3 Nene Hilario DEN 21.5
Al Horford* ATL 22.5 Tyson Chandler DAL 18.9

This year's consensus (mentioned on at least 3 teams) would be:

Deron Williams, Utah; Derrick Rose, Chicago; Dwyane Wade, Miami; LeBron James, Miami; Nene Hilario, Denver; Pau Gasol, Lakers; Paul Pierce, Boston; Al Horford, Atlanta; Chris Paul, New Orleans; Dirk Nowitzki, Dallas; Dwight Howard, Orlando; Kevin Durant, Oklahoma City; Kevin Garnett, Boston; Kevin Love, Minnesota; Kevin Martin, Houston; Kobe Bryant, Lakers; Manu Ginobili, San Antonio; Tyson Chandler, Dallas.

That's 18 out of the 24 available slots. If we fill the rest with players mentioned on 2 teams, we get these 2011 APBRmetric All-Star Teams:

Eastern Conference Western Conference
Guards Guards
Derrick Rose* CHI Deron Williams* UTA
Dwyane Wade* MIA Chris Paul* NOH
Ray Allen* BOS Kevin Martin HOU
Forwards Kobe Bryant* LAL
LeBron James* MIA Manu Ginobili* SAS
Paul Pierce* BOS Forwards
Kevin Garnett* BOS Pau Gasol* LAL
Elton Brand PHI Dirk Nowitzki* DAL
Amare Stoudemire* NYK Kevin Durant* OKC
Carlos Boozer CHI Kevin Love* MIN
Center Center
Al Horford* ATL Nene Hilario DEN
Dwight Howard* ORL Tyson Chandler DAL

All that's left is determining the final East guard and the final wild-card for the West. So I'll put those to a vote by our readers:

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142 Responses to “2011 APBRmetric All-Stars”

  1. Nick Says:

    2 things stand out: The PER starting line-up for the East is the actual Eastern All-Star team, and two of the Western starters show up exactly nowhere: Yao (obviously) and Melo.

  2. Jason J Says:

    Someone tell adjusted +/- that half a season of data is half a season of useless, Mr. Dooling.

  3. Anon Says:

    Why do people say Rose is the MVP again?

  4. EvanZ Says:

    My ezPM All-Stars:

    West
    Paul 6.72 (G)
    Love 6.14 (F)
    Bryant 5.75 (G)
    Nash 5.54 (G)
    Ginobili 5.43 (G)
    Gasol 4.95 (F)
    Odom 4.25 (F)
    Griffin 4.05 (F)
    Randolph 3.90 (WC)
    Nene 3.85 (C)
    Chandler 3.82 (C)
    Gay 3.48 (WC)

    East
    Howard 7.17 (C)
    James 6.80 (F)
    Wade 6.07 (G)
    Pierce 5.64 (F)
    Iguodala 4.85 (F)
    Horford 4.38 (C)
    Garnett 4.26 (F)
    Johnson 3.90 (G)
    Rondo 3.88 (G)
    Fields 3.71 (G)
    Allen 3.45 (WC)
    Rose 2.73 (WC)

  5. DSMok1 Says:

    For APM, you should use the RAPM for this year only: link

    I'll mention that I did an ASPM all-star report here.

  6. Jason J Says:

    People think Rose is the MVP because he plays for a major market team that has a lot of wins despite missing time from its starting center and powerforward, and he's a dynamic lead guard.

    I don't see how he could get it ahead of Chris Paul if you want to reward a point guard for carrying a banged up squad to a good record and being statistically dominant. But I guess Chicago's record is a little better, so there's that.

  7. Anon Says:

    Chicago's record is better, but looking at these metrics they also have a more consistent core than New Orleans. After CP3 and D. West, you don't see as many Hornets players occupying these value lists as you see Bulls players, nor are they ranked as high.

    Rose has played well this season. But CP3 is playing on another level - maybe some commercials with Ken Jeong will get him more exposure?

  8. AYC Says:

    Count me among the unwashed masses who believe Rose should be MVP. Advanced stats don't love him because he has a low FT rate. That's really the only area where he underperforms, and it's an area that many advanced stats overvalue IMO. Why should we value players based on the whims of refs, who have to blow the whistle before a FT can be attempted? (for the same reason, I think advanced stats in baseball overvalue walks)

  9. Joe Schaller Says:

    The most important consideration of all, the second half of last season, the stretch run going into the playoffs. We're just going to ignore the impressive performances of Steve Nash and Zach Randolph during that period and the less than stellar performance of Rajon Rondo? I would like to see the combined numbers for the two seasons.

  10. Drew Says:

    Help??
    Can someone tell me percentage wise, the direct corolation
    of the team that has more rebounds than their opponet, and the % of
    wins that comes from that scenerio?? Am I making since?
    Basically, how often does the team with the most Rebounds, win that Game??
    Thanks

  11. Zeiram Says:

    One thing that is obviously at fault here. The center position in the west is weak and de facto no real center made it to them team. Which makes the real west team stronger than the advanced stat team. Secondly win shares is astoundingly good in picking the allstars, I never would have thought that.

  12. Ian Says:

    LaMarcus Aldridge is also listed on 2 teams.

  13. Greyberger Says:

    That's really the only area where he underperforms, and it's an area that many advanced stats overvalue IMO. Why should we value players based on the whims of refs, who have to blow the whistle before a FT can be attempted? (for the same reason, I think advanced stats in baseball overvalue walks)

    Ah, so that explains it. You're crazy, you know, but now I understand you my brother.

  14. DWarner Says:

    Great post again. Gotta love advanced metrics!

    This clearly demonstrates why all this talk about Carmelo to NY and Carmelo to LA is irrelevant! His name is nowhere on any of these lists indicating he is basically a single dimensional performer who shouldn't be considered a top 25 talent. LA and NY fans are getting all geeked up at a proposition that in all likelihood will hurt their franchises...

  15. AYC Says:

    Greyburger, don't you have copy and paste?

    Here's my point: a player who shoots from the field is taking responsibility for his own fate. The player who throws himself at the defender hoping for a call is depending on the refs to bail him out. Sometimes he will get the call, and sometimes the ref will swallow the whistle. Sometimes he will get the call when he doesn't deserve it, and sometimes he won't get a call that he does deserve. And some players will get calls just because of who they are, while others will have calls go against them because of who they are. Btw, size is another reason for Rose to try to avoid contact; he is only 6'2; players that size who play recklessly tend to have inury problems and shortened careers.

  16. nms Says:

    Rose gets MVP buzz from those who are overly twisted up about what "valuable" means, seeing that as a reason to select someone other than the best player in the league. Once you introduce that twist, it's too easy to let the big market effect creep in. Paul is clearly both better and more valuable, particularly since it's harder to generate a better record in the brutal Southwest division of the West than in the, well, brutal Central in the East. Have the teams swap divisions, and NO probably does even better than Chicago has.

  17. Craig W. Says:

    All this proves is that stats aren't any more consistent than voting fans. Gee! Isn't that a revelation?

  18. The J Says:

    Nick said "two of the Western starters show up exactly nowhere: Yao (obviously) and Melo.". Actually you can make that three, as Tim Duncan shows up nowhere as well, but perhaps this is his lifetime achievement award.

    Joe Schaller, why would you consider the previous season for this year's all-star team. Doing so would not reward a player for turning things around or showing improvement. Just as doing so might reward a player for playing well one season, even though they have crashed this season. Take your Rondo example as a scenario. He would be punished for a bad last half of last year, while a player that was injured last season might be spared. Doesn't his solid first half of this season justify an all-star appearance?

  19. AYC Says:

    Personally, I'm glad there is no set criteria for MVP. Let the voters consider whatever information they think is relevent. If we based the MVP on some formula, David Robinson would have 4 or 5. It's not the "best player in the league according to your preferred metric" award.

    Is Paul "clearly" the better player than Rose? Not so fast.... Who plays more MPG? Who has the higher usage? Who is the better scorer? Whose team relies on whom more? Who is better at breaking down the defense?

  20. Dollar Man Says:

    Great post! Advanced statistics are getting more and more attention in the media and in front offices. Ask Erik Spoelstra about their importance. The reason for the Heat's strong play of late is a keen understanding of these data and how to apply them with actual NBA players in actual games. Don't be fooled: this stuff is real and underscores just how great Lebron James, Chris Paul, Dwight Howard Kevin Love, Paul Pierce and Dwyane Wade truly are.

  21. Anon Says:

    They already have a penalty for players who throw themselves into other player though, AYC. It's called the offensive foul.

    I think you're reaching a bit here. The refs aren't "out" to keep Rose from getting to the foul line.

    "Who plays more MPG? Who has the higher usage? Who is the better scorer? Whose team relies on whom more? Who is better at breaking down the defense?"

    Isn't Paul according to the usage/efficiency model and the +/- regressions? I realize that MVP can mean different things depending on whom you talk to, but as far as who is more relied upon by his team (and the Hornets cast isn't better than Chicago's after Paul and David West), the future bowler in NO has a great case to be made for him.

  22. huevonkiller Says:

    AYC, I have no idea what you're talking about.

