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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. Michael Says:

    They are both really good point guards.

  2. 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.

  3. 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.

  4. 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?

  5. 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.

  6. 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?

  7. 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

  8. 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.

  9. 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.

  10. 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?

  11. 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.

  12. 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.

  13. 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).

  14. 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).

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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?

  20. 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/

  21. 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.

  22. 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%.

  23. 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.

  24. 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.

  25. 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.

  26. 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.

  27. 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.

  28. 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.

  29. 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.

  30. 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%.

  31. EvanZ Says:

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

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

  32. EvanZ Says:

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

  33. DSMok1 Says:

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

  34. EvanZ Says:

    "The answer seems pretty clear..."

    you'd think so, right?

  35. 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)

  36. 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.

  37. 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.

  38. 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...

  39. DSMok1 Says:

    @137 precisely

  40. observer Says:

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

  41. EvanZ Says:

    thanks! i'll be here all the week.

  42. Ian Says:

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