Agreed with DevilHorns above. I think if we take one more factor into account which, in execution, didn't happen for us, it makes the intentional miss a better statistical proposition. What probably shouldn't have happened was (i) Hayward getting the rebound uncontested, (ii) almost at the free throw line, with (iii) the opportunity to go to his right and shoot from halfcourt in 3 seconds after getting a screen. My first thought after the final shot clanged off was "they shouldn't get that good of a look under the circumstances."
I think the basic decision was a good one, but I think Zoubek's missed shot should be lofted and aimed at the side of the rim, not ripped straight forward, and should go opposite where the most dangerous opponent is lined up. Banging it hard off the rim leads to unpredictibility, which does of course increase our chance of coming up with the rebound (game over), but in a situation where you're not sending anyone to really go after it for fear of fouling Butler, that's not much of a chance. As it is, we put Lance in the lane, but the way Butler set up, we could have prevented Hayward from ever touching the ball by simply putting Lance on the other side and telling him not to go for the ball but just to gently box out Hayward. If we force Howard to catch that ball, their odds of making a miracle shot are cut at least in half. Similarly, if Nored or whoever it was on the other side of the lane, gets it but gets it on the baseline instead of eight feet out, the buzzer shot is that much longer. Also, an arching shot leading to a high bouncing rebound allows Singler to get a running start toward a likely shot position after judging where it's going to land, rather than the ball ending up in a shooter's hands before anyone can even get moving on the perimeter.
All in all, a lot more fun to discuss this as a purely academic item than in light of it mattering, right?
FWIW, I think fatigue and momentum probably mattered in the decisionmaking, too. Butler's guys were tired, too, but our starters were out there the entire final 15 minutes and we had foul trouble. Had we been forced to overtime, the crowd frenzy would not have helped after we gave away a 5 point lead in the final 90 seconds of regulation. Regardless of the mental toughness of this team.
Also, I'm not upset with Howard screening Singler and not getting called for it, in and of itself. Kyle wasn't going to seriously contest the shot, anyway, as he was a full step behind, not looking to risk a foul, and Hayward was going to his right. And no ref is going to call something off the ball in the deciding seconds. But that cuts both ways. What *#%$es me off is the way Howard launched himself at a player who was not in position to impact the shot, lowered his shoulder into his chops, and got away with it when under any other circumstance he gets T'ed up. And I think he knew it. He did not set up in Kyle's path and stand his ground. He sought out a moving defensive player and initiated contact, and made that contact violent. It was not a basketball play. It was a football play. A cheap shot that adds an unnecessary blemish to what was otherwise a clean and classy game.