After Dereck Whittenburg tied the score of the 1983 national championship at 52 with another long jump shot, Houston got the ball back with a little under two minutes remaining, and the Cougars could have (would have) rolled the clock right down to the end before taking one more shot in regulation.
Jim Valvano opted not to let Houston dictate terms and instructed State to foul mediocre free throw shooter Alvin Franklin with more than a minute left. Franklin missed the front end and I'm pretty sure everybody remembers the rest.
I've always been fascinated by that decision to foul with the game tied; that's just not something you see in the modern game. It wasn't even the first time V'd done it in the tournament, but doing it in a national freakin' title game seemed borderline crazy and based on ... what? V probably didn't have any math on hand to justify that in-the-moment decision, but as some Ken Pomeroy research shows, the numbers back it up.
Pomeroy recently published a multi-part series (See Part 1, Part 2, Part 3) about the notion of fouling while on defense with the game tied and shot clock off, and the gist is this: if V had opted to play defense straight up against Houston and essentially pray for overtime, the Pack's win probability would have been around 25%. By fouling, that win probability improved to about 33%. State was a heavy dog in either circumstance, and given the balance of possible outcomes, it loses that game two out of every three times it sends Franklin to the line in that situation.
No matter what it does, State loses to Houston more often than not. The choice that Valvano made there moved State's odds from 3:1 to 2:1. That's huge. As Pomeroy said, "It's hard to imagine another single strategic decision that could affect a team's chances so dramatically."
Valvano could have been discouraged after this strategy nearly cost him against Virginia in the Elite Eight, but by sticking with what he felt worked for his underdog group, it turned out that he put them in a dream scenario, and they responded by delivering in historic fashion.