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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:

    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, 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.

    Last edited by ice-9; 04-06-2010 at 01:12 PM.

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