Zoubek Intentional Miss Free Throw - Probability Analysis

[ice-9]

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!!!

[Shane05]

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.

[Clipsfan]

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.

[tecumseh]

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

[alteran]

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

I absolutely think it was an illegal screen. He moved, leaned into contact, and then specifically moved his shoulder to blindside Singler in the head. He could have hindered Singler every bit as much without being vicious.

Wouldn't shock me if there was some frustration in what he did, and it also wouldn't shock me if he didn't intend it to be quite as vicious as it turned out to be.

[dukestheheat]

I absolutely think it was an illegal screen. He moved, leaned into contact, and then specifically moved his shoulder to blindside Singler in the head. He could have hindered Singler every bit as much without being vicious.

Wouldn't shock me if there was some frustration in what he did, and it also wouldn't shock me if he didn't intend it to be quite as vicious as it turned out to be.

That hit on Singler was assault and battery; there is no way it's going to get called there, but I saw some 'football player' in the Butler player as he was winding up to pop Kyle. Pop him, he did, and it was U-G-L-Y. That had to hurt. When we got cracked in football like that, we were wearing pads, at least, to absorb some of the blow.

dth.

[Spam Filter]

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.

[CDu]

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

[Starter]

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.

[dukestheheat]

To me, a missed shot or a clanged shot that caroms is less stable to grab; this makes the shock factor greater for the opponent and puts pressure on the opponent to a) control the carom and then b) get a decent pass to mid-court or closer, if possible, for some type of shot.

A made shot at least gives a usual in-bounder time to get the ball and take it out of bounds; screens can be set by players to free more shooters; one more pass can be made to get an even better shot, and possibly the chances of a made shot go up.

I wonder if K pulled the missed shot, at that time of that particular game, for the shock value?

Whatever the rationale, it worked and we are the National Champions yet again.

dth.

[SharkD]

There is an obscure, oft-forgotten game from nearly two decades ago, that saw a very similar situation to last night's conclusion.

Two fairly matched teams were in a slugfest, trading the lead back and forth in a game that was tied at the end of regulation.

The lower seed hit a running one-hander, to go up by one, with 2.1 seconds left on the overtime period. Everyone assumed the game was over. But, the young coach on the higher seed's bench knew that he had an advantage in that his players could run the baseline for the inbounds. The lower seed chose not to contest the inbound, but to double-team their opponent's best shooter, who'd shot a perfect 9-of-9 from the floor.

A sophomore forward threw the ball ¾ of the court, which was caught at the top of the key by the senior center, who turned around and shot a perfect arc to the bottom of the net, sending that team to it's 4th Final Four in four years.

What did the winning coach attribute the key factor in the win? Having the ability to run the baseline with the clock stopped, to set up the long inbounds pass.

18 years later, I'm pretty sure Mike Krzyzewski was thinking about what led the 1992 Duke Blue Devils to victory over the Kentucky Wildcats, when he told his senior center to miss his freethrow, preventing a stopped-clock inbounds play.

[BD80]

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

Was there any chance that Z gets the rebound on a missed free throw?


Mike Greenberg was going on, and on, and on, ... about the WORST that could happen if Z made the second free throw was overtime. I didn't realize that games could end in a tie.

Another issues is the number of timeouts remaining. I don't think we had one, and I wouldn't have take one anyway to give Butler a chance to plan for its options. Without a timeout, I would be less comfortable instructing the team to intentionally foul on the inbound pass (assuming Z made the second FT), and putting the game into the hands of the refs -where they could call a shooting foul or an intentional foul - particularly if Butler gets to run an inbound play and catch the ball much farther downcourt (remember "Pacer" and Bryce Drew's shot for Valpo with 2.5 seconds in '98?) or at least catch it moving fast toward the offensive end ala Ty Edney (went the length of the court in 4.8 seconds in '95).

[CDu]

Was there any chance that Z gets the rebound on a missed free throw?


Mike Greenberg was going on, and on, and on, ... about the WORST that could happen if Z made the second free throw was overtime. I didn't realize that games could end in a tie.

