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  1. Lightbulb Zoubek Intentional Miss Free Throw - Probability Analysis

    First of all, I love this team, this season and this national championship game. This thread is not meant to challenge what happened -- we won, and really that's all that matters -- but the intentionally missed free throw by Zoubek at the end of the game was a really interesting thing for me.

    Judging by the discussion in the post-game thread, a lot of you agree. So what I would like to do is discuss that event separately from the national championship. This thread isn't about bringing down what was a marvelously played game, this thread is an intellectual exercise in thinking through the pros and cons of that coaching decision.

    OK. That disclaimer aside, was the intentional miss really a good idea? It comes down to what you believe the probability of winning is with a miss and without a miss.

    Without a miss, i.e. Zoubek makes it, let's say for argument's sake that Butler has a 33% chance of making a 3 to tie the game. Certainly they would have enough time to set up their offense and execute a play -- a play they've probably practiced many times. 33% is what Butler had shot in the game from 3 point range, but really with the game on the line and all that adrenaline, a player like Hayward or Mack could probably do better than 33%. But let's say it's 33%.

    What's the probability then that Butler can win in overtime? Prior to the start of the game, KenPom had Duke winning at what...70%? 72% I don't remember the exact number, but I'd argue if at the end of 40 minutes of basketball the score is tied, the percentage is probably closer to 50%. Fine, you can make an argument that because we're deeper and they're more tired we'd likely do better in overtime. Let's say the probability is 40% that Butler wins in overtime. I'm comfortable with 40% as it was also the Butler win percentage KenPom had with about 45 seconds left in the game when Duke was up by only 1 point: http://www.kenpom.com/wp.php

    This means that if Zoubek made the free throw, the probability that Butler wins is 33% x 40% = 13%.

    So what's the probability of making a half court buzzer beater should Zoubek miss intentionally? With the intentional miss, the rebound was going to be unexpectedly long. The defender would have to be sharp to catch it, land and then turn to face the Duke basket. If it wasn't Hayward who caught the rebound, the rebounder would have to look for Hayward or Mack and then make a pass. All of this while Zoubek is there to block line of sight and force the dribbler off a linear path. Butler was in fact very lucky that it was Hayward who corralled the rebound instead of another player like Howard.

    Even in this best case scenario (for Butler), Hayward still needed the entire 3 seconds to get to half court. What if Howard or another Butler player had gotten the rebound? Would they even have time to pass to Hayward or Mack? Or would the Center, who is mediocre from long range, attempt the buzzer beater? Then, on top of that, as Coach K mentioned in the press conference, the defense was set up so that Singler could bother the half court shot. Of course Howard was there to clobber him. But if Singler was there as he was supposed to be, he would've made what was already a difficult half court shot almost impossible.

    So, bottom line, what is the probability of making that 45-47 foot shot under those circumstances?

    I don't have access to any databases, but the All-Star Game provides a clue. In the 2009 NBA All-Star game, according to Wikipedia, the winning Detroit team in the Shooting Stars Competition hit the half court shot in seven tries, or 14%. But in the first round, Detroit needed 13 attempts for 8%. Even worse, San Antonio and the Lakers required over 15 shots each, or 7%. Team Phoenix? 22 shots, or 5%. These are all straight-line attempts made with less time pressure and with likely more energy -- i.e., these should be MUCh easier to make than the one Hayward took, which in turn was already the best case scenario for Butler. (You can argue that using WNBA and retired players brought those percentages down, but I don't think that outweighs the advantages they had that Hayward didn't have.)

    Overall, in 2009, the half court shot percentage in the Shooting Stars Competition was 8%. Hayward's actual percentage under the game's difficult circumstances should be even lower, but let's assume then that the chances of winning the game for Butler after an intentional miss on a last second half court shot is 8%.

    8% < 13%. Coach K, I bow down to you!

    When we saw Hayward's shot hit the backboard and then the rim, it looked like he was close to making it. In reality, he wasn't. When you watch all those half court attempts in the All-Star game, a lot of shots clang off the rim just like Hayward's did. But it doesn't mean the shot was close to getting in, because in fact it went in only about 8% of the time.

    When I first watched Zoubek intentially miss that free throw, I thought there was a serious breakdown in communication or that the coaching staff were off their rockers. It's only after I worked through the percentages that I realized they were onto something.

    Still. If I was Coach K, I don't know if I'd have the guts to instruct an intentional miss. Because if the game turned out to be in that 8% and the half court shot went in...wow, I would never hear the end of it, from the media, analysts, fans... I don't know if I could live with that scenario. The mental anguish in that 8% would've been FAR greater than what it would be in the 13%.

    Then again, I don't have 11 Final Fours or 4 national championships. I'm not Coach K. Duke nation thanks God for that.

