Tight games in the NCAA Tournament bring up so many time and score situations that you can learn from.
Wichita State vs. Kentucky
Iowa St. Vs. North Carolina
Kentucky is on the free throw line with about 8 seconds left and has a 1 point lead. They make the first free throw to go up by 2 and then miss the second. Wichita State rebounds the ball and pushes it up the floor calling time out when they get it over half court in front of their bench. They end up with a side out of bounds situation with 3.2 seconds to play.
I'm a big believer in calling time out - if you are going to call time out - before they shoot the second free throw. I've always felt the offense has the advantage when the defense doesn't have a chance to get set. By calling time out after the first free throw, first of all you make the shooter think about it a little bit. Secondly you get the advantage of running up the floor off of a miss should he miss the second free throw, against a defense that isn't completely set. Not matter how much they've talked about it and practiced it, there is still an element of figuring it out on the run that the defense has to handle off of a miss. If I'm Wichita State, once they miss the free throw and the ball is live I want to attack.
Calling the time out before the second free throw forces you to be prepared. One disadvantage is you don't know what the score is going to be - you might be down 2, you might be down 3. But I think in your time and score package you can easily have a set that creates an advantage for a 3-point shooter or an ability to drive it (say a quick flair screen, or hand-off action). You can train your kids to know the time and score and make the right play. With proper attention in practice, it shouldn't be that hard.
The only way I call time out after that free throw miss is if I have 2 time outs left, and I call the first run right away. If you don't let any time go off the clock on the rebound - remember, the clock doesn't start until the ball is touched - you can then run something to get the ball to half court and call your second time out. You should have something in your package that allows you to do that, because from an inbounds set you can get the ball to half court without the clock even running. If you call time out right away a second time you can get a side out set without as much as a second going off the clock.
On another note, I loved the move by Gregg Marshall to go zone against Kentucky with a 1 point lead and about 1:30 to play. I thought it took a lot of guts, and Kentucky was getting the ball to the rim too easily and living at the free throw line. I'm not sure how many coaches would be confident enough to make a call like that, and I thought it worked. Kentucky stared at it, they just threw it around the perimeter and never looked comfortable. But then James Young stepped up and made a big time 3 with a hand in his face, probably the biggest reason Kentucky won the game. I thought the process worked, Kentucky's offensive set wasn't very good, but the result didn't turn out in Wichita State's favor. A talented kid made a talented play. It happens, but it doesn't mean it was the wrong move. I give Gregg Marshall credit for having the guts to do it.
In a tie game with the clock running down, Deandre Kane made a big time play to get to the rim (great teams get to the rim!) and finish with 1.6 seconds left. But if you watch the play closely, after the bucket, Kane makes no attempt to get back on defense or move on to the next play. His teammate in the front court actually falls down as Carolina goes to inbound the ball. Two of Iowa State's players were out of the play.
That play is exactly why I think you need to be prepared to attack on offense once your opponent scores. Look, the odds are against you in that situation no matter what - down 2 with 1.6 to play - but your best shot is to get the ball up the court as quickly as possible against a defense that isn't set. We tell our guys to run fly patterns - whoever is closest gets the ball out of bounds as quickly as possible and the other 4 players fly up the court. We don't want to enter it into the back court if we don't have to - as Carolina did. We want to take advantage of the ball being in the air so that the clock doesn't run, and see if we can get ahead of the defense while they are celebrating.
As a coach you may not like the lack of control in this situation, but the chaotic nature of the play at that point is your best shot. It's something you can work on in your time and score package in practice and get your kids pretty accustomed to over time. Sometimes as a coach the lack of control in a time and score situation can work in your favor. Roy Williams wasn't entirely certain what he wanted to do, and he got stuck trying to call time out after the ball was in play. The clock operator made a mistake and it was a tough way to lose the game, but the officials made the right call.
You can learn a great deal as a coach by paying close attention to these games and putting yourself in each situation. What would we do here? What are we running? The NCAA Tournament provides so many great high pressure basketball situations that make me a better coach.