    Not only does Rose have a lower eFG% than Kobe, who's probably better than him still, the Bulls are #1 in defense. What does that have to do with not getting to the free throw line? You are indeed part of the unwashed mass, none of that makes sense.

  23. Neil Paine Says:

    #16 - I so need to run a simulation to see how many wins Chicago and New Orleans would have if they switched divisions.

  24. Zeiram Says:

    @Neil

    Why run a simulation, you could just normalize winning % for opponent winning % and then compare No and CHI. Tells you the same thing but is much easier to do^^

    Something very similar is done here: http://espn.go.com/nba/stats/rpi

    And tada NO ranks above Chi but only by a hair.

  25. Neil Paine Says:

    Putting aside the flaws in RPI, that tells you how their record stacks up against a neutral schedule. But I literally want to know how many wins they'd have if they played each other's schedules. I can do that using maximum likelihood and simulating 2010-11 with the schedules transposed.

  26. huevonkiller Says:

    I think Basketball-reference has better rankings than RPI.

  27. AYC Says:

    Apparently you guys missed this:

    http://espn.go.com/blog/truehoop/post/_/id/23698/chris-paul-doing-more-less

    Huevon, I consider it a good sign that you didn't understand me, since I'm used to a large number of your comments not making any sense at all. Kobe's eFG% is .493 and Rose's is .486; that's a statistically insignificant difference. And did you fail to notice that Rose's assist% is almst 50% higher than Kobe's? (And why bring up Kobe in the first place?)

    Back to Rose vs. Paul. Rose has a usage rate about 50% higher than Paul's, and an assist% in the same ballpark, yet his TO% is lower than Paul's. He also has the much higher Orb% (nearly double) and block% (1.4% compared to 0.1% for cp3).

    PS Anon, did you catch Stephen Jackson trying to draw a foul, rather than attempt a real shot at the end of last night's game? And where exactly did I say the refs are conspiring against Rose?

  28. Neil Paine Says:

    #25 - OK, I ran this. In real life, Chicago has 35 wins and New Orleans has 32. Using Maximum Likelihood, we get these ratings:

    team_id games rating
    SAS 52 1.914
    DAL 52 1.144
    BOS 51 1.130
    MIA 52 1.094
    LAL 52 0.832
    OKC 51 0.817
    CHI 51 0.809
    ORL 54 0.633
    NOH 54 0.535
    ATL 52 0.470
    UTA 54 0.376
    DEN 53 0.260
    POR 52 0.223
    MEM 54 0.149
    NYK 51 0.020
    PHO 49 -0.009
    HOU 54 -0.052
    PHI 52 -0.218
    GSW 51 -0.227
    IND 50 -0.297
    CHA 52 -0.377
    MIL 51 -0.421
    LAC 52 -0.496
    DET 53 -0.560
    NJN 53 -0.985
    WAS 51 -1.151
    TOR 53 -1.205
    MIN 52 -1.212
    SAC 49 -1.374
    CLE 53 -1.875
    hca 0.566

    Simulating 1,000 seasons with Chicago in the Southwest and New Orleans in the Central, you get:

    Chicago - 34.8 wins
    New Orleans - 32.4 wins

    In other words, the SOS difference basically means nothing.

  29. Anon Says:

    And Paul has the better offensive rating, has the better ORtg after you account for Rose's higher usage, and also has the better +/- data (added differential to his team) on both ends of the floor. Just sayin'.

    If the MVP is "the player who contributes the most to his team's success on the floor", the burden of proof is with Paul here. And I'm a LBJ fan.

    Also, the Stephen Jackson botched foul call ;"(in your opinion) is a single example you provided. Thats's it.

  30. Jason J Says:

    Nice work, Neil!

  31. huevonkiller Says:

    Rose is Iverson. Another inefficient volume scorer on a great defensive team, and you're sucking up to him now for God knows what reason.

    Ah really AYC, and what exactly do you disagree with me about? The way I see it, I use a variety of metrics to basically come to the same conclusions as Neil, except in a handful of cases.

    Whereas you constantly cry about Chris Paul, you have crazy conspiracy theories about free throws, and you tell me to look at PER or defensive rating except when it doesn't support your case.

    Man up, your posts have been garbage recently. You constantly bring up zero evidence and selective unadjusted for pace stats.

  32. huevonkiller Says:

    Kobe 12.6 EWA (Per formula, since you hate win shares)

    Rose: 11.3

    Rose has a higher turnover rate and lower rebound rate. He uses the second most possessions in the NBA, and has the 13th highest PER. Kobe uses the most possessions in the NBA and has the 5th highest PER.

    Kobe allows 12 PER on the wing, Rose allows 14 per at PG.

    Yeah what were you whining about again?

  33. huevonkiller Says:

    Kobe is what Rose wishes he could be like when he grows up, that's why I brought it up. When you can get a real argument in here I'll be happy to change my opinion.

  34. AYC Says:

    I got your evidence right here...

    DR .472 fg%, .488 efg%
    KB .455 fg%, .488 efg%
    AI .425 fg%, .452 efg%

    Sure, he's just like Iverson. And when you bring up TOs without mentioning assists, you lose all credibility. Also, when do I ever bring up defensive rtg? I'll talk about DWS sometimes, but I don't put much stock in Drtg alone.

    Do I have "crazy conspiracy theories" about FTs? No, I just don't blindly accept what I'm told. I have a problem with TS%, but Neil has acknowledged having similar qualms. I also don't assume that box score stats tell us everything there is to know about how good a player is. And if boxscore stats don't tell the full story, than neither do the advanced metrics based on them. General rules for evaluating players don't always hold for a given individual. But you go on believing Nowitzki is better than Bird, and Drob is better than Hakeem because somebody made up a formula that "proves" it.

  35. B Says:

    @AYC:

    "Why should we value players based on the whims of refs, who have to blow the whistle before a FT can be attempted?"

    It's simple, really. You can ignore FT's all you want, but if you care about things like, say, winning basketball games, they matter. You'd be surprised by how well a players ability to get to the line correlates from year to year, by the way. It's not just some random, uncontrollable thing. Players that get themselves to the line more help their team win more games, as FT's are an incredibly efficient shot. It's only overrated if you don't care about winning games. Anything else is just trying to rationalize a conclusion you wish to be true. As long as you understand that's what you're doing, go for it.

  36. AYC Says:

    #28, I'm not surprised at all that the records barely change. People greatly overstate the supposed superiority of the West compared to the East. Also, over 70% of the schedule is exactly the samefor all teams. If there is a huge difference between east and west, it doesn't really become relevent until the postseason.

  37. B Says:

    (By the way, out of legitimate curiosity, what are these qualms with TS% you bring up? I have not heard of this before, if you care to let me know)

  38. AYC Says:

    #35, I'm not really denying the importance of getting to the line. I'm saying advanced stats overstate that importance, thanks to the way FTA are under-recognized when "possessions" are estimated. This allows players who get to the alot to be overvalued even when they shoot a terrible % from the line. I care more about shooting accuracy than "efficiency"

  39. B Says:

    "I'm saying advanced stats overstate that importance, thanks to the way FTA are under-recognized when "possessions" are estimated."

    Can you elaborate on that? I'm not sure what you mean.

  40. AYC Says:

    OK, #37, I'll keep it brief, since other commenters are prob sick of me ranting about this.

    True Shooting % is really points per estimated shooting possesion. The number is cut in half to approximate a shooting %. So it isn't really a percentage. That's one complaint. The other is that FTA are counted as 0.44 possessions instead of 0.5 (half a possesion), which makes it an incorrect measure of accuracy. If you have a high FT rate, your TS% will look good even if you shoot a terrible % on those free throws. So, TS% is not only not a %, it's also not really "true".

  41. Neil Paine Says:

    AYC, the average free throw does not use 0.5 possessions. It uses 0.44 possessions. I don't know why you keep harping on that, or how many times other commenters have to explain why 0.5 is incorrect.

    Once again...

    The average free throw uses 0.44 possessions.

  42. B Says:

    Right, but the .44 number, while it is an estimate that should be viewed with a standard error for a given sample, does hold true on average. So unless there's a known bias in it (like a certain player gets And1's at a very high rate compared to the rate he gets fouled and doesn't convert the FGA to the point where it makes a meaningful difference), I don't see any objection? As for it being a percentage, I also don't see what's wrong with that. It's all relative. Whether you express it in percentage terms, or PPP terms, what matters is how players compare to each other, and how you express it doesn't change that...

  43. B Says:

    A few more random points:

    "Someone tell adjusted +/- that half a season of data is half a season of useless, Mr. Dooling."

    It's not useless. It's just of very limited use. Small samples may not tell us enough to make any conclusions from, but they still tell us something.

    "Can someone tell me percentage wise, the direct corolation
    of the team that has more rebounds than their opponet, and the % of
    wins that comes from that scenerio?"

    Something to keep in mind is that on any missed given shot, it's more likely to be rebounded by the defense than offense (obviously). The thing is, the more shots a team misses, the more the opponent should outrebound them since more of those shots will become defensive rebounds than offensive rebounds. So a direct correlation without controlling for other factors is not only going to tell us about the importance of rebounding, but it's also going to include things like defense.