    NATIONAL CHAMPIONS BABY!!!
    Last edited by ice-9; 04-06-2010 at 02:12 PM.

  2. #2
    Nice post, very interesting, and I don't mean to detract from your great research by this short post, but my opinion boils down to this:

    If you miss, Butler has a chance to win the game. If you make, the worst they can do is tie. That ALONE makes up my mind.

    Coach K's argument that they had no timeouts and would've had to force a tough shot doesn't hold water, because that same lack of timeouts would've made it difficult for them to get a good shot even on an inbounds play.

    So your two outcomes are:

    1) Bad shot on a rebound, and they have a chance to win.
    2) Bad shot on an inbounds play, and the worst they can do is tie.

    I think it was a terrible decision, and I doubt you'll find many knowledgeable basketball minds who disagree.

  3. #3
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    As K pointed out, Kyle had Hayward covered and no shot would have been had, certainly not the look Hayward got off, had Kyle not gotten "killed" by a clearly illegal crack back block set by Hayward's teammate, Howard, right in front of the refs. So any discussion of the advisability of K's strategy that depends on what happened after the miss and looks back, has to take account of a horrendous performance by the refs, a performance one cannot expect with a Championship on the line.

    In a regular game, I don't know the term that would have applied to the call, but it would have resulted in two shots and ball. It was a dangerous play in the extreme.

    Second, K in the last three games was like freakin Stonewall Jackson in his strategies. He attacked Baylor from the outset going inside to the bigs and using Zoubek and Miles as pivots for offensive distribution. Against W. Virginia, he again crossed up the opposition with a fierce assault on the rim at the outset, an assault that I believe rocked West Virginia's confidence in their coach's ability to match K strategically.

    That last play, the Zoubek miss, was again an attack. Singler had shut down Hayward all game, was and remains the vastly superior athlete including the intuitive thinker in a one-on-one confrontation, and K the general got the confrontation he wanted on his terms. Was it the cautious, the percentage play? No. He didn't get Duke where he got by making cautious, percentage decisions. He had his team playing pro actively; he counted on players to assert their superiority on the opposition. They did!

  4. #4
    Interesting analysis. The only thing I wish they had done is have Singler double up Hayward earlier. Even before the "screen", Singler was trailing the play a little and I think Hayward could have gotten the shot off in about the same manner. Zoubek did a nice job of slowing him down initially, but I wish Singler had been a little closer.

  5. #5
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    Quote Originally Posted by Shane05 View Post
    Nice post, very interesting, and I don't mean to detract from your great research by this short post, but my opinion boils down to this:

    If you miss, Butler has a chance to win the game. If you make, the worst they can do is tie. That ALONE makes up my mind.

    Coach K's argument that they had no timeouts and would've had to force a tough shot doesn't hold water, because that same lack of timeouts would've made it difficult for them to get a good shot even on an inbounds play.

    So your two outcomes are:

    1) Bad shot on a rebound, and they have a chance to win.
    2) Bad shot on an inbounds play, and the worst they can do is tie.

    I think it was a terrible decision, and I doubt you'll find many knowledgeable basketball minds who disagree.
    I ran the same analysis quickly at the time the game ended and came to the same conclusion as the OP using close enough numbers (I didn't run the All-star research but assumed a 5% chance the desperation shot goes in). The assumption that the worst that can happen is a tie is a fallacy - the worst that can happen is a loss in OT. I fully agree with the last part of the OP's statement, though, which was that the loss on the half-court shot would be much more devastating emotionally (and in the press) than an OT loss. You see coaches make the smart, but unusual, plays rarely and when they don't work they receive a lot of flack (think Patriots going for it on 4th down at the end of the game against the Colts and not getting it). It doesn't change the fact that the numbers suggest that it's a smart play. Kudos to the OP for making the case clearly as to why it's the smart play.

  6. #6

    screen

    Do you really think it was an illegal screen? I looked like he was stationary. Imagine if he had hit the three and they had waved it off for offensive foul illegal screen

  7. #7
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    K has said until he is blue in the face that this run has not been about him and his storied past. It has not been about him as a coach. It is about a coach following the lead of his team, seeing what their tempermament and playing style dictated, measuring it at times from moment to moment.

    Anyone who thinks that K could not have lived with second guessing had the shot gone in simply does not believe anything that the guy has had to say.

    A surprise attack that depended on confidence in his athletes to prevent the very look that the kid got only because the refs did not do their jobs. Talking heads with their "what if" hypothicating and second guessing K without taking into account of the missed blatant foul against Kyle should not surprise. They are the same guys to a man who to a man had Duke going out early.

