April 6, 2010

Should Duke have Missed the Free Throw?

Filed under: Uncategorized — wwinston @ 2:02 pm

As you all know, with Duke up by 2, Coach K told Zubek to miss the 2nd  free throw. Was this a good idea?  My earlier post forgot chance of Zubek missing free throw even if he tried to make it (thanks to Michael for this point). Let’s assume Zubek is 50%-50% to make free throw if he tries. The results stay pretty similar.

Let 

Pobounds = chance Butler hits a 3 after a made free throw and

 PmissFT = chance Butler hits a 3 after a missed Free throw.

Butler’s chance of winning if  Duke misses free throw  intentionally is PmissFT and Butler’s chance of winning  if Zubek tries to make Free Throw is .5(.5Pobounds )+.5*PMissFt

(if you believe Butler has 50% chance of triumphing in OT) Therefore Duke should have missed the FT if  .5(.5Pobounds )+.5*PMissFT>PMissFT

orPobounds/PMissFT>=2.

My friend and I believe PMissFT = .10 and Pobounds = .20. Therefore decision looks like a wash. So when in doubt I would take the option that does not leave me open to second guessing (not missing FT). Clearly, this is a close call and you can defend either choice.

Of course, I am assuming Butler rebounds the missed free throw. .

5 Comments »

  1. I think it only makes sense to miss a free throw at the end of the game when (a) the other team has no timeouts; (b) there is no time for the other team to get a two-point shot (i.e., they will only be able to get off a long three off a rebound); and (c) your team is up by ONE point, not two. Because if you’re up one, then the extra point isn’t going to help out: a three-pointer beats you whether you make or miss the free throw, so you might as well miss it. But if you’re up two, you might as well (try to) make the free throw.

    Michigan State botched this strategy when they intentionally missed a FT while up one against Tennessee, since Tennessee still had a timeout. Duke (or maybe Zoubek acting on his own) messed it up last night because they were up by two. Earlier this season, N.C. State missed a free throw while up by two against Florida with about 2.3 seconds left, and they wound up losing by one on a 70-footer. That miss wasn’t intentional, but it shows how valuable that third point can be.

    Comment by WY — April 6, 2010 @ 2:22 pm

  2. This analysis is a bit too simplistic. First, if Zoubek attempts to sink the free throw, his probability of success is only 55% (that’s his FT% for 2009-10, although oddly, his FT% in 2008-09 was 82%). Second, if Zoubek misses the free throw and Butler rebounds, then Butler could try for a 2-pointer rather than a 3-pointer. In picking his strategy, Coach K needs to form some belief about the probabilities of Butler trying a 2-pointer to tie vs. a 3-pointer to win!

    Comment by Bhel Atlantic — April 6, 2010 @ 4:03 pm

  3. i think there is no chance they go for a 2 in with 3 seconds left.

    Comment by wwinston — April 6, 2010 @ 5:46 pm

  4. It may be post-outcome rationalizing, but on an espn radio show, Coach K said he thought Duke would lose in OT, so he took the chance.

    Not sure if I completely believe that.

    Comment by cg — April 8, 2010 @ 12:35 pm

  5. 1)try to make free throw 2) if you miss it -ends up being basically the same result as purposely missing it 3) if you make it-up 3 4) you foul on in bounds and put them line 4) they still down by 1 5) they foul you -meanwhile clock is minimal now–vs. missing on purpose and if ball is 3 inches to left you lose natl title

    Comment by john smith — April 9, 2010 @ 4:04 pm

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