  44. AYC Says:

    #42, the problem is that it's disingenuous. It's often used as a catch-all measure of shooting accuracy, but that's not quite what it is.

    Neil, my point isn't really about how possessions are calculated. I'm annoyed that TS% fails as a measure of shooting accuracy INDEPENDENT of estimated possessions. I'm thinking in terms of potential points, not possessions or fractions of possessions. To me a FGA is worth 2 potential pts and a FTA is worth 1 potential points (the extra point from made 3PAs is gravy). As I said earlier, I care more about shooting accuracy than "efficiency"

    The simple formula PTs/((2XFGA)+FTA) works as the independent measure of accuracy that TS% implies it is. Of course, I know I'm tilting at windmills. I'm making a resolution to accept the things I cannot change....

  45. huevonkiller Says:

    #34 Nah, you left something out. http://bkref.com/tiny/9LKLT

    Dude stop, Kobe and Iverson have those percentages on far more possessions. Are you also going to bring up Chris Paul's eFG%? Oh right that's what I thought.

  46. AYC Says:

    You said Rose is an inefficient volume scorer like AI, so I compared Rose to AI and the high-volume scorer you're slurping: Kobe. Rose has the highest fg% by far, and his efg% is equal to Kobe's. Rose is also the superior playmaker. Yeah, it's silly to compare a 3rd year player to two vets with 12+ years, but I wasn't the one who brought up Kobe and AI, you were. Did you forget?

  47. Art Says:

    @45

    Haha you killed AYC.
    Rose only scores an extra 1.1 points per 36 min, yet he averages 3.3 less assists, .6 less reb, and 1.5 less steals.
    Rose also has a .488 eFG while Paul's is .506. Paul also kills Rose in TS%, but AYC will get butthurt over that.
    To top it off, CHI has been the 13th fastest paced team the past 3 years. NOH is 27th.

    P.S. A comparison between Rose and Ellis would be more realistic than Rose/Iverson.

  48. Ian Says:

    Man, you guys are harsh! Why there is a need to attack people and not simply address their posts respectfully is beyond me.

  49. AYC Says:

    We were talking about who should win MVP, genius, not a lifetime achievement award; career stats aren't relevent to that discussion, only stats from this year.

  50. BSK Says:

    Can someone explain usage rates to me? Is a higher usage rate better or worse? Or does it depend on the player? It seems to me that, all things being equal, a lower usage rate is ideal, because it means you are doing the same with fewer touches. However, I wouldn't exactly get down on LeBron for having a higher usage rate than Brian Scalabrini. Is the state by itself particularly useful? Or does it need to be viewed in conjunction with others?

  51. Sam Says:

    Usage rate is an estimate of the % of team plays a player uses when he's on the floor, or, as this very site says:
    http://www.basketball-reference.com/about/glossary.html [ctrl+f 'Usage']
    In general, higher is better because it's harder to be efficient with a higher USG%.

  52. Anon Says:

    "To me a FGA is worth 2 potential pts and a FTA is worth 1 potential points (the extra point from made 3PAs is gravy)."

    There's no need to arbitrarily assign values here. As a matter of fact it should be avoided whenever possible.

    Better yet AYC, instead of complaining about this - why not show proof that the values used for TS% are wrong in the first place? And then present changes to the values that make TS% more accurate? I'm sure the APBRmetrics community would love to hear it. Complaining is one thing; work towards solutions to the problem.

  53. EvanZ Says:

    A missed FGA is worth the expected marginal point total for a possession minus the possibility of an offensive rebound. For example, let's take a 2-pt FGA. The league-average PPP (points per possession) in 2010 is about 1.06. That means the expected point total for each possession is 1.06 points. When a player makes a 2pt field goal attempt, that is (2-1.06)=0.94 pts better than the expected PPP, and he should be credited with that amount. If a player misses a FGA, the possession does not necessarily end, because of the chance for an offensive rebound. The offensive rebound rate (in 2010) is about 26%. Therefore, the player should only be debited 0.74*1.06 = 0.784 pts for a missed FGA. Debiting the entire 1.06 pts over-penalizes the player for missing a shot, because it assumes the expected PPP is entirely lost. If you don't believe me, answer the question I posed here:

    Which shooting performance is better?

  54. EvanZ Says:

    oops, link didn't work:

    http://thecity2.com/2010/12/07/debate-which-shooting-performance-is-better/

  55. AYC Says:

    Anon, how is it "arbitrary" to assign a value of 2pts to field goals, and 1 pt to free throws? Those ARE the values according to the rules... or at least those were the values before the 3pt-line; but TS% also treats 3PA the same as 2PA, so you can't be complaining about that right? The simple formula I listed produces very similar results as TS%; it just doesn't skew the numbers in favor of players with high FT rates.

    EvanZ, I think example A was the better shooting performance, even though that's supposed to be the "wrong" answer. A produces 5 defensive rebound opportunities for the opponent, one fewer than the 6 drb opportunites in example B. You'll say, "What about offensive rebounds?" And I will point out that offensive rebounds are only possible after missed shots. Teams that get alot of Orbs are teams that miss alot of shots.

  56. huevonkiller Says:

    #46, I compared Kobe vs. Rose THIS season and Iverson's MVP season. In response you did nothing to address Rose's inefficient 2011 season. You tried to mention his career eFG% for some odd reason. Without a usage-efficiency tradeoff it means nothing.

    It is unwise to nonchalantly compare eFG%. Even so that though only helps Chris Paul look better anyway according to your vague criteria.

  57. Anon Says:

    "The simple formula I listed produces very similar results as TS%; it just doesn't skew the numbers in favor of players with high FT rates."

    I am intrigued to see the reasoning, methods, and statistical work behind this conclusion.

    Can you provide them?

  58. huevonkiller Says:

    *Even so that only helps Chris Paul look better.

    Your own standards don't seem to support you. Since you've already pre-determined who should be the MVP, you just haven't noticed yet.

  59. Nick Says:

    AYC: "EvanZ, I think example A was the better shooting performance, even though that's supposed to be the "wrong" answer. A produces 5 defensive rebound opportunities for the opponent, one fewer than the 6 drb opportunites in example B. You'll say, "What about offensive rebounds?" And I will point out that offensive rebounds are only possible after missed shots. Teams that get alot of Orbs are teams that miss alot of shots."

    Ah. I see the problem. You aren't very good at logic.

    See, the reason shooting performance B is better is because they generate the same number of points from the same number of shots, but B took less shots, meaning his team as a whole had more chances (well, one more chance) to keep possession of the ball. In no way at all is making 7 of 12 for 14 better for your team than making 6 of 12 for 14 points.

    Your argument simply lacks perspective on what is and isn't valuable in a basketball game. A chance at an offensive rebound has a value greater than 0 (exactly how much is up for debate, but there is some positive value to the team), therefore when everything else ends up equal, you'd rather have an additional missed shot over not.

  60. AYC Says:

    #56, now you are just lying; the link you provided in #45 is for career stats. I'm done wasting my time with you.

    Anon, check out the examples Walter gives in comment #37 of this post

    http://www.basketball-reference.com/blog/?p=8669#comments

    The final values he comes up with are incorrect, but I calculated the correct ones in post #41

    "See, the reason shooting performance B is better is because they generate the same number of points from the same number of shots, but B took less shots, meaning his team as a whole had more chances (well, one more chance) to keep possession of the ball. In no way at all is making 7 of 12 for 14 better for your team than making 6 of 12 for 14 points."

    Um, if both players took 12 shots to score 14 points, how does player B take less shots? I assume you meant he made less shots, not took....

    Here's a question for you: on the last play of a game, down 1, would you rather have a 40% shooter from 3 attempting the go ahead basket from 3pt land, or a 60% shooter from 2pt range attempting a shot from inside the line? I'm tired of statheads acting like eFG% has made good old-fashioned FG% irrelevent. Threes are high risk, high reward; the reason we give a one point bonus on 3s is because those shots are HARDER to make on any single given attempt.

  61. Nick Says:

    "Here's a question for you: on the last play of a game, down 1, would you rather have a 40% shooter from 3 attempting the go ahead basket from 3pt land, or a 60% shooter from 2pt range attempting a shot from inside the line? I'm tired of statheads acting like eFG% has made good old-fashioned FG% irrelevent. Threes are high risk, high reward; the reason we give a one point bonus on 3s is because those shots are HARDER to make on any single given attempt."

    I'd rather have someone good at getting to the line. Which is why it's a valuable skill.

  62. DSMok1 Says:

    "Here's a question for you: on the last play of a game, down 1, would you rather have a 40% shooter from 3 attempting the go ahead basket from 3pt land, or a 60% shooter from 2pt range attempting a shot from inside the line? I'm tired of statheads acting like eFG% has made good old-fashioned FG% irrelevent. Threes are high risk, high reward; the reason we give a one point bonus on 3s is because those shots are HARDER to make on any single given attempt."