Another issues is the number of timeouts remaining. I don't think we had one, and I wouldn't have take one anyway to give Butler a chance to plan for its options. Without a timeout, I would be less comfortable instructing the team to intentionally foul on the inbound pass (assuming Z made the second FT), and putting the game into the hands of the refs -where they could call a shooting foul or an intentional foul - particularly if Butler gets to run an inbound play and catch the ball much farther downcourt (remember "Pacer" and Bryce Drew's shot for Valpo with 2.5 seconds in '98?) or at least catch it moving fast toward the offensive end ala Ty Edney (went the length of the court in 4.8 seconds in '95).

We had nobody else in the lane (or at least nobody but Zoubek tried for the rebound). The odds of the shooter getting the miss are VERY small. Further, there's the possibility that Zoubek gets an over-the-back call if he tries harder to get the rebound. I'm guessing the probability of Zoubek getting the rebound is smaller than the probability of Zoubek getting called for a foul.

[DukeFanInTerpLand]

Someone in this thread made an interesting point that Butler maximized their opportunity here. They got the rebound clean and in the hands of the right player. He was able to dribble relatively unimpeded up the court, and the shot almost went in.

Would we even have this thread if say, Singler was able to stay in front of Hayward, slowing him down and forcing a even longer, and contested shot? What if Howard had gotten the rebound and was forced to pass? etc. etc. We are looking at these probabilities based on the (almost) best possible outcome of events for Butler. There are many, many things that could have gone wrong to slow down Hayward just enough.

I like the call the more and more I think about it. 3.6 seconds is plenty of time for an inbounds play.

[Neals384]

We had nobody else in the lane (or at least nobody but Zoubek tried for the rebound).

Thomas was in the lane, right side. He made no effort to get the rebound, and was in a bear hug anyway. Singler was in the lane, left side, for the first free throw, but stepped back to the top of the circle for the second.

[Neals384]

Another issues is the number of timeouts remaining. I don't think we had one, and I wouldn't have take one anyway to give Butler a chance to plan for its options.

Duke had one Timeout left. But I agree it would have been dumb to use it.

[PensDevil]

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.

[Starter]

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.

[DukeCrow]

All of this talk of probabilities is nice, but what this really comes down to is risk management. That's what K does when he starts running his slow down offense when leading towards the end of the game. And that is what you want to do when managing end of game situations, as well (in my opinion).

The quants on Wall Street dealt in risk and probabilities but failed to pay attention to the most important thing -- not blowing up. In basketball, losing the game on a buzzer beating shot would be the equivalent of "blowing up" because the losing team has no chance of recovery. The game is over. There is no "next play." This is especially true in the NCAA tournament.

Any end of game strategy should take into account the probability of "blowing up." Going to overtime and possibly losing isn't the same as the possibility of losing on a buzzer beater. Going to overtime is not a "catastrophic" event because you're still playing and have a chance to win. But losing on a buzzer beater ends the game and the season. You need to avoid that at all costs, and then play the probabilities in order to maximize your chances of winning.

Maximize your chances of winning while minimizing your chances of a catastrophic loss. That's what risk management (and end game management) is all about, in my opinion.

[Lippl]

If you have a 1 point lead in that situation I think missing is the right call. Whether you're up 1 or 2, you still lose on a long 3.

With a 2 point lead, though, I think I'd rather make the third, then foul on the inbounds if they get the ball close to halfcourt and make them hit a FT and then get a tipin to tie. Put Zoubek on the inbounder on the baseline, remember Butler had no timeouts left. They might not even get a good pass in.

One other thing that I questioned in the last few seconds - originally at 13.6 sec K had Zoubek guarding Hayward as the inbounder. Did anybody else flash back to Laettner v. UConn 1990? I didn't like the choice given that Zoubek would have had a difficult time staying with Hayward had he managed to get the ball inbounds. I would have rather had Singler or Thomas guarding Hayward's inbound pass there. Of course Butler wound up using their last timeout, so it worked out great.