    Have you listened to their soft-pedal excuses? Know what they say, "We thought that this was the same Duke team of past years." Why, these genuises in past years rightly had Duke going deeper in the tournament than it did. Stuff happens. So they bail out this year when anyone who has been watching had to see what has been developing and developing in Durham since that game against Maryland. How they think that they can get away with passing off their miss on how good this Duke team has been and is as anything but their shallowness as experts speaks only to well, their shallowness as experts.

    A daring call by a daring coach who once again went for the element of surprise and put the game in the hands of his players, who had the play covered until the refs indefensibly blew a blatant-foul call committed in plain view of everyone.

  8. #8
    I think people are hung up on "you can't lose by a desperation heave" theory.

    But you know what, you can still lose in OT.

    Coach K has never been about playing "not to lose", he plays to win.

  9. #9
    I think your percentages are way off. You really think in less than 4 seconds Butler could get off a 33% 3-point shot after inbounding underneath their basket and Duke able to entirely ignore anything inside the 3-point arc?

    You are also ignoring the potential to make the foul shot and then foul Butler on the inbounds. Personally I don't really love this idea but it is something else to consider. You'd put Butler in a position where they'd have to make the 1st free throw, intentionally miss the 2nd, get the rebound and score just to tie.

    I just don't think the difference between the shot they'd get off w/ a miss and the shot they'd get off with a make is enough to counteract the extra point. If I'm Coach K I tell Zoubs to make the 2nd shot, and press the inbounds play.

  10. #10
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    jyuwono, this is a great discussion point. But let's do a sensitivity analysis:

    Let's say there's a 33% chance of making a 3 off an inbounds play and 14% chance of making a long three off a rebound (slightly different assumptions). Here's the analysis:

    Intentional miss (assume 100% probability of missing):
    14% chance of Butler winning.

    Attempted make:
    Assume a 60% chance of Zoubek making the FT (i.e., 40% chance of miss).

    So 40% of the time, the scenario is exactly the same as the intentional miss scenario (14% chance of Butler winning).

    The other 60% of the time, Butler gets the inbounds play. So there is a 33% chance of going to overtime. In overtime, let's assume it's a 40% chance of winning for Butler.

    So the probability of Butler winning is:
    60%*33%*40% + 40%*14% = 13.5%

    So by those assumptions, Butler's probability of winning was LESS if Zoubek attempts to make the FT. The difference is very small, and the decision is VERY sensitive to the other assumptions, though. Bas

  11. #11
    You are missing the 3rd possibility:

    Zoubs makes both free throws. Butler inbounds with 3.6 seconds to play, Howard drains the 3 & is fouled. He makes the free throw & we lose by 1.

    I am happy with the intentional miss if that is indeed what happened.

  12. #12
    Don't forget this -- Zoubek is a 52% foul shooter for the season. So there's a pretty decent chance he would have actually missed the second one, but probably a rim rattler and not an intentional one that caused a freakish long rebound and sent Hayward down the court on the gallop.

    I don't know, he should have tried to hit the shot. I want to leave no chance that Butler hits a three to win the National Title.
    Last edited by Starter; 04-06-2010 at 02:44 PM.

  13. #13
    I liked the call at the end as well. IMO the intentional miss was the risk taken in playing to win, whereas making the second free throw (not a guaranteed make either) is more like playing not to lose. A Butler 3 to tie at the buzzer gives them all the momentum going into OT and sends the crowd into a frenzy.

  14. #14
    Quote Originally Posted by PensDevil View Post
    whereas making the second free throw (not a guaranteed make either) is more like playing not to lose
    I realize this sort of contradicts what I just said, but I can't see how scoring more points is playing not to lose.

    If they really wanted to get cute, they could have attempted to hit the shot, and if successful, foul after the inbounds up 3 with like a second left.

  15. #15
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    I think the time left on the clock is the variable here to discuss

    If there are 2.6 on the clock, I think the strategy is brilliant. Heyward's heave is from three quarter court and I think those are all odds we'd be willing to take.

    If there are 4.6 on the clock, Heyward probably gets a look -- maybe even clean given the screen -- from 25 and none of us wanted that.

    3.6 is a gray area that make who gets the rebound somewhat important. The original poster is right that had Howard boarded rather than Heyward, they have less time to shoot and they get off a worse shot. Had Zoubek not bodied up Heyward, however, he probably gets a better look. It worked this time, and I think it was probably the right call, but 3.6 seconds is the outer boundary of the intentional miss I think.

  16. #16
    I posted this this morning in the post-game thread. Will re-post here now:

    You play to win the game, not to get to OT.

    What is Zís chance of making the 2d FT if he tries to make it? ... I say 60%.

    What is Dukeís chance of winning if Butler hits a 3 to send the game to OT? ... I say 60%.

    What is Butlerís chance of making a 3 off a missed FT (scramble play) versus Butlerís chance of making a 3 from an inbounds play? ... I say 1% off of a scramble play and 2% off of an inbounds play.

    The formula.