    That's a special case, analogous to the choice of kicking a FG on 1st and 10 from the 20 with :03 on the clock and down 1 or doing a normal play. Of course you kick the FG--but that's totally peripheral to normal play.

  63. EvanZ Says:

    @AYC

    "Here's a question for you: on the last play of a game, down 1, would you rather have a 40% shooter from 3 attempting the go ahead basket from 3pt land, or a 60% shooter from 2pt range attempting a shot from inside the line?"

    Pretty silly hypothetical. I assume you realize that the only players who actually have 2pt FG% even close to 60% are PF or C. And sure, every team would love to get the ball to their PF or C for the game winning slam dunk.

  64. AYC Says:

    Let's go back to EvanZ's example. Supposedly, player B helps his team more, because he scores the same # of pts on the same # of attempts, while giving his team an extra opportunity for an Orb. But his team only benefits IF they get the Orb, IF they get another FGA as a result (or FTAs), and IF the FGA (or FTs)is successful. That's alot of ifs; but say all of that happens; does player B deserve credit for the made FG? No. The player who grabs the Orb deserves credit for neutralizing player B's miss (that's all an Orb does), and the player who makes the FG deserves the credit for the pts scored. Now, player B could do all of these things himself, but we shouldn't pretend that the missed shot was a positive thing that somehow made the other two things happen. EvanZ's example tells us nothing meaningful, beyond the obvious fact that made threes are worth one more point than made twos....

  65. EvanZ Says:

    AYC, you clearly know how to make hypotheticals and arbitrary examples. Unfortunately, you don't seem to understand the importance of statistics and averages.

  66. EvanZ Says:

    If you had two players, A and B, who on average put up performances as in my example, who would you choose? The answer is that you would choose B, because your *team* would benefit from his higher PPP. Choosing A would be irrational (unless your rationale is to lose more often).

  67. AYC Says:

    Wow, all three of you avoided giving an honest answer to my question. #61, you have been given only two options; which do you prefer? #62, the relative inconsistency of 3-point accuracy is hardly a special case. #63, high% shooters aren't always low usage stiffs; Kareem in 1980 comes to mind; barkley was a high usage guy who shot 60% too.

  68. EvanZ Says:

    I love that AYC is challenging the problem, though. He's presenting exactly the arguments that lead to the wrong conclusion. I couldn't have planted a better foil if I tried.

  69. EvanZ Says:

    Kareem in 1980? Ok, I'll take him. Is he still available?

  70. Nick Says:

    "Now, player B could do all of these things himself, but we shouldn't pretend that the missed shot was a positive thing that somehow made the other two things happen"

    Yes. It absolutely is a positive thing that made the other 2 things happen. You cannot get an offensive rebound without a miss. You cannot make a shot after an offensive rebound unless a missed shot led to an offensive rebound. A missed shot has an actual value that can be actually be measured. In points, even, if you like. Assuming that a team averages getting 25% of their own misses and 1 point per shot attempt, each missed shot is worth .25 of a point (it's slightly higher than that actually, since a miss off an offense rebounded shot could be rebounded and shot again. But it's close enough).

    If you wanted to argue that made shots allow for better defense on the other end, you might have a point, but your current position is simply factually wrong.

  71. Nick Says:

    "#63, high% shooters aren't always low usage stiffs; Kareem in 1980 comes to mind; barkley was a high usage guy who shot 60% too."

    No, virtually no high% shooters are low usage stiffs. They are PFs and Cs like EvanZ said.

    You evidently don't understand what a "special case" is. Down by one with one possession to go? Yeah, you want to the 60% shooter. The other 99% of the game? You want the 40% 3-pt shooter.

  72. Ian Says:

    The shooting percentage debate is indeed an entertaining one!

    Here's a question I'll posit: Because different teams have different ORB rates, aren't there certain circumstances that would reduce the benefit (or even change the relation) of Player B? I suppose we could take it further and examine different 5-man lineups, for which I'd imagine ORB rate is even more variable.

  73. AYC Says:

    I have a problem with imputing positive value to something that is clearly negative (a missed FGA) based on what MIGHT happen afterwards. Don't the Orb and resulting made FG speak for themselves(if they even happen)? These are the intellectual contortions you have to go through when you don't treat offensive rebounds as new possessions. I'm sure that's a useful fiction for the development of advanced metrics, but it doesn't accurately represent what happens in reality.

  74. Nick Says:

    "Here's a question I'll posit: Because different teams have different ORB rates, aren't there certain circumstances that would reduce the benefit (or even change the relation) of Player B? I suppose we could take it further and examine different 5-man lineups, for which I'd imagine ORB rate is even more variable."

    Reduce, sure. But as long as a team or line-up gets ORebs at a greater than 0% rate it's still better to have the extra miss with all other things being equal. The nature of the question is such that player A is simply less valuable than player B, and even if you do hit 0% ORebs, A is just equally valuable as B.

  75. Ian Says:

    Does anybody know if there is data available on the proportion of offensive rebounds are procured off of missed shots from various places on the court?

  76. Ian Says:

    Proportion of offensive rebounds *that* are procured.

  77. Math2 Says:

    lol @Earl Watson

  78. EvanZ Says:

    Ian,

    http://www.82games.com/rebounds.htm

  79. Jason J Says:

    I have a similar player valuation issue regarding FTAs to AYC, but it strikes me from a different angle.

    AYC sites the impression that metrics give of Dirk being better than Bird (unless you narrow down to Larry's 4 or 5 best seasons), and whether it's right or wrong, when you look at the numbers, it really does come down to Dirk getting to the line more often and turning the ball over less.

    But how many team free throws did Bird's passing create? There's no way to factor it. Of course in terms of team stats and working out the four factors it doesn't matter if a pass leads to an FTA, but in terms of individual player value, it's completely unmeasured. I'd assume that a player who drops a lot of dimes probably helps his teammates draw fouls too unless he's all draw and kick to jump shooters. If I'm the Celtics I can have Bird running the offense and making great passes from the high post with McHale in the low post or vice versa, I'm going with option A. So Bird's not in a great position to get fouled. But he's in a great position to hit a cutting DJ or a post flash from Parish with a pinpoint pass that could lead to foul shots. Of course if Larry played with a superior playmaker, you'd want him to be getting to the line a lot since he shot them so well.

    Two other factors particular to cross-generation player comparisons, so maybe not that much of an issue since the value is lower obviously and there are so many issues anyway:

    1) Contact that would not have been a foul years ago is a foul now. That's not old man bias, that's the rules as written. Which isn't to say that FT rates for teams will necessarily go up, but what used to be good defense is now exploitable to get to the line. If Tim Hardaway was credited with one fewer FGA per game and got to take two more FTAs due simply to rule interpretation, how much better would his TS% (and every metric that factors it in) be?

    2) Play style has changed so much. There's more isolation, more high usage for star players, that it's just tough to tell relative ability. In the 60s when pace was so high, could usage possibly be as high for stars? Was there time to run a good set play to get your first option into position to isolate and draw a foul, when the strategy was clearly to get shots off early and often?

  80. DJ Says:

    Firstly, thanks for the cool post and the different All-Star teams. It's cool to see how the stats favor different players.

    I'm totally amused watching this train wreck of a comment thread. Is it really worth the effort to try to clear up an obvious misunderstanding of statistical principles? But if it hadn't happened, I wouldn't have seen EvanZ's post which is a nice little exercise in logic.

    Anyway, I can't resist my shot at education.

    I notice some logical problems here, AYC.

    In #8 you say:
    "Why should we value players based on the whims of refs, who have to blow the whistle before a FT can be attempted? (for the same reason, I think advanced stats in baseball overvalue walks)"

    And in #73 you say:
    "I have a problem with imputing positive value to something that is clearly negative (a missed FGA) based on what MIGHT happen afterwards. Don't the Orb and resulting made FG speak for themselves(if they even happen)? These are the intellectual contortions you have to go through when you don't treat offensive rebounds as new possessions. I'm sure that's a useful fiction for the development of advanced metrics, but it doesn't accurately represent what happens in reality."

    We are interested in what happens in reality. That's why FTA are taken into consideration. The only issue, statistically speaking, is whether there is an FTA or not. The reason that the FTA occurred has nothing to do with it. Corey Maggette (who I root for, but is hardly great) goes to the line 7 times a game. For seven years in a row, he went to the line 7.9 or more times a game. And he also got his opponents credited with fouls. That's real. It really happened. Some guys don't go to the line a lot. Whether that's because the refs hate them or because they don't draw contact or because they're laying off a beautiful dime, they don't go to the line. And don't get their opponents in foul trouble. And that's real, too.

    And as for a missed FGA being "clearly negative", well, no. At least not clearly negative if what you're interested in is which team wins the game. For example: A missed FGA attempt is not negative if it comes up off the rim and your big man happens to sky over someone to jam it down. That missed FGA would have been an assist if it missed the rim completely and the big man caught it and put it in. In reality--that is, in terms of what happens on the court--the two plays are identical in terms of effect on the game, nearly identical in the eyes of the viewers, and only in the eyes of the statistics do you have a big distinction: on the one hand you have a missed FGA, a rebound and a made FGA, and on other you have an assist and a made FGA. Would you say that miss is negative? And if so, why isn't the assist that leads to the alley oop negative?

    Or how about this: 6 point lead, you get the ball with two minutes left; at 23 seconds in the shot clock, your guard heaves up a missed FGA and then your team gets the ORb. Is that negative? I don't think so.

    If you want to talk about reality, you have to talk about what really happens. And what really happens is that guys go to the line to shoot FTAs because refs do blow the whistle. And some missed shots are not negative.

  81. AYC Says:

    DJ, I guess you missed post #38, where I said I don't deny the importance of getting to the line. My issue is with the way FT rates are overvalued because of the way possessions are defined; specifically,I mean the way in which the full point potential of FTAs isn't recognized. When all your made FTs are recognized, but not all attempts, shooting efficiency is overstated; and the higher the FT rate, the greater the overstatement. Is that logical enough for you?

    As for missed FGA, who knew that Iverson was helping his team so much with all those missed shots! Are missed FGA valuable like assists, or is shooting efficiency the most important thing in BBall? Which is it? You can't say both....

    You and the other commenters are treating the missed FGA as the start of a series that ends in a made FG. But I am looking at the FGA as an individual incident. Standing alone, a missed FGA is an entirely negative incident, always (for the offense). Standing alone, an offensive rebound is always a positive incident, as is a made field goal attempt. A missed FGA results in a defensive rebound the majority of the time. But even it is followed by an Orb and FG, the missed FGA still didn't accomplish anything. Let's compare two hypothetical "possessions":

    Player A attempts a FG and makes it for 2 pts
    Player B attempts a FG and misses, but his teammate, player C, gets the rb and puts it back for 2pts.

    Did player B help his team as much as player A? Of course not; player C deserves the credit for the offensive rebound and putback. In both cases the same amount of points were score; in example #2, the team needs 3 incidents (one negative, one positive to cancel out the negative, and another positive) to score the same points that Player A gets with one incident. In EvanZ's example, the value in terms of points per shot was the same, despite one fewer shot being made. Player B in his example gives his team one more opportunity for an Orb, but an Orb can only come after a missed shot; so how has the shooter helped his team more? Because his teammate might get a rebound, which might lead to another shot, which might go in? If all that does happen, we are merely back to the point where we would've been if the first shot had gone in.

  82. AYC Says:

    PS Great post, Jason J

  83. EvanZ Says:

    "Did player B help his team as much as player A? "

    Wait, what? Now you are somehow arguing that Player B is actually worse? lol

    I get that you don't understand the logic of why Player B is better. But at the very minimum, you have to see that even using your own logic, they would be equivalent, right? I mean, if you're arguing with that, there's not much left to discuss. Not in terms of logic, anyway.

  84. Zeiram Says:

    @EvanZ

    He is actually talking about a different Player B, don´t get that mixed up.

    @AYC

    I get what your problem is with assuming that a missed FGA is something positive. It isn´t of course but when all else is equal meaning that both players score the same amount of points and (that is important) take the same amount of FGA the player who misses more (Player B) is more beneficial to his team than the other. Why is that and why doesn´t this (as you said) clash with a value on shooting efficiency?

    This whole paradox you mentioned stems from the premium shooting efficiency stats put on 3ps. Therefore most of those stats only care how many FGA you needed to score a certain amount of points.
    Since FTA are not included in that and 3ps help you score more with less attempts they are so important.

    Player Z who converts 5/10 2p attempts for 10points and Player Y who converts 2/10 but those 2 are 3ps plus he converts 4 FT also scoring 10points. Now I understand how you would easily say that Player Z is better because he converts most of his attempts while Player Y misses a ludicrous 8 attempts! Yet in relation to shooting efficiency both players are equal.

    This is premise 1, are you with me on that?

    Now premise 2 states the following, which is also very simple:

    A missed FGA is not worth 0 points, thanks to Orebs it might be worth more than 0. (How much is irrelevant).
    Now understand that the player who misses has nothing to do with the Oreb (in most cases) and does nothing to ensure this net positive effect of his miss. Missing does not make him more valuable nor is missing better than scoring.

    Combining premise 1 and 2 however leads us to the following statement:

    In my earlier example of Player Z and Y, Player Y had more misses which because of the possibility of Orebs made his performance more valuable to his team than Player Zs performance.

    Basically this just means that a player who scores more of 3ps and FTs is better than his peer. Of course Player Y in above example would be better if he missed less.

  85. Zeiram Says:

    @AYC

    I want to add somehting important, as with FTs the positive value of FGAs in above example are beyond the players control so to speak. I understand why you wouldn´t put that in the player evaluation. How is it a skill to miss more, how is it a skill to get good calls?

    The important part here however is simply that certain behavior will lead to positive results with a high possibility.
    Shooting 3ps will help you migitate misses. (being a 33,3% 3p shooter is as valuable as being a 50% 2p shooter, even more so because of the value of misses).
    Driving to the rim hard will help you get FTs.

    This is why Kevin Martin is such an astounding scorer, he scores a lot of 3s and gets many FTAs.

  86. Anon Says:

    I'm not buying Walter's reasoning here, AYC. A 50% fg shooter and 50% ft shooter that can score 10 points from the line (10-20 ft) given the same number of possessions does it by putting the defense into foul trouble. All the other bonuses that result from going 4-8 from the field and 2-4 from the line still apply (drawing defensive attention towards himself to open up opprtunities for teammates, etc). It's not like the all-ft shooting player is being "rewarded" unnecessarily; he simply add an extra bonus for his team by not settlling for jumpers and getting defenses to foul him. That helps your team because defenses either foul out players in the process or play more conservatively to avoid foul trouble, hence opening up easier looks as players go to the basket.

    Why do you think coaches love it when guys like LBJ or Wade settle for shots instead of get to the rim? There's a value in shooting foul shots that goes towards helping your team win games.

  87. DSMok1 Says:

    "This is why Kevin Martin is such an astounding scorer, he scores a lot of 3s and gets many FTAs."

    A few days back, the Works had a post on who was the best scorer in the NBA . When I ran some rough numbers, I came to the conclusion that.... Kevin Martin is the best scorer. Of course, I didn't account for the fact that 59% of his made field goals are assisted, vs. Lebron's 30% or CP3's 20%, but outside of that fact his rates are remarkable.

  88. Greyberger Says:

    Going just by efficiency (TS%) volume (Usage%) and turnovers (TOV%), here's my top scorers of 2011:

    Dirk Nowitzki TS: .616 USG: 28.0 TOV: 9.8
    Kevin Martin TS: .613 USG: 30.1 TOV: 10.4
    Kevin Durant TS: .597 USG: 31.2 TOV: 11.5
    LeBron James TS: .581 USG: 32.1 TOV: 14.0
    Dwyane Wade TS: .578 USG: 31.6 TOV: 12.6
    Amare S. TS: .570 USG: 31.6 TOV: 13.0

    In no special order.

  89. huevonkiller Says:

    #60

    Seriously dude, you must be out of it mentally.

    In post #34 you shifted this to a career discussion for no reason at all. In post #45 that was a retort to your careless comparison.

    Again, Kobe is doing what rose does, except better. And he's ten years older.

  90. Unabashed Rose lover Says:

    I'm going to make an argument which doesn't prove that Rose is MVP (though I do think he's worthy and should be in the top 3-5 for the discussion), but I'm convinced that Paul is not an MVP candidate.

    It all comes down to usage usage usage. Paul doesn't take enough shots. He defers to his teammates too much, and they are worse than him, which in turn makes the team worse. Right now Paul's TS% is a stratospheric .611. Which is awesome, until you see that it's the highest TS% on his team of anyone with more than 220 minutes played. But his USG% is 4th among that same criteria. He's letting Marcus Thornton take 7 shots per game while shooting 40%. If Paul took more shots, taking shots away from his teammates. Let's say his TS% fell to .55 or so, but it meant Trevor Ariza, Marco Belinelli, Willie Green, Quincy Pondextor, and Jason Smith all took less shots (they all have TS% lower than .55). The team as a whole would better, yet ironically, Paul's advanced stats would probably look worse.

    In my opinion, Rose understand this. He realizes Keith Bogans and Kurt Thomas need to have their shot attempts limited, and he needs to take on the scoring burden. For what it's worth the Bulls score more points per possession than the Hornets and have a better record. So there is some evidence I'm right.

    As for the AI comparisons, they are not even close to accurate. Rose is more efficient and dishes out more assists than AI did.

  91. huevonkiller Says:

    #61 Yeah you'd have to imagine just getting to the line is valuable. Getting another team into the penalty, or someone into foul trouble opens up the game for everyone else.

    #79 Free throw rates seem pretty stable. Teams attempt slightly more shots before getting to the line, compared to the 1990-1991 NBA season. "Illegal defense" is now legal as well.

  92. huevonkiller Says:

    #90 More efficient in what sense?

    Chris Paul is more efficient than Rose, so clearly it isn't all about efficiency. AI takes on a greater amount of possessions, in his prime he's beating Rose in points per shot as well.

    http://www.basketball-reference.com/blog/?p=8632

    The usage-efficiency tradeoff, Chris Paul's Offensive rating is monstrous.