    1. Z intentionally misses the FT.

    Butler has a .01 chance of winning the game. (1% chance of hitting the 3 on the scramble play, and we lose).

    2. Z tries to make the FT.

    Butler has a .088 chance of winning the game. ((40% Z misses anyway * 1% they hit scramble 3 for win) + (60% Z makes it * 2% they make inbounds 3 to tie * .40% Butler wins in OT)).

    So, using my values, I would have had Z try to make the FT.

    However, if you believe Butler is three times as likely to make a 3 off a set-inbounds play than it is off a scramble play (say, 3% to 1% rather than the 2% to 1% I used), and the other values are the same (60% Z makes it; 60% chance we win in OT) ... then it makes sense to try to miss the FT on purpose.

    The strategic call was not unreasonable. Depends on what you believe the various probabilities were.

  17. #17
    No one from Duke tried to get the rebound on the free throw... so if Howard had gotten the rebound what would Duke have done? If Zoubs goes towards Howard then it's just a quick pass to Heyward and I think he still gets the same quick start up the court. Obviously he's probably not there to set the pick on Singler though.

    It seems like in all of those situations you should just double team the ball. If you force any sort of pass from Heyward in that situation there's no way they get off such a good shot. Must be easier said than done though because we all remember Evan Turner's last second shot which was very similiar.

  18. #18
    Quote Originally Posted by Shane05 View Post
    Nice post, very interesting, and I don't mean to detract from your great research by this short post, but my opinion boils down to this:

    If you miss, Butler has a chance to win the game. If you make, the worst they can do is tie. That ALONE makes up my mind.

    Coach K's argument that they had no timeouts and would've had to force a tough shot doesn't hold water, because that same lack of timeouts would've made it difficult for them to get a good shot even on an inbounds play.

    So your two outcomes are:

    1) Bad shot on a rebound, and they have a chance to win.
    2) Bad shot on an inbounds play, and the worst they can do is tie.

    I think it was a terrible decision, and I doubt you'll find many knowledgeable basketball minds who disagree.
    I must have bad basketball mind because I think what K did was perfect in that situation. With no timeouts left, Butler can't set up for a reasonable shot. With a Butler timeout remaining, then K doesn't have Zoubs miss. I never have liked playing to do no worse than OT.

  19. Quote Originally Posted by InSpades View Post
    I think your percentages are way off. You really think in less than 4 seconds Butler could get off a 33% 3-point shot after inbounding underneath their basket and Duke able to entirely ignore anything inside the 3-point arc?
    This is an excellent point, and one that I wrestled with quite a bit. Is 33% the right number? I went with it because most teams would have practiced buzzer beater plays after a made basket -- surely Butler would've given their low scoring style and the fact that they were in the Final Four. 3.6 seconds is not much time, but it's enough time.

    In any case, even if we lower the percentage, it's still better to intentionally miss the free throw as long as it's above 20%.

    20% x 40% = 8%.

    Can Butler execute a play to get a 3-point shot with >20% probability of making it? 20% somehow feels low to me.

    You are also ignoring the potential to make the foul shot and then foul Butler on the inbounds. Personally I don't really love this idea but it is something else to consider. You'd put Butler in a position where they'd have to make the 1st free throw, intentionally miss the 2nd, get the rebound and score just to tie.
    True, but I wanted to keep the analysis simple. In that scenario, you'd also have to consider the possibility that the shot to tie could be a 3-point shot to win.

    I just don't think the difference between the shot they'd get off w/ a miss and the shot they'd get off with a make is enough to counteract the extra point. If I'm Coach K I tell Zoubs to make the 2nd shot, and press the inbounds play.
    That's the beauty of this thread! Because there are compelling arguments for and against the decision.

    It seems like in all of those situations you should just double team the ball. If you force any sort of pass from Heyward in that situation there's no way they get off such a good shot. Must be easier said than done though because we all remember Evan Turner's last second shot which was very similiar.
    For that Evan Turner shot, I believe it was off a set play and that Turner was able to get well past half court; i.e. more 40 feet than 47. To me that seems like the kind of play that has >20% chance of success and it's one that Butler could've pulled off had Zoubek made his second free throw.
    Last edited by ice-9; 04-06-2010 at 03:03 PM.

  20. #20
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    Thanks to all for their statistical analysis.

    I don't think that Coach K was doing calculations to make his decision. The intentional miss (if indeed intentional)

    (1) forced Butler to use clock getting the ball up court rather than have the clock start when touched on a long pass and

    (2) put the game more into the players hands and less under the refs control.

    But has Coach K said that he told Brian to miss? In the post game presser, when asked if he missed intentionally Brian said "yup" and further when asked if he was free lancing he said "no, definitely not freelancing". The implication is that he was instructed to miss. Has K said anything to confirm that?

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