  93. DJ Says:

    In #8 you say:
    "Why should we value players based on the whims of refs, who have to blow the whistle before a FT can be attempted? (for the same reason, I think advanced stats in baseball overvalue walks)"

    In #81 you say:
    "My issue is with the way FT rates are overvalued because of the way possessions are defined."

    So is it that you object to the whims of the refs playing a role, or do you object to the definition of possession? Because you're saying different things at different times. What you said in #8 is just wrong--it's not statistical reasoning.

    What you said in #81 is a perfectly reasonable argument, except...how would you define possession, and how would you go about identifying the value of a FTA? You say these things are valued incorrectly, but I personally don't see logical errors in the derivation of the estimation of possession for a free throw (0.44). If you have some method, some reasoning by which you can show that this number is wrong, then I absolutely promise you that every single stat geek on this website would be thrilled to actually see some math that works it out. No sarcasm. That kind of mathematical derivation is something geeks like me enjoy. (And I hope no one out there is offended by the word "geek"; I use it as praise.) On the other hand, if you're just dropping a number without any demonstration of why that number is being used, then it seems arbitrary and therefore unconvincing.

  94. Unabashed Rose lover Says:

    #92

    All I said was that the comparisons aren't accurate.

    Statistically, Rose is not like Iverson.

  95. DJ Says:

    My previous and this to AYC, of course...

    In #81 you say:
    "As for missed FGA, who knew that Iverson was helping his team so much with all those missed shots! Are missed FGA valuable like assists, or is shooting efficiency the most important thing in BBall? Which is it? You can't say both.... "

    Well, maybe read what I said again. I didn't say that all missed FGA are valuable, and I never said anything about shooting efficiency. So, in fact, I didn't say either.

    What I said was: there are some missed FGA which are not negative, and even some that are positive. Some not all. Situation matters. It's great if you want to view each FGA as an "individual incident". Totally killer. Those of us who are interested in understanding basketball, however, recognize that FGA do not occur in stop motion, but as part of the flow of the game. What happens after matters. If the shot is made, the other team gets the ball. Guaranteed. They are taking the ball out, and if they're the Showtime Lakers, you may not even get a chance to set up your defense. If the shot is missed, both teams have a chance at the ball. And that chance is valuable--we know, in fact, that there's about 25% chance of an offensive rebound. This is basic calculation of expected value:

    expected value (in points) of a missed FGA = (probability of getting a rebound) * (points per possession)

    Calculation of expected value based on probability is a common-place mathematical practice not just in basketball statistics, but in statistics in general.

    We know that the probability of getting a rebound is greater than zero, and we know that points per possession is greater than zero, so the expected value of a missed FGA is greater than zero. (If ORb = 25% and ppp = 1, then the expected value of a missed FGA is 1/4th of a point, which is pretty low, but definitely better than zero). Really, though, the missed FGA is like a lottery ticket: most of the time it's worth nothing, but on rare occasions it pays off.

  96. AYC Says:

    Sorry Evan, I should have used different designations to avoid confusion.

    Zeiram, in your example player Z attempts more shots; those 4 free throw attempts count too; my whole complaint is that FTAs aren't fully recognized. As my previous comments suggested, I don't think the way "possessions" are calculated reflects reality. All rebounds are new possessions as far as I'm concerned, not just Drbs; when you acknowledge that, the idea that a missed shot is a good thing is revealed for the nonsense that it really is. A missed FGA is something to be overcome, not the necessary first step before an offensive rebound.

    Anon, you're making a valid point; there is value in getting your opponent in foul trouble. But that's not the rationale behind how FTAs are treated in TS% or PPP. And the value in causing foul trouble is represented already in the boxscore: opposing players with foul trouble may see their minutes reduced, your team will shoot more FTs because of the penalty, and your shooting efficiency may go up because the opponent wants to avoid a DQ. If the foul trouble doesn't cause any of these things to happen, then it didn't really help your team.

  97. Anon Says:

    #90

    I don't think Paul is out there thinking about the stats on BR-com when running the team's offense. He certainly COULD take more shots - and he's done it before while maintaining high efficiency - but the offense they run doesn't call for a scoring point guard like Rose in Chicago. That's more a reflection of the coaching and system in place than Chris Paul. His job is to get at opposing defense so other players can get easy shots, and he does a great job at it.

  98. Anon Says:

    "But that's not the rationale behind how FTAs are treated in TS% or PPP."

    Other people here have told you what that rationale is though (a rationale that is supported by plenty of evidence), and you keep insisting that it should be otherwise without ANY proof or data to support your claim. Walter provided hypotheticals where TS% is "overstated" for players with alot of foul shots, but he ALSO assumed that tech foul shots and and-1s weren't taken - these things happen in basketball though and it's precisely what TS% accounts for in the first place!

    Greyberger already did a great job explaining all of this to you before.

  99. AYC Says:

    DJ, Anon, what you say is true, IF you accept Dean Oliver's definition of what a possession is; if you read my last post, you saw I personally don't accept that definition. I consider offensive rebounds to be the start of a new possession, just like defensive rebounds. The goal of the offense is to score points, not to grab Orbs. Each FGA is a different possession, and a missed FGA is a failed attempt to score IMO; the rebound and shot attempts that follow are part of a new possession. And a FTA should be half a possession, because it's worth half as many points. Can you give me a good reason why I shouldn't look at it that way?

    EvanZ, I've changed my mind about your example. Player A and player B were equally valuable, because they scored the same amount of points on the same number of shots. I still won't give player B credit for offensive rebounds off his misses... unless he is rebounding his own miss.

  100. DJ Says:

    #99:
    "Can you give me a good reason why I shouldn't look at it that way?"

    Well, depends on what you consider a good reason. Lots of people in this thread have already explained to you how the numbers are derived. You don't like those explanations, but to lots of us those explanations are good reasons. Since the derivations of the formulas are public, we can check them and choose whether we disagree. Lots of us think the explanations provided are good enough--that they're at least the best so far. And that the reasoning is good enough to spend time on it. As I said before, if you can show good reasons why we should do things differently, we would welcome that advance. But--to me, at least--the explanations that you offer are flawed.

    For example:
    "And a FTA should be half a possession, because it's worth half as many points."

    Well, strictly speaking, a possession has no point value. You would agree, I hope, that you only get points for putting the ball through the hoop; Only made FGs and made FTs are worth any points. Taking possession of the ball does not automatically give you points. Stepping up to the line for a FTA does not automatically give you points. So neither a possession nor an FTA is worth any points and therefore an FTA cannot be worth half as many points as a possession.

    But, both possessions and FTA are lottery tickets of sorts--they present an uncertain opportunity to score points: they may result in points, and they may not--and therefore they have "expected values", which is how mathematicians evaluate lottery tickets and other probabilistic events.

    To calculate expected value of a possession (however you choose to define it), you have to know all the different possible outcomes of a possession, the point value of each outcome and the probability of the outcome. The same is true for the expected value of FTAs. And I don't want to spend the time on that, but if you want to show us math that convinces us that a FTA is worth half a possession (in terms of expected value, of course), that's how you can do it--define the outcomes, show the probabilities and calculate the numbers.

  101. Michael Says:

    They are both really good point guards.

  102. Ian Says:

    I'm loving this discussion! I'm a stats PhD student, so any kind of discussion that links 2 of my biggest passions is a big win for me.

    Further to EvanZ's example, which I didn't articulate fully as I should have:

    Player A makes 14 points through 12 shots, with 5 missed field goals. Player B makes 14 points through 12 shots, with 6 missed field goals. The extra opportunity for an offensive rebound is what supposedly gives Player B the edge.

    However, what if Player A's team rebounds 30% of its misses, while Player B's team rebounds 20% of its misses? Then Player A's misses result in 1.5 extra opportunities to score in expected value, while Player B's misses result in only 1.2 extra opportunities to score.

    I still want to pour over details of the proportion of rebounds grabbed by the team on offense from different areas on the floor, as that would also have an impact on the value of each miss.

  103. DJ Says:

    #102:
    Absolutely--if you add additional detail, you can tell a different story. But even as you change those proportions, you're really just emphasizing the point of EvanZ example, which was that there is some expected value in a missed FGA due to the fact that there's a chance of getting an offensive rebound.

  104. Zeiram Says:

    @AYC

    Now that is an alltogether different argument. If you attack the premise there is no reason in arguing for the conclusion.

    Now let´s start over:

    1. Orebs

    If you define an Oreb as a new possesion or not is irrelevant to the discussion. Without a miss there would not be the possibility of an Oreb. Again this does not give value to the skill of missing or whatsoever. It is just a fact that because there are Orebs in games a missed FGA does not have a value of 0 but rather something higher than zero.
    You don´t have to credit Player B with the Oreb just understand that because of his miss a Oreb could be made. But what does make him more valuable isn´t that miss but rather his ability (through 3ps) to score more points with less attempts which in essence allowed him to make an additional miss without negativly effecting his shooting efficiency. That additional miss (which did not negativly affect his offense due to his efg%) would allow an Oreb therefore having value.
    Just understand that also Player B does nothing valuable by missing, his miss does indeed have value. Again what makes him valuable is his 3pshooting which jsut allows him to miss without hurting the offense. Player B has more value that is a fact, regardless of your definition of possesion.

    2. FTA as half possessions

    This has nothing to do with possessions but I get what you are saying: Why isn´t the attempt factoring into Ts% and efg%. Rather than arguing against it I would propose a mind experiment:

    Calculate Dwight Howards ts% with your definition.
    Calculate Shaqs ts% and so on. Realize something?

  105. AYC Says:

    DJ,I guess I should be more careful using the word possession, since the word is loaded with meanings I don't necs accept. As I said earlier, I think in terms of potential points, not possessions. A FGA is worth 2 potential points, and a FTA is worth 1 potential point; starting from that premise, if a FGA is treated as one "possession", a FTA attempt should be a half-possession. The idea that some shot attempts aren't counted really bothers me; the goal of the game is to score more points than your opponent, yet we are told that some shot attempts shouldn't be counted (And1s and techs). And that skews the numbers of players with high FT rates, so that a player like Shaq who shoots a LOWER % from the line than the field gets credit for attempts even though they are misses.

  106. EvanZ Says:

    AYC, the commonly accepted terminology for what *you* are calling "possession" is actually a "play". A FGA is a play. A rebound is a play. This discussion is more productive, if we agree to use the same terminology, as opposed to using whatever you feel like. Going forward, can you agree with this?

    As for this:

    "The idea that some shot attempts aren't counted really bothers me"

    You might be interested to know that in my metric (ezPM), I treat And1's differently than other free throw attempts. If a player misses an And1, he doesn't get penalized at all (why should he, if he already made the shot?). If he makes the And1, he gets +1 pt. Would you do it differently?

  107. AYC Says:

    Zeiram, in 1) you are making the same point I made in post #64, except for your conclusion. The shooter should get credit for hitting 3s, not for his misses. The offensive rebound isn't necessary if he hits the shot in the first place. If a teammate rebounds and puts it back, I believe he alone deserves credit.

    Regarding 2), I assume you are suggesting that TS% produces a very similar result to the formula I would use. I was aware of that, but close isn't good enough.

    I actually did this a couple months ago, so the numbers for active players might be a little off:

    MJ .569 TS% .558 -.011
    EJ .610 TS% .595 -.015
    LB .564 TS% .557 -.007
    SO .586 TS% .570 -.016
    HO .553 TS% .543 -.010
    TD .552 TS% .541 -.011
    JS .608 TS% .595 -.013
    KM .577 TS% .563 -.014
    CB .612 TS% .596 -.016
    DR .583 TS% .567 -.016
    KG .548 TS% .540 -.008
    KB .556 TS% .545 -.011
    DN .582 TS% .571 -.011
    LBJ .563 TS% .551 -.012
    DWD .565 TS% .551 -.014

  108. Anon Says:

    "The idea that some shot attempts aren't counted really bothers me; the goal of the game is to score more points than your opponent, yet we are told that some shot attempts shouldn't be counted (And1s and techs)."

    It's not that they're "not counted"; they just don't take up a WHOLE POSSESION. There's a difference.

  109. AYC Says:

    EvanZ, the problem is with how plays are included, or not included, in the accepted possession model. Also, it sound like your metric treats And1s the same as WS and PER. Is the difference that you use actual And1 data, rather than an estimate? Anyway, I think in terms of potential points, so yes, I would count the missed And1 attempt, because the player is leaving potential points on the board. I think poor FT% is a major weakness that advanced stats under-recognize by not counting all misses.

  110. Anon Says:

    The shooter should get credit for hitting 3s, not for his misses. The offensive rebound isn't necessary if he hits the shot in the first place. If a teammate rebounds and puts it back, I believe he alone deserves credit.

    Ah, I see now. The issue here is that you inherently see everything in basketball as "black and white". In your mind, "made FG" = good; "missed FG = bad". The end.

    It's a pretty close-minded way to think about the sport, isn't it?

  111. AYC Says:

    Anon, made And1s and techs are counted, but missed ones are not counted; that is the rationale behind the 0.44 value rather than 1/2.

  112. EvanZ Says:

    AYC, you've gone about as far as this line of logic will take you. The problem is you won't be able to get past the next step.

    What is the next step? Accounting for defense.

    How's that?

    You say (or at least, imply) that a player should be penalized for missing an And1, right? If that's true, would you credit the defender for that miss? In other words, if we put this in terms of +/-, you are giving the player who misses the And1 -1. Assuming you want to have some logic to the accounting, that means you must balance this deduction with a credit to the defense. Therefore, either the player who committed the foul receives +1, or that +1 must be split amongst his teammates (+0.2 to each).

    The problem with that is that the player who committed the foul already gave up two points. In a marginal point system, he has already been deducted 1pt. But now you're going to give it back to him. That means that he comes out of the situation appearing to have a net 0.

    Furthermore, the player who scored the points and got fouled, was previously credited +1 for the field goal. But now you want to deduct 1 pt for missing the And1. So he comes away with a net 0.

    BUT HIS TEAM ACTUALLY SCORED 2 PTS!

    Logic wins out my friend. And you are on the wrong side of it.

  113. EvanZ Says:

    Here's the corollary:

    For every credit you give to the offense (defense), there must be a debit applied to the defense (offense). Without that as are basic constraint, your value system is inherently flawed (and meaningless, I would argue).

  114. EvanZ Says:

    BTW, if anyone is curious (or bored enough to care), And1's account for about 0.02 PPP this season (by my own calculation).

  115. Anon Says:

    "Anon, made And1s and techs are counted, but missed ones are not counted; that is the rationale behind the 0.44 value rather than 1/2."

    No, it's not.

    This is just ridiculous now.

  116. AYC Says:

    Evan, I have said all along that I am interested in an independent measure of shooting accuracy. In order to do that, you have to recognize ALL missed shots. I was talking about how we evaluate individual offensive players, not the opposing defense.

  117. EvanZ Says:

    "Evan, I have said all along that I am interested in an independent measure of shooting accuracy. In order to do that, you have to recognize ALL missed shots."

    Do you honestly believe it makes a big deal? All you're doing is lowering the mean by about 1% point. You know, I took that list you gave above. If you rank the players using TS% calculated each way, the only two players that switch places are LB and DWD. The variance in FG% from year-to-year is much, much larger than this effect, so that it is practically meaningless. But whatever floats your boat, I guess.

  118. DJ Says:

    AYC, yes, as a rule it is good to be careful about how you use words.

    But it's not how possession is defined that makes me think your argument problematic. (As it happens, I'm not sure that your definition is different from the official one in the NBA rules: Rule 4: Section XVIII-Team Possession: A team is in possession when a player is holding, dribbling or passing the ball. Team possession ends when the defensive team gains possession or there is a field goal attempt..)

    What makes your argument problematic to me are the logical flaws. If you want to redefine possession, fine, but show me the definition (actually, you say you're not interested in possession, so that's kind of beside the point). If you say that a FTA is worth 1 "potential point", fine--I don't know what a potential point is, but at least you're setting up a system, and I understand that the maximum return on a FTA is 1 pt.

    But "A FGA is worth 2 potential points, and a FTA is worth 1 potential point"? You can start from the premise if you want, but that doesn't seem real with respect to the basketball games I've seen. In basketball some shots are worth 3 points, and if I want to describe basketball, then I want to take the 3 point shot into account. And some shots are worth 0 points, and these also need to be taken into account. You don't seem to be doing this when you say a FGA is worth 2 potential points.

    The very idea of potential points is kind of comic. What's a potential point? Where does it exist? Who counts them? In basketball, there are actual points that are recorded when the ball goes through the hoop.

    As I previously noted, there is a common mathematical concept called "expected value" that is used to estimate the potential return on an uncertain investment--like a lottery ticket (which sometimes pays off in $ and sometimes is worthless) or a possession (as defined by the NBA, which sometimes pays off in points, and sometimes pays nothing). Expected value is basically a weighted average of the values of the different outcomes, with the probabilities as weights. Expected value recognizes that sometimes a your lottery ticket is valuable and sometimes it isn't--just like a shot or possession.

    But really, as you haven't shown the work you're using in any structured form, it's hard to take it all that seriously when it seems like you're just ignoring how basketball is played. It's easy to say "an FGA is worth 2 potential points," but I've watched basketball and I want to know why an FGA isn't worth 3 potential points, because sometimes guys get 3 when they shoot. And when you say things like missed FGA are clearly negative and that they are individual incidents, it's a long way from what I've seen watching ball games. Not all misses are equal--some are terrible, and in some rare occasions they're good. If your analysis is so limited that it can't handle things like 3-pointers, or recognize that some misses get put back in by a teammate and others get taken by the opponent, then it seems simplistic compared to TS%, even if TS% is far from perfect.

  119. AYC Says:

    DJ, you act like I havn't addressed this, when I have. The extra point from made threes is a bonus, and I treat it as such; and that is no different than the way TS% treats threes. We give a bonus because those shots are harder to hit. When we look at the league-wide eFG% on 3PA, we find it isn't much higher than the eFG% on 2PA, because the positive effect of the bonus is largely canceled out by the lower shooting percentages from that range. The bonus is enough to make shooting 3s worthwhile, but not a huge difference. Missed 3PA are also no different in their effect than missed 2PA. And why are you calling my definition of a possession illogical, when you admit it's the definition the league uses?

  120. EvanZ Says:

    " The bonus is enough to make shooting 3s worthwhile, but not a huge difference."

    Actually...the eFG% on all attempts is 50%. The eFG% on 3pt attempts is 54%. So, that's at least 4 points right there. It's even more than that, however, because the overall number includes those three-pointers. But let's stick with the 4 points, just to make life easy. Every one point increase in eFG% for a team is worth about 1.5 in point differential (* see link below). That means a team that has a eFG% that is 4 points higher than another team would be about +6. Do you know what +6 means, in terms of wins? It's about 15 wins over the course of a season.

    Yeah, not a huge difference, I guess. (Oh, and let's not forget it's actually more than that, if you take out 3pt shots from the overall average.)

    *For more details:

    http://thecity2.com/2010/12/21/regressing-point-differential-on-the-four-factors-part-2/

  121. AYC Says:

    Anon, if you can explain why my post (#111) was "ridiculous", please do. Whatever points are scored are counted in the possession model, but And1 attempts and techs are not counted.

    EvanZ, I have admitted all along that the difference between TS% and my formula is small. But I think it does matter. People make proclamations all the time about one player being better than another based on tiny differences in PER and WS48. Chris Paul's PER of 25.1 is less than 10% higher than Rose's PER of 22.9; and on a per game basis, his production is less than 3% higher. If we valued FTA at 0.5 instead of 0.44, those stats would be even closer.

    And I can ask you a variation of the same question: how much would counting missed And1s change your defensive stats? Would it make that big of a difference? In BBall, some fouls are considered "good" fouls. Hacking a terrible foul-shooter like Shaq at the end of games has been considered a sound strategy. If you hack him and he misses the and1, your foul didn't hurt your team.

  122. AYC Says:

    For the last full season the eFG% on 2PA was .492, and on 3PA it was .532; that's a difference of about 8%.

  123. AYC Says:

    PS Three point shooting is also more selective. The avg team attempted 63.6 shots per game from two, and 18.1 per game from three. If the percentage of attempts from three was significantly higher, the eFG% on those attempts would most likely be lower; it's also likely the eFG% on 2PA would go up if that happened.

  124. EvanZ Says:

    All that is possible. But it doesn't negate the fact that a good 3-pt shooter is clearly valuable. You seem to be the only one who doesn't understand that, or maybe you're too proud to admit it. There's a reason the "3-point specialist" exists.

  125. Zeiram Says:

    @AYC

    I´ll leave the discussion about ts% and FTs for another day (and arguer) but I can´t rest on the Oreb thing.
    Please understand that regardless of whom you would credit with the positive outcome of a Oreb it would not have been possible without the miss first. This has nothing to do with individual player evaluation. A player is not better because he misses more (not even when he has the same output, see player and player be example). Missing does not make him a better player and when a Oreb occurs whe should (and we do) credit the player who actually makes the Oreb. But and that is the core of it, an Oreb can´t occur if nobody misses. Missing is in essence better than to not shot at all.

    I don´t want to write a novel here mainly because I don´t quite know where your biggest problem with this notion is.

    Is it A) that a negative Action (a miss) can have positive value or B) that the positive value is not produced by the missing player but still is credited to him?

    If it is B, then look at my explanation above. The positive value is not credited to him but rather we only acknowledge that all things being equal player B in EvanZ example helped his team more (without actually being helpful). The lesson here is not to miss more but to shot more 3ps.

    If it is A) than check back with me because that is harder to explain but nonetheless true.

  126. AYC Says:

    Zeiram, I actually agree with you. If a team ends a possession without a shot, that means they had the ball stolen or turned it over; a missed FGA is better, because of the Orb opportunity. My argument relates to the evaluation of individual players, not at the team level. I don't think the player has somehow done something good by missing a shot; I think he has done something bad, but less bad than turning the ball over.

    EvanZ, I never denied the value of 3pt shooting. I was responding to a question by DJ about why I treat three point attempts just like 2PA, which is effectively the same as how TS% treats them.

  127. EvanZ Says:

    "My argument relates to the evaluation of individual players, not at the team level. I don't think the player has somehow done something good by missing a shot; I think he has done something bad, but less bad than turning the ball over."

    lol

    this is why the word "counterintuitive" was invented

    Stop thinking about the missed shot. Instead, think about the extra possessions that are potentially created by his hitting the two 3pt shots.

    The missed shot *is* bad, it's just not as bad as you think. And it's better than the alternative scenario created in A.

  128. AYC Says:

    "Stop thinking about the missed shot. Instead, think about the extra possessions that are potentially created by his hitting the two 3pt shots."

    If we are using Dean Oliver's definition of a possession, it's not possible to create "extra" possessions. The two made threes add two extra points, and that's all. An offensive rebound makes an extra shot attempt possible on the possession, but making that extra attempt accomplishes nothing more than if the first shot had been hit. And the point I'm making hold's true if you use my definition of a possession.

  129. EvanZ Says:

    "If we are using Dean Oliver's definition of a possession, it's not possible to create "extra" possessions."

    It doesn't matter what definition of possession you use. What matters is that an extra rebound opportunity increases the expected point total. Somehow, you still don't get that.

    You still don't seem to get that B enables one more offensive rebound opportunity. Or you do, but you want to give credit for the missed shot to his teammate, which makes no sense.

  130. DSMok1 Says:

    Simple thought experiment:

    4 possessions, 2 alternatives. The players take the first shot on each possession for their team:
    Player A: 3/4 from 2 Pt range
    Player B: 2/4 from 3 Pt range

    Both have scored 6 points in the 4 possessions for their team. What would the team likely score on the possessions not ended by a made shot? Each would be estimated as 25% ORB%, and a play after an ORB may be estimated at worth on average 1 point.

    The team, over the 4 possessions with Player A, would be estimated to have scored 6.25 points. Over the 4 possessions with Player B, the team would be estimated to have scored 6.5 points.

    Thus the marginal value of shooting 3's over shooting 2's, given the same eFG%.

  131. EvanZ Says:

    Daniel, that's what we've been talking about:

    http://thecity2.com/2010/12/07/debate-which-shooting-performance-is-better/

  132. EvanZ Says:

    I should add, most of us have been trying to convince AYC of this advantage. He does not accept it.

  133. DSMok1 Says:

    Ha! I didn't know you had done it first. The answer seems pretty clear...

  134. EvanZ Says:

    "The answer seems pretty clear..."

    you'd think so, right?

  135. Zeiram Says:

    I don´t want to denounce AYC here! This is similar to the Monty Hall problem of mathematics, you can be a very intelligent mathematician and yet fail to "believe" the solution. It is all hard to understand and almost has to be understood intuitively, yet and this is the important part: IT IS STILL A FACT. (Had to get that out of me)

  136. AYC Says:

    "It doesn't matter what definition of possession you use."

    I'm glad we can agree on that.

    "What matters is that an extra rebound opportunity increases the expected point total."

    Yes, that's why I credit the rebounder.

    "You still don't seem to get that B enables one more offensive rebound opportunity"

    My point is that the Orb and putback doesn't accomplish anything more than if the original shot attempt had been made in the first place. The goal of the offense is not to grab Orbs, but to shoot more efficiently than the opponent; that's how you win games. It's possible to get more shot attempts than your opponent, but usually not that many more, thanks to the shot-clock; and teams win games with fewer shot attempts than their opponents all the time. Usually the team that attempts more shots just has more misses.

    There are three ways I can think of to get more shot attempts: you can steal the ball, benefit from a turnover, or get an Orb. In the first two cases it's possible to get consecutive made field goals, but in the case of Orbs, it's not possible. Because the ORb merely cancels out the missed shot that made the Orb possible/necessary. I get the value that hitting 3s adds, but not missing shots.

    Anyway, it's been fun. I think I've made my point, and we're starting to go 'round in circles, so this is my final post on the matter.

  137. EvanZ Says:

    "I get the value that hitting 3s adds, but not missing shots."

    I don't think you do in this particular situation. The 3's are what created the value by potentially saving an extra possession.

    That's why when you're down by 6 points with 20 seconds left, you need to go for 2 3's, not 3 2's.

  138. Anon Says:

    "This is similar to the Monty Hall problem of mathematics, you can be a very intelligent mathematician and yet fail to "believe" the solution."

    You can lead a horse to water...

  139. DSMok1 Says:

    @137 precisely

  140. observer Says:

    I'd like to congratulate EvanZ and AYC for their intellectual stamina. This argument has been going on for almost 5 days!

  141. EvanZ Says:

    thanks! i'll be here all the week.

  142. Ian Says:

    Another potential wrinkle to consider: What about fast break opportunities created by defensive rebounds?